MACHINE LEARNING TO PREDICT BLOWCOUNTS NEEDED FOR THE INSTALLATION OF JACKET PILES

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1 INTRODUCTION

This post includes a comprehensive summary of the process we at Green Geotechnics went through to build a machine learning (ML) model for the Data Science Prediction Event created under the framework of the ISFOG2020 conference, to be held in Texas (August 16-19, 2020). The competition was hosted in Kaggle and run through a period of eight months, from April to December 2019. The problem proposed for the prediction event is to use piezocone (CPTu, herein and after denoted as CPT) data to predict blowcounts needed for the installation of jacket piles, located in North Sea soil. A detailed description of the problem can be found here.

We start with loading the data and by doing some exploratory data analysis (EDA), trying to get some initial insights. Then we explore possibilities to incorporate engineering/geotechnical knowledge by introducing new parameters in the analysis. Next, we dive into the model-building process, where we train various ML models, moving from Simple Linear Regressions to more complex models like Neural Networks.

All the analysis is performed using R and the RStudio environment. This report is generated using R Markdown.

2 DATA

We have previously downloaded the data from here and saved them locally. We set the working directory so all the work is saved in one location. Various data sets were provided so we are going to separately load and comment on them.

setwd("F:/isfog2020")

2.1 Basic data

The available data contain information about the soil conditions and installation of 114 jacket piles. The data are divided into two groups:

• training - contains information on 94 piles;
• validation - contains information on 20 piles.

The training data will be used to train the ML model while the validation data will be used to validate the model and assess its performance. Let’s read and view the data.

library(tidyverse)

training <- read_csv("F:/isfog2020/training_data_cleaned.csv")
validation <- read_csv("F:/isfog2020/validation_data_cleaned.csv")

library(knitr)
library(kableExtra)

kable(top_n(training, 100),
      digits = 3,
      caption = "Training data.",
      align = "r") %>%
  kable_styling(font_size = 11) %>%
  row_spec(0, color = "grey10", background = "#F4F5F6") %>%
  scroll_box(height = "300px")

Training data.

z [m]	qc [MPa]	fs [MPa]	u2 [MPa]	ID	Location ID	Blowcount [Blows/m]	Normalised ENTRHU [-]	Normalised hammer energy [-]	Number of blows	Diameter [m]	Bottom wall thickness [mm]	Pile penetration [m]
4.0	11.434	0.082	0.036	AA__4_0	AA	8	0.130	0.173	8.00	2.48	55	34
4.5	14.955	0.109	0.035	AA__4_5	AA	8	0.140	0.187	11.00	2.48	55	34
5.0	15.722	0.125	0.037	AA__5_0	AA	8	0.151	0.201	14.00	2.48	55	34
5.5	15.727	0.123	0.039	AA__5_5	AA	16	0.131	0.175	29.00	2.48	55	34
6.0	11.347	0.111	0.045	AA__6_0	AA	24	0.112	0.149	44.00	2.48	55	34
6.5	13.989	0.105	0.051	AA__6_5	AA	22	0.147	0.195	55.00	2.48	55	34
7.0	16.632	0.098	0.058	AA__7_0	AA	20	0.182	0.242	66.00	2.48	55	34
7.5	24.536	0.146	0.063	AA__7_5	AA	24	0.174	0.233	77.50	2.48	55	34
8.0	24.622	0.183	0.059	AA__8_0	AA	28	0.167	0.223	89.00	2.48	55	34
8.5	24.245	0.191	0.058	AA__8_5	AA	34	0.171	0.228	105.50	2.48	55	34
9.0	28.871	0.175	0.058	AA__9_0	AA	40	0.175	0.233	122.00	2.48	55	34
9.5	25.603	0.181	0.061	AA__9_5	AA	64	0.181	0.242	162.00	2.48	55	34
10.0	28.036	0.153	0.069	AA__10_0	AA	88	0.188	0.251	202.00	2.48	55	34
10.5	25.148	0.132	0.089	AA__10_5	AA	88	0.206	0.274	245.50	2.48	55	34
11.0	24.442	0.203	0.087	AA__11_0	AA	88	0.223	0.298	289.00	2.48	55	34
11.5	6.894	0.084	0.085	AA__11_5	AA	74	0.225	0.300	325.50	2.48	55	34
12.0	5.528	0.039	0.020	AA__12_0	AA	60	0.227	0.302	362.00	2.48	55	34
12.5	6.805	0.052	0.097	AA__12_5	AA	36	0.251	0.334	372.00	2.48	55	34
13.0	6.492	0.048	0.106	AA__13_0	AA	12	0.275	0.367	382.00	2.48	55	34
13.5	8.541	0.032	-0.043	AA__13_5	AA	10	0.269	0.358	387.50	2.48	55	34
14.0	28.151	0.167	-0.114	AA__14_0	AA	8	0.262	0.350	393.00	2.48	55	34
14.5	23.779	0.187	-0.067	AA__14_5	AA	10	0.214	0.286	398.50	2.48	55	34
15.0	12.522	0.118	-0.362	AA__15_0	AA	12	0.166	0.221	404.00	2.48	55	34
15.5	6.764	0.043	-0.339	AA__15_5	AA	20	0.187	0.249	414.50	2.48	55	34
16.0	7.552	0.052	-0.261	AA__16_0	AA	28	0.208	0.277	425.00	2.48	55	34
16.5	5.400	0.022	-0.145	AA__16_5	AA	22	0.213	0.284	432.50	2.48	55	34
17.0	5.900	0.017	-0.093	AA__17_0	AA	16	0.219	0.292	440.00	2.48	55	34
17.5	4.048	0.024	-0.144	AA__17_5	AA	28	0.213	0.284	450.50	2.48	55	34
18.0	20.823	0.108	-0.294	AA__18_0	AA	40	0.207	0.276	461.00	2.48	55	34
18.5	27.700	0.225	-0.238	AA__18_5	AA	70	0.214	0.286	507.00	2.48	55	34
19.0	25.179	0.177	-0.188	AA__19_0	AA	100	0.222	0.296	553.00	2.48	55	34
19.5	22.926	0.151	-0.069	AA__19_5	AA	108	0.255	0.341	611.00	2.48	55	34
20.0	20.674	0.124	0.049	AA__20_0	AA	116	0.289	0.386	669.00	2.48	55	34
20.5	25.997	0.231	0.185	AA__20_5	AA	126	0.293	0.390	733.00	2.48	55	34
21.0	29.572	0.304	0.175	AA__21_0	AA	136	0.296	0.395	797.00	2.48	55	34
21.5	40.627	0.408	0.158	AA__21_5	AA	128	0.311	0.415	859.50	2.48	55	34
22.0	39.834	0.368	0.170	AA__22_0	AA	120	0.326	0.434	922.00	2.48	55	34
22.5	34.681	0.356	0.163	AA__22_5	AA	122	0.324	0.432	988.50	2.48	55	34
23.0	26.795	0.273	0.166	AA__23_0	AA	124	0.322	0.430	1055.00	2.48	55	34
23.5	21.606	0.222	0.205	AA__23_5	AA	124	0.352	0.469	1118.50	2.48	55	34
24.0	27.394	0.295	0.197	AA__24_0	AA	124	0.381	0.508	1182.00	2.48	55	34
24.5	20.538	0.258	0.198	AA__24_5	AA	122	0.388	0.517	1239.50	2.48	55	34
25.0	27.088	0.211	-0.038	AA__25_0	AA	120	0.395	0.526	1297.00	2.48	55	34
25.5	35.413	0.319	0.210	AA__25_5	AA	104	0.426	0.568	1354.50	2.48	55	34
26.0	36.892	0.315	0.215	AA__26_0	AA	88	0.457	0.609	1412.00	2.48	55	34
26.5	46.709	0.456	0.250	AA__26_5	AA	94	0.489	0.653	1459.50	2.48	55	34
27.0	45.741	0.473	0.238	AA__27_0	AA	100	0.522	0.696	1507.00	2.48	55	34
27.5	50.310	0.469	0.211	AA__27_5	AA	92	0.573	0.763	1553.00	2.48	55	34
28.0	42.441	0.388	0.267	AA__28_0	AA	84	0.623	0.831	1599.00	2.48	55	34
28.5	42.527	0.487	0.292	AA__28_5	AA	84	0.618	0.824	1643.00	2.48	55	34
29.0	53.361	0.661	0.297	AA__29_0	AA	84	0.613	0.817	1687.00	2.48	55	34
29.5	47.392	0.373	0.302	AA__29_5	AA	88	0.622	0.830	1731.50	2.48	55	34
30.0	44.926	0.521	0.308	AA__30_0	AA	92	0.632	0.843	1776.00	2.48	55	34
30.5	46.653	0.574	0.313	AA__30_5	AA	92	0.630	0.840	1820.00	2.48	55	34
31.0	51.331	0.652	0.318	AA__31_0	AA	92	0.628	0.837	1864.00	2.48	55	34
31.5	48.796	0.531	0.323	AA__31_5	AA	90	0.628	0.837	1909.00	2.48	55	34
32.0	46.261	0.411	0.328	AA__32_0	AA	88	0.628	0.837	1954.00	2.48	55	34
32.5	59.915	0.812	0.333	AA__32_5	AA	90	0.630	0.841	2001.00	2.48	55	34
33.0	60.356	0.810	0.338	AA__33_0	AA	92	0.633	0.844	2048.00	2.48	55	34
33.5	57.943	0.757	0.343	AA__33_5	AA	90	0.649	0.865	2094.00	2.48	55	34
34.0	58.148	0.677	0.348	AA__34_0	AA	88	0.664	0.886	2140.00	2.48	55	34
5.0	15.722	0.125	0.037	AB__5_0	AB	8	0.117	0.157	14.00	2.48	55	34
5.5	15.727	0.123	0.039	AB__5_5	AB	8	0.115	0.154	20.50	2.48	55	34
6.0	11.347	0.111	0.045	AB__6_0	AB	8	0.113	0.151	27.00	2.48	55	34
6.5	13.989	0.105	0.051	AB__6_5	AB	6	0.151	0.202	30.00	2.48	55	34
7.0	16.632	0.098	0.058	AB__7_0	AB	4	0.189	0.252	33.00	2.48	55	34
7.5	24.536	0.146	0.063	AB__7_5	AB	16	0.152	0.202	43.00	2.48	55	34
8.0	24.622	0.183	0.059	AB__8_0	AB	28	0.114	0.152	53.00	2.48	55	34
8.5	24.245	0.191	0.058	AB__8_5	AB	66	0.113	0.150	98.50	2.48	55	34
9.0	28.871	0.175	0.058	AB__9_0	AB	104	0.112	0.149	144.00	2.48	55	34
9.5	25.603	0.181	0.061	AB__9_5	AB	90	0.137	0.182	182.00	2.48	55	34
10.0	28.036	0.153	0.069	AB__10_0	AB	76	0.162	0.216	220.00	2.48	55	34
10.5	25.148	0.132	0.089	AB__10_5	AB	96	0.165	0.220	266.50	2.48	55	34
11.0	24.442	0.203	0.087	AB__11_0	AB	116	0.168	0.224	313.00	2.48	55	34
11.5	6.894	0.084	0.085	AB__11_5	AB	98	0.205	0.273	362.50	2.48	55	34
12.0	5.528	0.039	0.020	AB__12_0	AB	80	0.242	0.322	412.00	2.48	55	34
12.5	6.805	0.052	0.097	AB__12_5	AB	68	0.244	0.325	448.50	2.48	55	34
13.0	6.492	0.048	0.106	AB__13_0	AB	56	0.246	0.328	485.00	2.48	55	34
13.5	8.541	0.032	-0.043	AB__13_5	AB	38	0.242	0.322	495.00	2.48	55	34
14.0	28.151	0.167	-0.114	AB__14_0	AB	20	0.237	0.316	505.00	2.48	55	34
14.5	23.779	0.187	-0.067	AB__14_5	AB	20	0.208	0.278	515.50	2.48	55	34
15.0	12.522	0.118	-0.362	AB__15_0	AB	20	0.180	0.240	526.00	2.48	55	34
15.5	6.764	0.043	-0.339	AB__15_5	AB	24	0.188	0.250	546.50	2.48	55	34
16.0	7.552	0.052	-0.261	AB__16_0	AB	28	0.195	0.260	567.00	2.48	55	34
16.5	5.400	0.022	-0.145	AB__16_5	AB	28	0.198	0.264	581.00	2.48	55	34
17.0	5.900	0.017	-0.093	AB__17_0	AB	28	0.201	0.268	595.00	2.48	55	34
17.5	4.048	0.024	-0.144	AB__17_5	AB	48	0.196	0.261	615.50	2.48	55	34
18.0	20.823	0.108	-0.294	AB__18_0	AB	68	0.191	0.255	636.00	2.48	55	34
18.5	27.700	0.225	-0.238	AB__18_5	AB	82	0.225	0.299	684.50	2.48	55	34
19.0	25.179	0.177	-0.188	AB__19_0	AB	96	0.258	0.344	733.00	2.48	55	34
19.5	22.926	0.151	-0.069	AB__19_5	AB	90	0.313	0.418	779.00	2.48	55	34
20.0	20.674	0.124	0.049	AB__20_0	AB	84	0.369	0.492	825.00	2.48	55	34
20.5	25.997	0.231	0.185	AB__20_5	AB	92	0.383	0.510	871.00	2.48	55	34
21.0	29.572	0.304	0.175	AB__21_0	AB	100	0.397	0.529	917.00	2.48	55	34
21.5	40.627	0.408	0.158	AB__21_5	AB	104	0.385	0.513	968.00	2.48	55	34
22.0	39.834	0.368	0.170	AB__22_0	AB	108	0.373	0.498	1019.00	2.48	55	34
22.5	34.681	0.356	0.163	AB__22_5	AB	102	0.419	0.559	1067.00	2.48	55	34
23.0	26.795	0.273	0.166	AB__23_0	AB	96	0.465	0.620	1115.00	2.48	55	34
23.5	21.606	0.222	0.205	AB__23_5	AB	90	0.495	0.661	1159.50	2.48	55	34
24.0	27.394	0.295	0.197	AB__24_0	AB	84	0.526	0.702	1204.00	2.48	55	34
24.5	20.538	0.258	0.198	AB__24_5	AB	86	0.553	0.738	1248.50	2.48	55	34
25.0	27.088	0.211	-0.038	AB__25_0	AB	88	0.580	0.774	1293.00	2.48	55	34
25.5	35.413	0.319	0.210	AB__25_5	AB	86	0.590	0.787	1336.50	2.48	55	34
26.0	36.892	0.315	0.215	AB__26_0	AB	84	0.600	0.799	1380.00	2.48	55	34
26.5	46.709	0.456	0.250	AB__26_5	AB	84	0.594	0.792	1432.00	2.48	55	34
27.0	45.741	0.473	0.238	AB__27_0	AB	84	0.589	0.785	1484.00	2.48	55	34
27.5	50.310	0.469	0.211	AB__27_5	AB	84	0.601	0.801	1528.00	2.48	55	34
28.0	42.441	0.388	0.267	AB__28_0	AB	84	0.613	0.817	1572.00	2.48	55	34
28.5	42.527	0.487	0.292	AB__28_5	AB	86	0.610	0.813	1618.00	2.48	55	34
29.0	53.361	0.661	0.297	AB__29_0	AB	88	0.606	0.808	1664.00	2.48	55	34
29.5	47.392	0.373	0.302	AB__29_5	AB	92	0.606	0.808	1710.50	2.48	55	34
30.0	44.926	0.521	0.308	AB__30_0	AB	96	0.607	0.809	1757.00	2.48	55	34
30.5	46.653	0.574	0.313	AB__30_5	AB	96	0.615	0.820	1803.50	2.48	55	34
31.0	51.331	0.652	0.318	AB__31_0	AB	96	0.623	0.830	1850.00	2.48	55	34
31.5	48.796	0.531	0.323	AB__31_5	AB	96	0.617	0.822	1898.50	2.48	55	34
32.0	46.261	0.411	0.328	AB__32_0	AB	96	0.610	0.814	1947.00	2.48	55	34
32.5	59.915	0.812	0.333	AB__32_5	AB	102	0.600	0.800	2000.50	2.48	55	34
33.0	60.356	0.810	0.338	AB__33_0	AB	108	0.590	0.786	2054.00	2.48	55	34
33.5	57.943	0.757	0.343	AB__33_5	AB	106	0.573	0.764	2112.50	2.48	55	34
34.0	58.148	0.677	0.348	AB__34_0	AB	104	0.556	0.742	2171.00	2.48	55	34
4.0	11.434	0.082	0.036	AC__4_0	AC	6	0.118	0.158	6.50	2.48	55	34
4.5	14.955	0.109	0.035	AC__4_5	AC	5	0.112	0.150	7.25	2.48	55	34
5.0	15.722	0.125	0.037	AC__5_0	AC	4	0.106	0.142	8.00	2.48	55	34
5.5	15.727	0.123	0.039	AC__5_5	AC	10	0.104	0.139	14.50	2.48	55	34
6.0	11.347	0.111	0.045	AC__6_0	AC	16	0.103	0.137	21.00	2.48	55	34
6.5	13.989	0.105	0.051	AC__6_5	AC	20	0.104	0.139	31.00	2.48	55	34
7.0	16.632	0.098	0.058	AC__7_0	AC	24	0.106	0.142	41.00	2.48	55	34
7.5	24.536	0.146	0.063	AC__7_5	AC	38	0.122	0.163	63.00	2.48	55	34
8.0	24.622	0.183	0.059	AC__8_0	AC	52	0.138	0.184	85.00	2.48	55	34
8.5	24.245	0.191	0.058	AC__8_5	AC	48	0.169	0.225	112.00	2.48	55	34
9.0	28.871	0.175	0.058	AC__9_0	AC	44	0.199	0.265	139.00	2.48	55	34
9.5	25.603	0.181	0.061	AC__9_5	AC	62	0.191	0.255	171.00	2.48	55	34
10.0	28.036	0.153	0.069	AC__10_0	AC	80	0.183	0.244	203.00	2.48	55	34
10.5	25.148	0.132	0.089	AC__10_5	AC	88	0.204	0.272	251.00	2.48	55	34
11.0	24.442	0.203	0.087	AC__11_0	AC	96	0.225	0.300	299.00	2.48	55	34
11.5	6.894	0.084	0.085	AC__11_5	AC	84	0.258	0.344	342.50	2.48	55	34
12.0	5.528	0.039	0.020	AC__12_0	AC	72	0.290	0.387	386.00	2.48	55	34
12.5	6.805	0.052	0.097	AC__12_5	AC	76	0.267	0.356	427.00	2.48	55	34
13.0	6.492	0.048	0.106	AC__13_0	AC	80	0.244	0.325	468.00	2.48	55	34
13.5	8.541	0.032	-0.043	AC__13_5	AC	54	0.244	0.325	491.00	2.48	55	34
14.0	28.151	0.167	-0.114	AC__14_0	AC	28	0.243	0.324	514.00	2.48	55	34
14.5	23.779	0.187	-0.067	AC__14_5	AC	28	0.289	0.385	525.50	2.48	55	34
15.0	12.522	0.118	-0.362	AC__15_0	AC	28	0.334	0.445	537.00	2.48	55	34
15.5	6.764	0.043	-0.339	AC__15_5	AC	26	0.322	0.429	547.00	2.48	55	34
16.0	7.552	0.052	-0.261	AC__16_0	AC	24	0.310	0.413	557.00	2.48	55	34
16.5	5.400	0.022	-0.145	AC__16_5	AC	20	0.300	0.400	565.50	2.48	55	34
17.0	5.900	0.017	-0.093	AC__17_0	AC	16	0.290	0.387	574.00	2.48	55	34
17.5	4.048	0.024	-0.144	AC__17_5	AC	18	0.267	0.356	583.50	2.48	55	34
18.0	20.823	0.108	-0.294	AC__18_0	AC	20	0.244	0.326	593.00	2.48	55	34
18.5	27.700	0.225	-0.238	AC__18_5	AC	72	0.217	0.290	626.50	2.48	55	34
19.0	25.179	0.177	-0.188	AC__19_0	AC	124	0.190	0.254	660.00	2.48	55	34
19.5	22.926	0.151	-0.069	AC__19_5	AC	100	0.279	0.372	709.00	2.48	55	34
20.0	20.674	0.124	0.049	AC__20_0	AC	76	0.368	0.490	758.00	2.48	55	34
20.5	25.997	0.231	0.185	AC__20_5	AC	90	0.387	0.516	808.00	2.48	55	34
21.0	29.572	0.304	0.175	AC__21_0	AC	104	0.407	0.543	858.00	2.48	55	34
21.5	40.627	0.408	0.158	AC__21_5	AC	98	0.452	0.603	903.50	2.48	55	34
22.0	39.834	0.368	0.170	AC__22_0	AC	92	0.498	0.664	949.00	2.48	55	34
22.5	34.681	0.356	0.163	AC__22_5	AC	92	0.507	0.677	994.50	2.48	55	34
23.0	26.795	0.273	0.166	AC__23_0	AC	92	0.517	0.690	1040.00	2.48	55	34
23.5	21.606	0.222	0.205	AC__23_5	AC	90	0.518	0.691	1088.50	2.48	55	34
24.0	27.394	0.295	0.197	AC__24_0	AC	88	0.519	0.692	1137.00	2.48	55	34
24.5	20.538	0.258	0.198	AC__24_5	AC	94	0.531	0.709	1184.50	2.48	55	34
25.0	27.088	0.211	-0.038	AC__25_0	AC	100	0.544	0.725	1232.00	2.48	55	34
25.5	35.413	0.319	0.210	AC__25_5	AC	98	0.560	0.746	1280.50	2.48	55	34
26.0	36.892	0.315	0.215	AC__26_0	AC	96	0.576	0.768	1329.00	2.48	55	34
26.5	46.709	0.456	0.250	AC__26_5	AC	94	0.582	0.776	1373.00	2.48	55	34
27.0	45.741	0.473	0.238	AC__27_0	AC	92	0.588	0.784	1417.00	2.48	55	34
27.5	50.310	0.469	0.211	AC__27_5	AC	92	0.593	0.790	1464.00	2.48	55	34
28.0	42.441	0.388	0.267	AC__28_0	AC	92	0.597	0.796	1511.00	2.48	55	34
28.5	42.527	0.487	0.292	AC__28_5	AC	94	0.586	0.781	1557.50	2.48	55	34
29.0	53.361	0.661	0.297	AC__29_0	AC	96	0.574	0.766	1604.00	2.48	55	34
29.5	47.392	0.373	0.302	AC__29_5	AC	108	0.516	0.689	1670.00	2.48	55	34
30.0	44.926	0.521	0.308	AC__30_0	AC	120	0.459	0.612	1736.00	2.48	55	34
30.5	46.653	0.574	0.313	AC__30_5	AC	110	0.502	0.670	1784.50	2.48	55	34
31.0	51.331	0.652	0.318	AC__31_0	AC	100	0.546	0.728	1833.00	2.48	55	34
31.5	48.796	0.531	0.323	AC__31_5	AC	98	0.562	0.750	1883.00	2.48	55	34
32.0	46.261	0.411	0.328	AC__32_0	AC	96	0.579	0.771	1933.00	2.48	55	34
32.5	59.915	0.812	0.333	AC__32_5	AC	94	0.589	0.786	1981.00	2.48	55	34
33.0	60.356	0.810	0.338	AC__33_0	AC	92	0.600	0.800	2029.00	2.48	55	34
33.5	57.943	0.757	0.343	AC__33_5	AC	102	0.591	0.788	2080.00	2.48	55	34
34.0	58.148	0.677	0.348	AC__34_0	AC	112	0.583	0.777	2131.00	2.48	55	34

kable(top_n(validation, 100),
      digits = 3,
      caption = "Validation data.",
      align = "r") %>%
  kable_styling(font_size = 11) %>%
  row_spec(0, color = "grey10", background = "#F4F5F6") %>%
  scroll_box(height = "300px")

Validation data.

z [m]	qc [MPa]	fs [MPa]	u2 [MPa]	ID	Location ID	Normalised ENTRHU [-]	Normalised hammer energy [-]	Diameter [m]	Bottom wall thickness [mm]	Pile penetration [m]
3.0	8.859	0.071	0.041	CG__3_0	CG	0.120	0.160	2.48	50	33
3.5	12.484	0.111	0.041	CG__3_5	CG	0.122	0.162	2.48	50	33
4.0	26.119	0.214	0.052	CG__4_0	CG	0.124	0.165	2.48	50	33
4.5	31.922	0.298	0.066	CG__4_5	CG	0.118	0.157	2.48	50	33
5.0	31.822	0.292	0.079	CG__5_0	CG	0.112	0.149	2.48	50	33
5.5	29.064	0.268	0.090	CG__5_5	CG	0.117	0.155	2.48	50	33
6.0	25.606	0.216	0.078	CG__6_0	CG	0.121	0.162	2.48	50	33
6.5	28.187	0.251	0.062	CG__6_5	CG	0.124	0.165	2.48	50	33
7.0	22.891	0.232	0.078	CG__7_0	CG	0.126	0.168	2.48	50	33
7.5	22.283	0.199	0.090	CG__7_5	CG	0.137	0.183	2.48	50	33
8.0	25.220	0.240	0.099	CG__8_0	CG	0.148	0.198	2.48	50	33
8.5	24.819	0.244	0.107	CG__8_5	CG	0.174	0.232	2.48	50	33
9.0	25.353	0.235	0.109	CG__9_0	CG	0.200	0.267	2.48	50	33
9.5	29.594	0.261	0.101	CG__9_5	CG	0.233	0.311	2.48	50	33
10.0	33.834	0.287	0.094	CG__10_0	CG	0.267	0.356	2.48	50	33
10.5	27.980	0.143	0.075	CG__10_5	CG	0.295	0.393	2.48	50	33
11.0	25.273	0.217	0.121	CG__11_0	CG	0.323	0.431	2.48	50	33
11.5	14.002	0.148	0.132	CG__11_5	CG	0.322	0.430	2.48	50	33
12.0	15.830	0.118	0.126	CG__12_0	CG	0.322	0.429	2.48	50	33
12.5	11.260	0.110	0.143	CG__12_5	CG	0.318	0.424	2.48	50	33
13.0	9.934	0.119	0.097	CG__13_0	CG	0.314	0.419	2.48	50	33
13.5	18.624	0.144	0.126	CG__13_5	CG	0.310	0.413	2.48	50	33
14.0	13.182	0.109	0.136	CG__14_0	CG	0.306	0.408	2.48	50	33
14.5	10.605	0.092	0.126	CG__14_5	CG	0.301	0.402	2.48	50	33
15.0	8.276	0.083	0.092	CG__15_0	CG	0.297	0.396	2.48	50	33
15.5	14.220	0.140	0.132	CG__15_5	CG	0.334	0.445	2.48	50	33
16.0	21.716	0.156	0.116	CG__16_0	CG	0.371	0.494	2.48	50	33
16.5	19.388	0.134	0.129	CG__16_5	CG	0.394	0.526	2.48	50	33
17.0	16.566	0.136	0.155	CG__17_0	CG	0.418	0.557	2.48	50	33
17.5	22.589	0.174	0.172	CG__17_5	CG	0.454	0.606	2.48	50	33
18.0	31.932	0.247	0.007	CG__18_0	CG	0.491	0.654	2.48	50	33
18.5	50.331	0.298	0.192	CG__18_5	CG	0.507	0.676	2.48	50	33
19.0	35.054	0.305	0.161	CG__19_0	CG	0.524	0.698	2.48	50	33
19.5	38.511	0.366	0.179	CG__19_5	CG	0.525	0.700	2.48	50	33
20.0	41.968	0.426	0.197	CG__20_0	CG	0.526	0.702	2.48	50	33
20.5	43.108	0.460	0.196	CG__20_5	CG	0.534	0.712	2.48	50	33
21.0	44.592	0.520	0.161	CG__21_0	CG	0.541	0.722	2.48	50	33
21.5	47.682	0.567	0.155	CG__21_5	CG	0.558	0.744	2.48	50	33
22.0	36.740	0.394	-0.059	CG__22_0	CG	0.574	0.766	2.48	50	33
22.5	30.662	0.268	-0.259	CG__22_5	CG	0.590	0.787	2.48	50	33
23.0	29.587	0.362	-0.180	CG__23_0	CG	0.606	0.807	2.48	50	33
23.5	33.710	0.410	0.222	CG__23_5	CG	0.608	0.810	2.48	50	33
24.0	40.111	0.503	0.287	CG__24_0	CG	0.610	0.813	2.48	50	33
24.5	40.079	0.511	0.291	CG__24_5	CG	0.612	0.816	2.48	50	33
25.0	32.575	0.505	0.285	CG__25_0	CG	0.614	0.819	2.48	50	33
25.5	25.071	0.499	0.279	CG__25_5	CG	0.617	0.823	2.48	50	33
26.0	17.567	0.493	0.273	CG__26_0	CG	0.619	0.826	2.48	50	33
26.5	23.495	0.550	0.272	CG__26_5	CG	0.616	0.821	2.48	50	33
27.0	31.133	0.600	0.277	CG__27_0	CG	0.612	0.816	2.48	50	33
27.5	33.581	0.524	0.282	CG__27_5	CG	0.604	0.805	2.48	50	33
28.0	29.700	0.528	0.287	CG__28_0	CG	0.596	0.794	2.48	50	33
28.5	30.296	0.590	0.292	CG__28_5	CG	0.594	0.792	2.48	50	33
29.0	29.597	0.565	0.297	CG__29_0	CG	0.593	0.791	2.48	50	33
29.5	32.513	0.582	0.302	CG__29_5	CG	0.592	0.790	2.48	50	33
30.0	35.430	0.600	0.308	CG__30_0	CG	0.591	0.788	2.48	50	33
30.5	48.335	0.804	0.313	CG__30_5	CG	0.592	0.790	2.48	50	33
31.0	30.961	0.550	0.318	CG__31_0	CG	0.593	0.791	2.48	50	33
31.5	29.890	0.543	0.323	CG__31_5	CG	0.595	0.794	2.48	50	33
32.0	22.136	0.416	0.328	CG__32_0	CG	0.598	0.797	2.48	50	33
4.0	26.119	0.214	0.052	CH__4_0	CH	0.126	0.168	2.48	50	33
4.5	31.922	0.298	0.066	CH__4_5	CH	0.122	0.162	2.48	50	33
5.0	31.822	0.292	0.079	CH__5_0	CH	0.117	0.156	2.48	50	33
5.5	29.064	0.268	0.090	CH__5_5	CH	0.117	0.156	2.48	50	33
6.0	25.606	0.216	0.078	CH__6_0	CH	0.117	0.157	2.48	50	33
6.5	28.187	0.251	0.062	CH__6_5	CH	0.140	0.186	2.48	50	33
7.0	22.891	0.232	0.078	CH__7_0	CH	0.162	0.216	2.48	50	33
7.5	22.283	0.199	0.090	CH__7_5	CH	0.175	0.233	2.48	50	33
8.0	25.220	0.240	0.099	CH__8_0	CH	0.188	0.251	2.48	50	33
8.5	24.819	0.244	0.107	CH__8_5	CH	0.188	0.251	2.48	50	33
9.0	25.353	0.235	0.109	CH__9_0	CH	0.189	0.252	2.48	50	33
9.5	29.594	0.261	0.101	CH__9_5	CH	0.232	0.309	2.48	50	33
10.0	33.834	0.287	0.094	CH__10_0	CH	0.275	0.367	2.48	50	33
10.5	27.980	0.143	0.075	CH__10_5	CH	0.295	0.393	2.48	50	33
11.0	25.273	0.217	0.121	CH__11_0	CH	0.314	0.419	2.48	50	33
11.5	14.002	0.148	0.132	CH__11_5	CH	0.312	0.416	2.48	50	33
12.0	15.830	0.118	0.126	CH__12_0	CH	0.310	0.413	2.48	50	33
12.5	11.260	0.110	0.143	CH__12_5	CH	0.314	0.419	2.48	50	33
13.0	9.934	0.119	0.097	CH__13_0	CH	0.318	0.424	2.48	50	33
13.5	18.624	0.144	0.126	CH__13_5	CH	0.314	0.419	2.48	50	33
14.0	13.182	0.109	0.136	CH__14_0	CH	0.311	0.414	2.48	50	33
14.5	10.605	0.092	0.126	CH__14_5	CH	0.305	0.407	2.48	50	33
15.0	8.276	0.083	0.092	CH__15_0	CH	0.300	0.400	2.48	50	33
15.5	14.220	0.140	0.132	CH__15_5	CH	0.329	0.439	2.48	50	33
16.0	21.716	0.156	0.116	CH__16_0	CH	0.359	0.478	2.48	50	33
16.5	19.388	0.134	0.129	CH__16_5	CH	0.392	0.523	2.48	50	33
17.0	16.566	0.136	0.155	CH__17_0	CH	0.426	0.568	2.48	50	33
17.5	22.589	0.174	0.172	CH__17_5	CH	0.478	0.637	2.48	50	33
18.0	31.932	0.247	0.007	CH__18_0	CH	0.529	0.706	2.48	50	33
18.5	50.331	0.298	0.192	CH__18_5	CH	0.525	0.700	2.48	50	33
19.0	35.054	0.305	0.161	CH__19_0	CH	0.521	0.695	2.48	50	33
19.5	38.511	0.366	0.179	CH__19_5	CH	0.517	0.690	2.48	50	33
20.0	41.968	0.426	0.197	CH__20_0	CH	0.513	0.684	2.48	50	33
20.5	43.108	0.460	0.196	CH__20_5	CH	0.512	0.682	2.48	50	33
21.0	44.592	0.520	0.161	CH__21_0	CH	0.510	0.680	2.48	50	33
21.5	47.682	0.567	0.155	CH__21_5	CH	0.510	0.680	2.48	50	33
22.0	36.740	0.394	-0.059	CH__22_0	CH	0.510	0.680	2.48	50	33
22.5	30.662	0.268	-0.259	CH__22_5	CH	0.529	0.705	2.48	50	33
23.0	29.587	0.362	-0.180	CH__23_0	CH	0.548	0.731	2.48	50	33
23.5	33.710	0.410	0.222	CH__23_5	CH	0.554	0.738	2.48	50	33
24.0	40.111	0.503	0.287	CH__24_0	CH	0.559	0.746	2.48	50	33
24.5	40.079	0.511	0.291	CH__24_5	CH	0.561	0.748	2.48	50	33
25.0	32.575	0.505	0.285	CH__25_0	CH	0.563	0.751	2.48	50	33
25.5	25.071	0.499	0.279	CH__25_5	CH	0.567	0.756	2.48	50	33
26.0	17.567	0.493	0.273	CH__26_0	CH	0.571	0.761	2.48	50	33
26.5	23.495	0.550	0.272	CH__26_5	CH	0.576	0.768	2.48	50	33
27.0	31.133	0.600	0.277	CH__27_0	CH	0.581	0.775	2.48	50	33
27.5	33.581	0.524	0.282	CH__27_5	CH	0.587	0.782	2.48	50	33
28.0	29.700	0.528	0.287	CH__28_0	CH	0.592	0.789	2.48	50	33
28.5	30.296	0.590	0.292	CH__28_5	CH	0.598	0.797	2.48	50	33
29.0	29.597	0.565	0.297	CH__29_0	CH	0.603	0.804	2.48	50	33
29.5	32.513	0.582	0.302	CH__29_5	CH	0.601	0.801	2.48	50	33
30.0	35.430	0.600	0.308	CH__30_0	CH	0.599	0.798	2.48	50	33
30.5	48.335	0.804	0.313	CH__30_5	CH	0.597	0.795	2.48	50	33
31.0	30.961	0.550	0.318	CH__31_0	CH	0.594	0.792	2.48	50	33
31.5	29.890	0.543	0.323	CH__31_5	CH	0.594	0.792	2.48	50	33
32.0	22.136	0.416	0.328	CH__32_0	CH	0.594	0.792	2.48	50	33
32.5	62.235	0.873	0.333	CH__32_5	CH	0.585	0.780	2.48	50	33
33.0	77.961	1.010	0.338	CH__33_0	CH	0.577	0.769	2.48	50	33
5.0	31.822	0.292	0.079	CI__5_0	CI	0.121	0.162	2.48	50	33
5.5	29.064	0.268	0.090	CI__5_5	CI	0.122	0.163	2.48	50	33
6.0	25.606	0.216	0.078	CI__6_0	CI	0.124	0.165	2.48	50	33
6.5	28.187	0.251	0.062	CI__6_5	CI	0.122	0.162	2.48	50	33
7.0	22.891	0.232	0.078	CI__7_0	CI	0.119	0.159	2.48	50	33
7.5	22.283	0.199	0.090	CI__7_5	CI	0.116	0.155	2.48	50	33
8.0	25.220	0.240	0.099	CI__8_0	CI	0.113	0.151	2.48	50	33
8.5	24.819	0.244	0.107	CI__8_5	CI	0.146	0.195	2.48	50	33
9.0	25.353	0.235	0.109	CI__9_0	CI	0.179	0.239	2.48	50	33
9.5	29.594	0.261	0.101	CI__9_5	CI	0.190	0.254	2.48	50	33
10.0	33.834	0.287	0.094	CI__10_0	CI	0.201	0.268	2.48	50	33
10.5	27.980	0.143	0.075	CI__10_5	CI	0.244	0.325	2.48	50	33
11.0	25.273	0.217	0.121	CI__11_0	CI	0.287	0.382	2.48	50	33
11.5	14.002	0.148	0.132	CI__11_5	CI	0.288	0.384	2.48	50	33
12.0	15.830	0.118	0.126	CI__12_0	CI	0.289	0.386	2.48	50	33
12.5	11.260	0.110	0.143	CI__12_5	CI	0.289	0.385	2.48	50	33
13.0	9.934	0.119	0.097	CI__13_0	CI	0.288	0.384	2.48	50	33
13.5	18.624	0.144	0.126	CI__13_5	CI	0.290	0.387	2.48	50	33
14.0	13.182	0.109	0.136	CI__14_0	CI	0.292	0.389	2.48	50	33
14.5	10.605	0.092	0.126	CI__14_5	CI	0.298	0.398	2.48	50	33
15.0	8.276	0.083	0.092	CI__15_0	CI	0.305	0.407	2.48	50	33
15.5	14.220	0.140	0.132	CI__15_5	CI	0.342	0.456	2.48	50	33
16.0	21.716	0.156	0.116	CI__16_0	CI	0.379	0.505	2.48	50	33
16.5	19.388	0.134	0.129	CI__16_5	CI	0.401	0.534	2.48	50	33
17.0	16.566	0.136	0.155	CI__17_0	CI	0.422	0.563	2.48	50	33
17.5	22.589	0.174	0.172	CI__17_5	CI	0.434	0.579	2.48	50	33
18.0	31.932	0.247	0.007	CI__18_0	CI	0.446	0.595	2.48	50	33
18.5	50.331	0.298	0.192	CI__18_5	CI	0.453	0.605	2.48	50	33
19.0	35.054	0.305	0.161	CI__19_0	CI	0.461	0.614	2.48	50	33
19.5	38.511	0.366	0.179	CI__19_5	CI	0.490	0.654	2.48	50	33
20.0	41.968	0.426	0.197	CI__20_0	CI	0.520	0.693	2.48	50	33
20.5	43.108	0.460	0.196	CI__20_5	CI	0.518	0.690	2.48	50	33
21.0	44.592	0.520	0.161	CI__21_0	CI	0.515	0.687	2.48	50	33
21.5	47.682	0.567	0.155	CI__21_5	CI	0.514	0.686	2.48	50	33
22.0	36.740	0.394	-0.059	CI__22_0	CI	0.514	0.685	2.48	50	33
22.5	30.662	0.268	-0.259	CI__22_5	CI	0.509	0.679	2.48	50	33
23.0	29.587	0.362	-0.180	CI__23_0	CI	0.505	0.673	2.48	50	33
23.5	33.710	0.410	0.222	CI__23_5	CI	0.514	0.685	2.48	50	33
24.0	40.111	0.503	0.287	CI__24_0	CI	0.522	0.697	2.48	50	33
24.5	40.079	0.511	0.291	CI__24_5	CI	0.549	0.732	2.48	50	33
25.0	32.575	0.505	0.285	CI__25_0	CI	0.576	0.768	2.48	50	33
25.5	25.071	0.499	0.279	CI__25_5	CI	0.574	0.765	2.48	50	33
26.0	17.567	0.493	0.273	CI__26_0	CI	0.571	0.762	2.48	50	33
26.5	23.495	0.550	0.272	CI__26_5	CI	0.570	0.760	2.48	50	33
27.0	31.133	0.600	0.277	CI__27_0	CI	0.568	0.757	2.48	50	33
27.5	33.581	0.524	0.282	CI__27_5	CI	0.581	0.775	2.48	50	33
28.0	29.700	0.528	0.287	CI__28_0	CI	0.594	0.792	2.48	50	33
28.5	30.296	0.590	0.292	CI__28_5	CI	0.596	0.794	2.48	50	33
29.0	29.597	0.565	0.297	CI__29_0	CI	0.597	0.796	2.48	50	33
29.5	32.513	0.582	0.302	CI__29_5	CI	0.596	0.795	2.48	50	33
30.0	35.430	0.600	0.308	CI__30_0	CI	0.596	0.794	2.48	50	33
30.5	48.335	0.804	0.313	CI__30_5	CI	0.608	0.811	2.48	50	33
31.0	30.961	0.550	0.318	CI__31_0	CI	0.621	0.828	2.48	50	33
31.5	29.890	0.543	0.323	CI__31_5	CI	0.619	0.825	2.48	50	33
32.0	22.136	0.416	0.328	CI__32_0	CI	0.618	0.823	2.48	50	33
32.5	62.235	0.873	0.333	CI__32_5	CI	0.615	0.820	2.48	50	33
33.0	77.961	1.010	0.338	CI__33_0	CI	0.613	0.817	2.48	50	33

The above tables show the first 100 rows of the training and validation datasets. The two datasets have the same structure. The parameters included in the data can be divided into four categories:

• CPT test data:
  • z [m] - depth;
  • qc [MPa] - cone tip resistance;
  • fs [MPa - cone sleeve friction;
  • u2 [MPa] - pore pressure;
• pile foundations data:
  • Diameter [m] - pile outer diameter;
  • Bottom wall thickness [mm] - wall thickness at the bottom of the pile;
• pile installation data:
  • Pile penetration [m] - final penetration of the pile below mudline;
  • Normalised ENTRHU [-] - energy transmitted to the pile (normalised to be between 0 and 1);
  • Normalised hammer energy [-] - energy provided by the hammer (normalised to be between 0 and 1);
  • Blowcount [Blows/m] - number of blows required for an additional meter of pile penetration;
  • Number of blows - total number of blows to reach the selected depth;
• identification data:
  • Location ID - anonymized location ID;
  • ID - a unique ID combining the location name and depth.

To facilitate the model-building process, the data have been pre-processed to a regular grid with a vertical spacing of 0.5m (notice the values of z [m]). In overall there are 4610 and 1008 data points in the training and validation datasets, respectively.

Note that for the validation dataset, Blowcount [Blows/m] and Number of blows are not provided, as these are the parameters to be predicted by the model (i.e. outcome). The remaining 11 variables can potentially be used as input to build the predictive model (i.e. features).

2.2 Normalised data

In addition, normalised data for CPT registrations, for both training and validation, are also provided. We load and view these data here but, for now, we are not really going to detail them.

training_no <- read_csv("F:/isfog2020/training_data_withnormalised.csv")
validation_no <- read_csv("F:/isfog2020/validation_data_withnormalised.csv")

kable(top_n(training_no, 100),
      digits = 3,
      caption = "Normalised training data.",
      align = "r") %>%
  kable_styling(font_size = 11) %>%
  row_spec(0, color = "grey10", background = "#F4F5F6") %>%
  scroll_box(height = "300px")

Normalised training data.

z [m]	qc [MPa]	fs [MPa]	u2 [MPa]	ID	Location ID	Blowcount [Blows/m]	Normalised ENTRHU [-]	Normalised hammer energy [-]	Number of blows	Diameter [m]	Bottom wall thickness [mm]	Pile penetration [m]	area ratio [-]	Push	Total unit weight [kN/m3]	Layer no	Vertical total stress [kPa]	Water pressure [kPa]	Vertical effective stress [kPa]	qt [MPa]	Delta u2 [MPa]	Rf [%]	Bq [-]	Qt [-]	Fr [%]	qnet [MPa]	Ic [-]
11.5	1.641	0.024	0.080	CD__11_5	CD	28	0.228	0.304	224.0	2.48	70	32	0.75	1	19	1	218.5	117.875	100.625	1.661	-0.038	1.433	-0.026	14.338	1.650	1.443	2.724
25.0	6.689	0.296	0.550	CD__25_0	CD	72	0.534	0.711	1102.0	2.48	70	32	0.75	1	19	1	475.0	256.250	218.750	6.826	0.294	4.333	0.046	29.034	4.657	6.351	2.756
25.5	4.287	0.121	0.665	CD__25_5	CD	64	0.533	0.711	1131.5	2.48	70	32	0.75	1	19	1	484.5	261.375	223.125	4.454	0.404	2.712	0.102	17.789	3.043	3.969	2.798
26.0	4.829	0.160	1.263	CD__26_0	CD	56	0.533	0.710	1161.0	2.48	70	32	0.75	1	19	1	494.0	266.500	227.500	5.145	0.996	3.114	0.214	20.444	3.444	4.651	2.784
26.5	5.456	0.128	1.912	CD__26_5	CD	56	0.541	0.722	1190.5	2.48	70	32	0.75	1	19	1	503.5	271.625	231.875	5.934	1.640	2.162	0.302	23.418	2.363	5.430	2.627
27.0	5.487	0.105	0.113	CD__27_0	CD	56	0.550	0.733	1220.0	2.48	70	32	0.75	1	19	1	513.0	276.750	236.250	5.515	-0.164	1.911	-0.033	21.172	2.107	5.002	2.633
10.5	2.046	0.060	0.133	CA__10_5	CA	34	0.170	0.226	196.5	2.48	50	27	0.75	1	19	1	199.5	107.625	91.875	2.079	0.026	2.881	0.014	20.463	3.186	1.880	2.764
11.5	2.311	0.057	0.219	CA__11_5	CA	32	0.173	0.230	230.0	2.48	50	27	0.75	1	19	1	218.5	117.875	100.625	2.366	0.102	2.396	0.047	21.342	2.640	2.148	2.698
27.5	4.705	0.126	0.179	DW__27_5	DW	100	0.386	0.514	1934.0	2.48	50	32	0.75	1	19	1	522.5	281.875	240.625	4.750	-0.102	2.652	-0.024	17.567	2.980	4.227	2.797
10.5	3.111	0.114	0.262	AU__10_5	AU	70	0.229	0.310	253.0	2.48	55	32	0.75	1	19	1	199.5	107.625	91.875	3.177	0.154	3.595	0.052	32.403	3.836	2.977	2.666
13.5	3.585	0.131	-0.140	EC__13_5	EC	24	0.328	0.438	163.0	2.48	70	27	0.75	1	19	1	256.5	138.375	118.125	3.550	-0.278	3.695	-0.084	27.886	3.983	3.294	2.720
15.0	2.971	0.062	-0.284	AR__15_0	AR	60	0.466	0.621	229.0	2.48	55	29	0.75	1	19	1	285.0	153.750	131.250	2.900	-0.438	2.153	-0.167	19.924	2.388	2.615	2.690
25.5	4.827	0.187	0.269	CM__25_5	CM	72	0.533	0.711	1277.0	2.48	50	30	0.75	1	19	1	484.5	261.375	223.125	4.895	0.008	3.814	0.002	19.766	4.233	4.410	2.853
12.5	2.705	0.115	-0.082	CY__12_5	CY	26	0.233	0.310	170.0	2.48	70	25	0.75	1	19	1	237.5	128.125	109.375	2.685	-0.210	4.298	-0.086	22.377	4.715	2.448	2.842
11.5	3.228	0.098	0.126	EE__11_5	EE	52	0.242	0.323	387.5	2.48	50	30	0.75	1	19	1	218.5	117.875	100.625	3.259	0.008	3.007	0.003	30.216	3.223	3.041	2.635
11.0	2.627	0.074	0.126	DK__11_0	DK	20	0.237	0.316	121.0	2.48	50	31	0.75	1	19	1	209.0	112.750	96.250	2.658	0.013	2.795	0.005	25.448	3.033	2.449	2.677
1.0	0.347	0.016	0.025	AL__1_0	AL	NA	NA	NA	NA	2.48	55	30	0.75	1	19	1	19.0	10.250	8.750	0.353	0.015	4.490	0.044	38.200	4.745	0.334	2.750
38.5	9.247	0.236	-0.208	BA__38_5	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	731.5	394.625	336.875	9.195	-0.602	2.563	-0.071	25.124	2.785	8.464	2.656
41.0	6.616	0.212	-0.119	BA__41_0	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	779.0	420.250	358.750	6.586	-0.539	3.222	-0.093	16.187	3.654	5.807	2.879
41.5	5.836	0.231	0.353	BA__41_5	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	788.5	425.375	363.125	5.925	-0.072	3.894	-0.014	14.144	4.492	5.136	2.981
42.0	5.571	0.215	1.179	BA__42_0	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	798.0	430.500	367.500	5.865	0.749	3.664	0.148	13.789	4.241	5.067	2.974
42.5	5.012	0.201	1.243	BA__42_5	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	807.5	435.625	371.875	5.322	0.808	3.784	0.179	12.141	4.461	4.515	3.031
43.0	3.789	0.151	0.760	BA__43_0	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	817.0	440.750	376.250	3.979	0.319	3.787	0.101	8.404	4.766	3.162	3.175
43.5	3.956	0.176	1.057	BA__43_5	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	826.5	445.875	380.625	4.221	0.611	4.158	0.180	8.917	5.171	3.394	3.176
44.0	6.573	0.196	1.105	BA__44_0	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	836.0	451.000	385.000	6.850	0.654	2.869	0.109	15.620	3.268	6.014	2.862
45.5	7.516	0.169	-0.260	BA__45_5	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	864.5	466.375	398.125	7.451	-0.727	2.267	-0.110	16.544	2.564	6.586	2.779
46.5	4.458	0.179	-0.241	BA__46_5	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	883.5	476.625	406.875	4.398	-0.718	4.077	-0.204	8.637	5.102	3.514	3.184
47.0	4.204	0.169	0.021	BA__47_0	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	893.0	481.750	411.250	4.209	-0.461	4.011	-0.139	8.063	5.091	3.316	3.207
47.5	4.129	0.106	0.374	BA__47_5	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	902.5	486.875	415.625	4.222	-0.113	2.519	-0.034	7.988	3.204	3.320	3.094
48.0	6.130	0.196	-0.424	BA__48_0	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	912.0	492.000	420.000	6.024	-0.916	3.254	-0.179	12.171	3.834	5.112	2.990
48.5	3.613	0.098	1.463	BA__48_5	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	921.5	497.125	424.375	3.979	0.966	2.470	0.316	7.205	3.215	3.058	3.132
49.5	6.013	0.172	-0.499	BA__49_5	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	940.5	507.375	433.125	5.888	-1.007	2.920	-0.203	11.423	3.474	4.947	2.987
50.0	4.809	0.111	0.340	BA__50_0	BA	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	950.0	512.500	437.500	4.894	-0.172	2.266	-0.044	9.015	2.812	3.944	3.018
14.5	3.169	0.129	0.127	DB__14_5	DB	44	0.237	0.315	209.0	2.48	50	26	0.75	1	19	1	275.5	148.625	126.875	3.201	-0.021	4.024	-0.007	23.058	4.403	2.925	2.812
11.5	1.641	0.024	0.080	CE__11_5	CE	58	0.217	0.289	352.0	2.48	70	32	0.75	1	19	1	218.5	117.875	100.625	1.661	-0.038	1.433	-0.026	14.338	1.650	1.443	2.724
25.0	6.689	0.296	0.550	CE__25_0	CE	72	0.576	0.768	1383.0	2.48	70	32	0.75	1	19	1	475.0	256.250	218.750	6.826	0.294	4.333	0.046	29.034	4.657	6.351	2.756
25.5	4.287	0.121	0.665	CE__25_5	CE	76	0.569	0.759	1421.0	2.48	70	32	0.75	1	19	1	484.5	261.375	223.125	4.454	0.404	2.712	0.102	17.789	3.043	3.969	2.798
26.0	4.829	0.160	1.263	CE__26_0	CE	80	0.562	0.750	1459.0	2.48	70	32	0.75	1	19	1	494.0	266.500	227.500	5.145	0.996	3.114	0.214	20.444	3.444	4.651	2.784
26.5	5.456	0.128	1.912	CE__26_5	CE	78	0.565	0.753	1495.5	2.48	70	32	0.75	1	19	1	503.5	271.625	231.875	5.934	1.640	2.162	0.302	23.418	2.363	5.430	2.627
27.0	5.487	0.105	0.113	CE__27_0	CE	76	0.567	0.756	1532.0	2.48	70	32	0.75	1	19	1	513.0	276.750	236.250	5.515	-0.164	1.911	-0.033	21.172	2.107	5.002	2.633
10.5	2.046	0.060	0.133	CB__10_5	CB	32	0.159	0.212	142.5	2.48	50	27	0.75	1	19	1	199.5	107.625	91.875	2.079	0.026	2.881	0.014	20.463	3.186	1.880	2.764
11.5	2.311	0.057	0.219	CB__11_5	CB	30	0.142	0.189	169.0	2.48	50	27	0.75	1	19	1	218.5	117.875	100.625	2.366	0.102	2.396	0.047	21.342	2.640	2.148	2.698
27.5	4.705	0.126	0.179	DX__27_5	DX	90	0.487	0.649	1904.5	2.48	50	32	0.75	1	19	1	522.5	281.875	240.625	4.750	-0.102	2.652	-0.024	17.567	2.980	4.227	2.797
10.5	3.111	0.114	0.262	AV__10_5	AV	28	0.317	0.422	295.5	2.48	55	32	0.75	1	19	1	199.5	107.625	91.875	3.177	0.154	3.595	0.052	32.403	3.836	2.977	2.666
15.0	2.971	0.062	-0.284	AS__15_0	AS	84	0.476	0.634	366.0	2.48	55	29	0.75	1	19	1	285.0	153.750	131.250	2.900	-0.438	2.153	-0.167	19.924	2.388	2.615	2.690
25.5	4.827	0.187	0.269	CN__25_5	CN	88	0.491	0.655	1569.0	2.48	50	30	0.75	1	19	1	484.5	261.375	223.125	4.895	0.008	3.814	0.002	19.766	4.233	4.410	2.853
12.5	2.705	0.115	-0.082	CZ__12_5	CZ	38	0.181	0.242	175.5	2.48	70	25	0.75	1	19	1	237.5	128.125	109.375	2.685	-0.210	4.298	-0.086	22.377	4.715	2.448	2.842
11.5	3.228	0.098	0.126	EF__11_5	EF	82	0.254	0.338	498.0	2.48	50	30	0.75	1	19	1	218.5	117.875	100.625	3.259	0.008	3.007	0.003	30.216	3.223	3.041	2.635
11.0	2.627	0.074	0.126	DL__11_0	DL	24	0.223	0.297	259.0	2.48	50	31	0.75	1	19	1	209.0	112.750	96.250	2.658	0.013	2.795	0.005	25.448	3.033	2.449	2.677
1.0	0.347	0.016	0.025	AM__1_0	AM	NA	NA	NA	NA	2.48	55	30	0.75	1	19	1	19.0	10.250	8.750	0.353	0.015	4.490	0.044	38.200	4.745	0.334	2.750
38.5	9.247	0.236	-0.208	BB__38_5	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	731.5	394.625	336.875	9.195	-0.602	2.563	-0.071	25.124	2.785	8.464	2.656
41.0	6.616	0.212	-0.119	BB__41_0	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	779.0	420.250	358.750	6.586	-0.539	3.222	-0.093	16.187	3.654	5.807	2.879
41.5	5.836	0.231	0.353	BB__41_5	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	788.5	425.375	363.125	5.925	-0.072	3.894	-0.014	14.144	4.492	5.136	2.981
42.0	5.571	0.215	1.179	BB__42_0	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	798.0	430.500	367.500	5.865	0.749	3.664	0.148	13.789	4.241	5.067	2.974
42.5	5.012	0.201	1.243	BB__42_5	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	807.5	435.625	371.875	5.322	0.808	3.784	0.179	12.141	4.461	4.515	3.031
43.0	3.789	0.151	0.760	BB__43_0	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	817.0	440.750	376.250	3.979	0.319	3.787	0.101	8.404	4.766	3.162	3.175
43.5	3.956	0.176	1.057	BB__43_5	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	826.5	445.875	380.625	4.221	0.611	4.158	0.180	8.917	5.171	3.394	3.176
44.0	6.573	0.196	1.105	BB__44_0	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	836.0	451.000	385.000	6.850	0.654	2.869	0.109	15.620	3.268	6.014	2.862
45.5	7.516	0.169	-0.260	BB__45_5	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	864.5	466.375	398.125	7.451	-0.727	2.267	-0.110	16.544	2.564	6.586	2.779
46.5	4.458	0.179	-0.241	BB__46_5	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	883.5	476.625	406.875	4.398	-0.718	4.077	-0.204	8.637	5.102	3.514	3.184
47.0	4.204	0.169	0.021	BB__47_0	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	893.0	481.750	411.250	4.209	-0.461	4.011	-0.139	8.063	5.091	3.316	3.207
47.5	4.129	0.106	0.374	BB__47_5	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	902.5	486.875	415.625	4.222	-0.113	2.519	-0.034	7.988	3.204	3.320	3.094
48.0	6.130	0.196	-0.424	BB__48_0	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	912.0	492.000	420.000	6.024	-0.916	3.254	-0.179	12.171	3.834	5.112	2.990
48.5	3.613	0.098	1.463	BB__48_5	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	921.5	497.125	424.375	3.979	0.966	2.470	0.316	7.205	3.215	3.058	3.132
49.5	6.013	0.172	-0.499	BB__49_5	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	940.5	507.375	433.125	5.888	-1.007	2.920	-0.203	11.423	3.474	4.947	2.987
50.0	4.809	0.111	0.340	BB__50_0	BB	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	950.0	512.500	437.500	4.894	-0.172	2.266	-0.044	9.015	2.812	3.944	3.018
14.5	3.169	0.129	0.127	DC__14_5	DC	62	0.319	0.425	486.0	2.48	50	26	0.75	1	19	1	275.5	148.625	126.875	3.201	-0.021	4.024	-0.007	23.058	4.403	2.925	2.812
11.5	1.641	0.024	0.080	CF__11_5	CF	34	0.268	0.357	295.5	2.48	70	32	0.75	1	19	1	218.5	117.875	100.625	1.661	-0.038	1.433	-0.026	14.338	1.650	1.443	2.724
25.0	6.689	0.296	0.550	CF__25_0	CF	72	0.555	0.740	1252.0	2.48	70	32	0.75	1	19	1	475.0	256.250	218.750	6.826	0.294	4.333	0.046	29.034	4.657	6.351	2.756
25.5	4.287	0.121	0.665	CF__25_5	CF	72	0.550	0.733	1289.5	2.48	70	32	0.75	1	19	1	484.5	261.375	223.125	4.454	0.404	2.712	0.102	17.789	3.043	3.969	2.798
26.0	4.829	0.160	1.263	CF__26_0	CF	72	0.544	0.726	1327.0	2.48	70	32	0.75	1	19	1	494.0	266.500	227.500	5.145	0.996	3.114	0.214	20.444	3.444	4.651	2.784
26.5	5.456	0.128	1.912	CF__26_5	CF	66	0.556	0.741	1361.5	2.48	70	32	0.75	1	19	1	503.5	271.625	231.875	5.934	1.640	2.162	0.302	23.418	2.363	5.430	2.627
27.0	5.487	0.105	0.113	CF__27_0	CF	60	0.567	0.756	1396.0	2.48	70	32	0.75	1	19	1	513.0	276.750	236.250	5.515	-0.164	1.911	-0.033	21.172	2.107	5.002	2.633
10.5	2.046	0.060	0.133	CC__10_5	CC	20	0.180	0.240	102.0	2.48	50	27	0.75	1	19	1	199.5	107.625	91.875	2.079	0.026	2.881	0.014	20.463	3.186	1.880	2.764
11.5	2.311	0.057	0.219	CC__11_5	CC	20	0.164	0.218	124.5	2.48	50	27	0.75	1	19	1	218.5	117.875	100.625	2.366	0.102	2.396	0.047	21.342	2.640	2.148	2.698
27.5	4.705	0.126	0.179	DY__27_5	DY	90	0.478	0.638	1988.5	2.48	50	32	0.75	1	19	1	522.5	281.875	240.625	4.750	-0.102	2.652	-0.024	17.567	2.980	4.227	2.797
10.5	3.111	0.114	0.262	AW__10_5	AW	46	0.301	0.402	337.0	2.48	55	32	0.75	1	19	1	199.5	107.625	91.875	3.177	0.154	3.595	0.052	32.403	3.836	2.977	2.666
13.5	3.585	0.131	-0.140	ED__13_5	ED	28	0.313	0.417	254.5	2.48	70	27	0.75	1	19	1	256.5	138.375	118.125	3.550	-0.278	3.695	-0.084	27.886	3.983	3.294	2.720
15.0	2.971	0.062	-0.284	AT__15_0	AT	72	0.478	0.637	353.0	2.48	55	29	0.75	1	19	1	285.0	153.750	131.250	2.900	-0.438	2.153	-0.167	19.924	2.388	2.615	2.690
25.5	4.827	0.187	0.269	CO__25_5	CO	86	0.523	0.698	1482.5	2.48	50	30	0.75	1	19	1	484.5	261.375	223.125	4.895	0.008	3.814	0.002	19.766	4.233	4.410	2.853
12.5	2.705	0.115	-0.082	DA__12_5	DA	24	0.218	0.290	143.0	2.48	70	25	0.75	1	19	1	237.5	128.125	109.375	2.685	-0.210	4.298	-0.086	22.377	4.715	2.448	2.842
11.5	3.228	0.098	0.126	EG__11_5	EG	50	0.262	0.349	310.5	2.48	50	30	0.75	1	19	1	218.5	117.875	100.625	3.259	0.008	3.007	0.003	30.216	3.223	3.041	2.635
11.0	2.627	0.074	0.126	DM__11_0	DM	24	0.243	0.324	225.0	2.48	50	31	0.75	1	19	1	209.0	112.750	96.250	2.658	0.013	2.795	0.005	25.448	3.033	2.449	2.677
1.0	0.347	0.016	0.025	AN__1_0	AN	NA	NA	NA	NA	2.48	55	30	0.75	1	19	1	19.0	10.250	8.750	0.353	0.015	4.490	0.044	38.200	4.745	0.334	2.750
38.5	9.247	0.236	-0.208	BC__38_5	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	731.5	394.625	336.875	9.195	-0.602	2.563	-0.071	25.124	2.785	8.464	2.656
41.0	6.616	0.212	-0.119	BC__41_0	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	779.0	420.250	358.750	6.586	-0.539	3.222	-0.093	16.187	3.654	5.807	2.879
41.5	5.836	0.231	0.353	BC__41_5	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	788.5	425.375	363.125	5.925	-0.072	3.894	-0.014	14.144	4.492	5.136	2.981
42.0	5.571	0.215	1.179	BC__42_0	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	798.0	430.500	367.500	5.865	0.749	3.664	0.148	13.789	4.241	5.067	2.974
42.5	5.012	0.201	1.243	BC__42_5	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	807.5	435.625	371.875	5.322	0.808	3.784	0.179	12.141	4.461	4.515	3.031
43.0	3.789	0.151	0.760	BC__43_0	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	817.0	440.750	376.250	3.979	0.319	3.787	0.101	8.404	4.766	3.162	3.175
43.5	3.956	0.176	1.057	BC__43_5	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	826.5	445.875	380.625	4.221	0.611	4.158	0.180	8.917	5.171	3.394	3.176
44.0	6.573	0.196	1.105	BC__44_0	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	836.0	451.000	385.000	6.850	0.654	2.869	0.109	15.620	3.268	6.014	2.862
45.5	7.516	0.169	-0.260	BC__45_5	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	864.5	466.375	398.125	7.451	-0.727	2.267	-0.110	16.544	2.564	6.586	2.779
46.5	4.458	0.179	-0.241	BC__46_5	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	883.5	476.625	406.875	4.398	-0.718	4.077	-0.204	8.637	5.102	3.514	3.184
47.0	4.204	0.169	0.021	BC__47_0	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	893.0	481.750	411.250	4.209	-0.461	4.011	-0.139	8.063	5.091	3.316	3.207
47.5	4.129	0.106	0.374	BC__47_5	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	902.5	486.875	415.625	4.222	-0.113	2.519	-0.034	7.988	3.204	3.320	3.094
48.0	6.130	0.196	-0.424	BC__48_0	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	912.0	492.000	420.000	6.024	-0.916	3.254	-0.179	12.171	3.834	5.112	2.990
48.5	3.613	0.098	1.463	BC__48_5	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	921.5	497.125	424.375	3.979	0.966	2.470	0.316	7.205	3.215	3.058	3.132
49.5	6.013	0.172	-0.499	BC__49_5	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	940.5	507.375	433.125	5.888	-1.007	2.920	-0.203	11.423	3.474	4.947	2.987
50.0	4.809	0.111	0.340	BC__50_0	BC	NA	NA	NA	NA	NA	NA	NA	0.75	1	19	1	950.0	512.500	437.500	4.894	-0.172	2.266	-0.044	9.015	2.812	3.944	3.018
14.5	3.169	0.129	0.127	DD__14_5	DD	42	0.366	0.488	356.5	2.48	50	26	0.75	1	19	1	275.5	148.625	126.875	3.201	-0.021	4.024	-0.007	23.058	4.403	2.925	2.812

kable(top_n(validation_no, 100),
      digits = 3,
      caption = "Normalised validation data.",
      align = "r") %>%
  kable_styling(font_size = 11) %>%
  row_spec(0, color = "grey10", background = "#F4F5F6") %>%
  scroll_box(height = "300px")

Normalised validation data.

z [m]	qc [MPa]	fs [MPa]	u2 [MPa]	ID	Location ID	Normalised ENTRHU [-]	Normalised hammer energy [-]	Diameter [m]	Bottom wall thickness [mm]	Pile penetration [m]	area ratio [-]	Push	Total unit weight [kN/m3]	Layer no	Vertical total stress [kPa]	Water pressure [kPa]	Vertical effective stress [kPa]	qt [MPa]	Delta u2 [MPa]	Rf [%]	Bq [-]	Qt [-]	Fr [%]	qnet [MPa]	Ic [-]
32.5	7.863	0.224	0.906	BX__32_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	617.5	333.125	284.375	8.089	0.573	2.773	0.077	26.275	3.003	7.472	2.662
33.0	3.015	0.050	1.318	BX__33_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	627.0	338.250	288.750	3.344	0.980	1.491	0.361	9.411	1.835	2.717	2.904
33.5	2.712	0.038	1.438	BX__33_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	636.5	343.375	293.125	3.072	1.095	1.228	0.450	8.307	1.549	2.435	2.914
34.0	3.168	0.069	0.041	BX__34_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	646.0	348.500	297.500	3.178	-0.308	2.184	-0.121	8.512	2.741	2.532	3.033
36.0	5.779	0.215	0.123	BX__36_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	684.0	369.000	315.000	5.810	-0.246	3.693	-0.048	16.272	4.186	5.126	2.914
36.5	8.903	0.267	-0.316	BX__36_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	693.5	374.125	319.375	8.824	-0.690	3.022	-0.085	25.457	3.280	8.130	2.697
40.0	10.292	0.257	-0.386	BX__40_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	760.0	410.000	350.000	10.195	-0.796	2.517	-0.084	26.958	2.720	9.435	2.626
40.5	3.886	0.079	-0.395	BX__40_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	769.5	415.125	354.375	3.787	-0.810	2.085	-0.269	8.516	2.617	3.018	3.022
41.0	3.027	0.046	-0.380	BX__41_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	779.0	420.250	358.750	2.932	-0.800	1.583	-0.372	6.001	2.156	2.153	3.108
41.5	4.140	0.140	-0.362	BX__41_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	788.5	425.375	363.125	4.049	-0.788	3.452	-0.242	8.980	4.287	3.261	3.125
42.0	4.848	0.141	-0.216	BX__42_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	798.0	430.500	367.500	4.794	-0.646	2.944	-0.162	10.872	3.532	3.996	3.008
42.5	5.117	0.194	0.067	BX__42_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	807.5	435.625	371.875	5.134	-0.369	3.781	-0.085	11.634	4.487	4.327	3.047
43.0	5.387	0.247	0.349	BX__43_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	817.0	440.750	376.250	5.474	-0.091	4.514	-0.020	12.379	5.306	4.657	3.071
43.5	7.043	0.235	0.580	BX__43_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	826.5	445.875	380.625	7.188	0.134	3.274	0.021	16.713	3.699	6.361	2.872
44.5	8.339	0.251	0.085	BX__44_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	845.5	456.125	389.375	8.360	-0.371	2.997	-0.049	19.299	3.334	7.515	2.795
45.0	8.044	0.239	0.279	BX__45_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	855.0	461.250	393.750	8.114	-0.182	2.947	-0.025	18.435	3.294	7.259	2.807
45.5	4.854	0.206	0.189	BX__45_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	864.5	466.375	398.125	4.901	-0.278	4.195	-0.069	10.139	5.093	4.037	3.128
46.0	3.901	0.183	0.697	BX__46_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	874.0	471.500	402.500	4.076	0.225	4.482	0.070	7.954	5.705	3.202	3.242
46.5	4.080	0.236	0.684	BX__46_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	883.5	476.625	406.875	4.251	0.208	5.548	0.062	8.277	7.004	3.368	3.283
47.0	4.199	0.195	0.450	BX__47_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	893.0	481.750	411.250	4.312	-0.031	4.515	-0.009	8.313	5.694	3.419	3.226
47.5	4.333	0.198	0.348	BX__47_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	902.5	486.875	415.625	4.420	-0.138	4.475	-0.039	8.463	5.623	3.518	3.216
48.0	4.478	0.263	1.248	BX__48_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	912.0	492.000	420.000	4.790	0.756	5.486	0.195	9.233	6.776	3.878	3.237
48.5	4.854	0.256	2.002	BX__48_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	921.5	497.125	424.375	5.355	1.505	4.778	0.340	10.446	5.771	4.433	3.152
49.0	5.238	0.210	2.240	BX__49_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	931.0	502.250	428.750	5.798	1.738	3.630	0.357	11.351	4.324	4.867	3.046
49.5	4.987	0.199	2.080	BX__49_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	940.5	507.375	433.125	5.507	1.572	3.615	0.344	10.543	4.359	4.566	3.073
50.0	4.736	0.188	1.919	BX__50_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	950.0	512.500	437.500	5.216	1.406	3.598	0.330	9.751	4.400	4.266	3.103
50.5	8.496	0.234	0.502	BX__50_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	959.5	517.625	441.875	8.621	-0.016	2.709	-0.002	17.339	3.048	7.662	2.807
51.0	3.739	0.102	2.134	BX__51_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	969.0	522.750	446.250	4.272	1.611	2.386	0.488	7.403	3.086	3.303	3.112
51.5	4.661	0.199	0.870	BX__51_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	978.5	527.875	450.625	4.878	0.342	4.087	0.088	8.654	5.113	3.900	3.184
52.0	11.025	0.235	-0.570	BX__52_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	988.0	533.000	455.000	10.882	-1.103	2.161	-0.112	21.746	2.377	9.894	2.664
52.5	14.213	0.437	-0.415	BX__52_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	997.5	538.125	459.375	14.109	-0.954	3.101	-0.073	28.542	3.337	13.112	2.664
54.0	11.391	0.420	0.123	BX__54_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	1026.0	553.500	472.500	11.422	-0.430	3.675	-0.041	22.002	4.038	10.396	2.804
57.5	5.914	0.269	-0.017	BX__57_5	BX	NA	NA	NA	NA	NA	0.75	1	19	1	1092.5	589.375	503.125	5.910	-0.606	4.559	-0.126	9.575	5.593	4.817	3.173
58.0	10.613	0.352	-0.069	BX__58_0	BX	NA	NA	NA	NA	NA	0.75	1	19	1	1102.0	594.500	507.500	10.596	-0.663	3.326	-0.070	18.707	3.712	9.494	2.834
32.5	7.863	0.224	0.906	BY__32_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	617.5	333.125	284.375	8.089	0.573	2.773	0.077	26.275	3.003	7.472	2.662
33.0	3.015	0.050	1.318	BY__33_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	627.0	338.250	288.750	3.344	0.980	1.491	0.361	9.411	1.835	2.717	2.904
33.5	2.712	0.038	1.438	BY__33_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	636.5	343.375	293.125	3.072	1.095	1.228	0.450	8.307	1.549	2.435	2.914
34.0	3.168	0.069	0.041	BY__34_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	646.0	348.500	297.500	3.178	-0.308	2.184	-0.121	8.512	2.741	2.532	3.033
36.0	5.779	0.215	0.123	BY__36_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	684.0	369.000	315.000	5.810	-0.246	3.693	-0.048	16.272	4.186	5.126	2.914
36.5	8.903	0.267	-0.316	BY__36_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	693.5	374.125	319.375	8.824	-0.690	3.022	-0.085	25.457	3.280	8.130	2.697
40.0	10.292	0.257	-0.386	BY__40_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	760.0	410.000	350.000	10.195	-0.796	2.517	-0.084	26.958	2.720	9.435	2.626
40.5	3.886	0.079	-0.395	BY__40_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	769.5	415.125	354.375	3.787	-0.810	2.085	-0.269	8.516	2.617	3.018	3.022
41.0	3.027	0.046	-0.380	BY__41_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	779.0	420.250	358.750	2.932	-0.800	1.583	-0.372	6.001	2.156	2.153	3.108
41.5	4.140	0.140	-0.362	BY__41_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	788.5	425.375	363.125	4.049	-0.788	3.452	-0.242	8.980	4.287	3.261	3.125
42.0	4.848	0.141	-0.216	BY__42_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	798.0	430.500	367.500	4.794	-0.646	2.944	-0.162	10.872	3.532	3.996	3.008
42.5	5.117	0.194	0.067	BY__42_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	807.5	435.625	371.875	5.134	-0.369	3.781	-0.085	11.634	4.487	4.327	3.047
43.0	5.387	0.247	0.349	BY__43_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	817.0	440.750	376.250	5.474	-0.091	4.514	-0.020	12.379	5.306	4.657	3.071
43.5	7.043	0.235	0.580	BY__43_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	826.5	445.875	380.625	7.188	0.134	3.274	0.021	16.713	3.699	6.361	2.872
44.5	8.339	0.251	0.085	BY__44_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	845.5	456.125	389.375	8.360	-0.371	2.997	-0.049	19.299	3.334	7.515	2.795
45.0	8.044	0.239	0.279	BY__45_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	855.0	461.250	393.750	8.114	-0.182	2.947	-0.025	18.435	3.294	7.259	2.807
45.5	4.854	0.206	0.189	BY__45_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	864.5	466.375	398.125	4.901	-0.278	4.195	-0.069	10.139	5.093	4.037	3.128
46.0	3.901	0.183	0.697	BY__46_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	874.0	471.500	402.500	4.076	0.225	4.482	0.070	7.954	5.705	3.202	3.242
46.5	4.080	0.236	0.684	BY__46_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	883.5	476.625	406.875	4.251	0.208	5.548	0.062	8.277	7.004	3.368	3.283
47.0	4.199	0.195	0.450	BY__47_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	893.0	481.750	411.250	4.312	-0.031	4.515	-0.009	8.313	5.694	3.419	3.226
47.5	4.333	0.198	0.348	BY__47_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	902.5	486.875	415.625	4.420	-0.138	4.475	-0.039	8.463	5.623	3.518	3.216
48.0	4.478	0.263	1.248	BY__48_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	912.0	492.000	420.000	4.790	0.756	5.486	0.195	9.233	6.776	3.878	3.237
48.5	4.854	0.256	2.002	BY__48_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	921.5	497.125	424.375	5.355	1.505	4.778	0.340	10.446	5.771	4.433	3.152
49.0	5.238	0.210	2.240	BY__49_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	931.0	502.250	428.750	5.798	1.738	3.630	0.357	11.351	4.324	4.867	3.046
49.5	4.987	0.199	2.080	BY__49_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	940.5	507.375	433.125	5.507	1.572	3.615	0.344	10.543	4.359	4.566	3.073
50.0	4.736	0.188	1.919	BY__50_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	950.0	512.500	437.500	5.216	1.406	3.598	0.330	9.751	4.400	4.266	3.103
50.5	8.496	0.234	0.502	BY__50_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	959.5	517.625	441.875	8.621	-0.016	2.709	-0.002	17.339	3.048	7.662	2.807
51.0	3.739	0.102	2.134	BY__51_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	969.0	522.750	446.250	4.272	1.611	2.386	0.488	7.403	3.086	3.303	3.112
51.5	4.661	0.199	0.870	BY__51_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	978.5	527.875	450.625	4.878	0.342	4.087	0.088	8.654	5.113	3.900	3.184
52.0	11.025	0.235	-0.570	BY__52_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	988.0	533.000	455.000	10.882	-1.103	2.161	-0.112	21.746	2.377	9.894	2.664
52.5	14.213	0.437	-0.415	BY__52_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	997.5	538.125	459.375	14.109	-0.954	3.101	-0.073	28.542	3.337	13.112	2.664
54.0	11.391	0.420	0.123	BY__54_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	1026.0	553.500	472.500	11.422	-0.430	3.675	-0.041	22.002	4.038	10.396	2.804
57.5	5.914	0.269	-0.017	BY__57_5	BY	NA	NA	NA	NA	NA	0.75	1	19	1	1092.5	589.375	503.125	5.910	-0.606	4.559	-0.126	9.575	5.593	4.817	3.173
58.0	10.613	0.352	-0.069	BY__58_0	BY	NA	NA	NA	NA	NA	0.75	1	19	1	1102.0	594.500	507.500	10.596	-0.663	3.326	-0.070	18.707	3.712	9.494	2.834
32.5	7.863	0.224	0.906	BZ__32_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	617.5	333.125	284.375	8.089	0.573	2.773	0.077	26.275	3.003	7.472	2.662
33.0	3.015	0.050	1.318	BZ__33_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	627.0	338.250	288.750	3.344	0.980	1.491	0.361	9.411	1.835	2.717	2.904
33.5	2.712	0.038	1.438	BZ__33_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	636.5	343.375	293.125	3.072	1.095	1.228	0.450	8.307	1.549	2.435	2.914
34.0	3.168	0.069	0.041	BZ__34_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	646.0	348.500	297.500	3.178	-0.308	2.184	-0.121	8.512	2.741	2.532	3.033
36.0	5.779	0.215	0.123	BZ__36_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	684.0	369.000	315.000	5.810	-0.246	3.693	-0.048	16.272	4.186	5.126	2.914
36.5	8.903	0.267	-0.316	BZ__36_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	693.5	374.125	319.375	8.824	-0.690	3.022	-0.085	25.457	3.280	8.130	2.697
40.0	10.292	0.257	-0.386	BZ__40_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	760.0	410.000	350.000	10.195	-0.796	2.517	-0.084	26.958	2.720	9.435	2.626
40.5	3.886	0.079	-0.395	BZ__40_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	769.5	415.125	354.375	3.787	-0.810	2.085	-0.269	8.516	2.617	3.018	3.022
41.0	3.027	0.046	-0.380	BZ__41_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	779.0	420.250	358.750	2.932	-0.800	1.583	-0.372	6.001	2.156	2.153	3.108
41.5	4.140	0.140	-0.362	BZ__41_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	788.5	425.375	363.125	4.049	-0.788	3.452	-0.242	8.980	4.287	3.261	3.125
42.0	4.848	0.141	-0.216	BZ__42_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	798.0	430.500	367.500	4.794	-0.646	2.944	-0.162	10.872	3.532	3.996	3.008
42.5	5.117	0.194	0.067	BZ__42_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	807.5	435.625	371.875	5.134	-0.369	3.781	-0.085	11.634	4.487	4.327	3.047
43.0	5.387	0.247	0.349	BZ__43_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	817.0	440.750	376.250	5.474	-0.091	4.514	-0.020	12.379	5.306	4.657	3.071
43.5	7.043	0.235	0.580	BZ__43_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	826.5	445.875	380.625	7.188	0.134	3.274	0.021	16.713	3.699	6.361	2.872
44.5	8.339	0.251	0.085	BZ__44_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	845.5	456.125	389.375	8.360	-0.371	2.997	-0.049	19.299	3.334	7.515	2.795
45.0	8.044	0.239	0.279	BZ__45_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	855.0	461.250	393.750	8.114	-0.182	2.947	-0.025	18.435	3.294	7.259	2.807
45.5	4.854	0.206	0.189	BZ__45_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	864.5	466.375	398.125	4.901	-0.278	4.195	-0.069	10.139	5.093	4.037	3.128
46.0	3.901	0.183	0.697	BZ__46_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	874.0	471.500	402.500	4.076	0.225	4.482	0.070	7.954	5.705	3.202	3.242
46.5	4.080	0.236	0.684	BZ__46_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	883.5	476.625	406.875	4.251	0.208	5.548	0.062	8.277	7.004	3.368	3.283
47.0	4.199	0.195	0.450	BZ__47_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	893.0	481.750	411.250	4.312	-0.031	4.515	-0.009	8.313	5.694	3.419	3.226
47.5	4.333	0.198	0.348	BZ__47_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	902.5	486.875	415.625	4.420	-0.138	4.475	-0.039	8.463	5.623	3.518	3.216
48.0	4.478	0.263	1.248	BZ__48_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	912.0	492.000	420.000	4.790	0.756	5.486	0.195	9.233	6.776	3.878	3.237
48.5	4.854	0.256	2.002	BZ__48_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	921.5	497.125	424.375	5.355	1.505	4.778	0.340	10.446	5.771	4.433	3.152
49.0	5.238	0.210	2.240	BZ__49_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	931.0	502.250	428.750	5.798	1.738	3.630	0.357	11.351	4.324	4.867	3.046
49.5	4.987	0.199	2.080	BZ__49_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	940.5	507.375	433.125	5.507	1.572	3.615	0.344	10.543	4.359	4.566	3.073
50.0	4.736	0.188	1.919	BZ__50_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	950.0	512.500	437.500	5.216	1.406	3.598	0.330	9.751	4.400	4.266	3.103
50.5	8.496	0.234	0.502	BZ__50_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	959.5	517.625	441.875	8.621	-0.016	2.709	-0.002	17.339	3.048	7.662	2.807
51.0	3.739	0.102	2.134	BZ__51_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	969.0	522.750	446.250	4.272	1.611	2.386	0.488	7.403	3.086	3.303	3.112
51.5	4.661	0.199	0.870	BZ__51_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	978.5	527.875	450.625	4.878	0.342	4.087	0.088	8.654	5.113	3.900	3.184
52.0	11.025	0.235	-0.570	BZ__52_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	988.0	533.000	455.000	10.882	-1.103	2.161	-0.112	21.746	2.377	9.894	2.664
52.5	14.213	0.437	-0.415	BZ__52_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	997.5	538.125	459.375	14.109	-0.954	3.101	-0.073	28.542	3.337	13.112	2.664
54.0	11.391	0.420	0.123	BZ__54_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	1026.0	553.500	472.500	11.422	-0.430	3.675	-0.041	22.002	4.038	10.396	2.804
57.5	5.914	0.269	-0.017	BZ__57_5	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	1092.5	589.375	503.125	5.910	-0.606	4.559	-0.126	9.575	5.593	4.817	3.173
58.0	10.613	0.352	-0.069	BZ__58_0	BZ	NA	NA	NA	NA	NA	0.75	1	19	1	1102.0	594.500	507.500	10.596	-0.663	3.326	-0.070	18.707	3.712	9.494	2.834

2.3 Interdistance data

An additional file, which classifies the interdistance between each location pair, is provided. This file can be used to explore spatial correlation between locations.

interdistance <- read_csv("F:/isfog2020/interdistance_data.csv")

kable(top_n(interdistance, 100),
      digits = 3,
      caption = "Interdistance data.",
      align = "r") %>%
  kable_styling(full_width = T, font_size = 11, position = "center") %>%
  row_spec(0, color = "grey10", background = "#F4F5F6") %>%
  scroll_box(height = "300px")

Interdistance data.

ID location 1	ID location 2	Interdistance class
AA	AD	500m - 1500m
AA	AE	500m - 1500m
AA	AL	500m - 1500m
AA	AM	500m - 1500m
AA	AN	500m - 1500m
AA	AO	500m - 1500m
AA	AP	500m - 1500m
AA	AQ	500m - 1500m
AB	AD	500m - 1500m
AB	AE	500m - 1500m
AB	AL	500m - 1500m
AB	AM	500m - 1500m
AB	AN	500m - 1500m
AB	AO	500m - 1500m
AB	AP	500m - 1500m
AB	AQ	500m - 1500m
AC	AD	500m - 1500m
AC	AE	500m - 1500m
AC	AL	500m - 1500m
AC	AM	500m - 1500m
AC	AN	500m - 1500m
AC	AO	500m - 1500m
AC	AP	500m - 1500m
AC	AQ	500m - 1500m
AD	AA	500m - 1500m
AD	AB	500m - 1500m
AD	AC	500m - 1500m
AD	AF	500m - 1500m
AD	AG	500m - 1500m
AD	AH	500m - 1500m
AD	AL	500m - 1500m
AD	AM	500m - 1500m
AD	AN	500m - 1500m
AD	AO	500m - 1500m
AD	AP	500m - 1500m
AD	AQ	500m - 1500m
AD	AR	500m - 1500m
AD	AS	500m - 1500m
AD	AT	500m - 1500m
AE	AA	500m - 1500m
AE	AB	500m - 1500m
AE	AC	500m - 1500m
AE	AF	500m - 1500m
AE	AG	500m - 1500m
AE	AH	500m - 1500m
AE	AL	500m - 1500m
AE	AM	500m - 1500m
AE	AN	500m - 1500m
AE	AO	500m - 1500m
AE	AP	500m - 1500m
AE	AQ	500m - 1500m
AE	AR	500m - 1500m
AE	AS	500m - 1500m
AE	AT	500m - 1500m
AF	AD	500m - 1500m
AF	AE	500m - 1500m
AF	AI	500m - 1500m
AF	AJ	500m - 1500m
AF	AK	500m - 1500m
AF	AO	500m - 1500m
AF	AP	500m - 1500m
AF	AQ	500m - 1500m
AF	AR	500m - 1500m
AF	AS	500m - 1500m
AF	AT	500m - 1500m
AF	AU	500m - 1500m
AF	AV	500m - 1500m
AF	AW	500m - 1500m
AG	AD	500m - 1500m
AG	AE	500m - 1500m
AG	AI	500m - 1500m
AG	AJ	500m - 1500m
AG	AK	500m - 1500m
AG	AO	500m - 1500m
AG	AP	500m - 1500m
AG	AQ	500m - 1500m
AG	AR	500m - 1500m
AG	AS	500m - 1500m
AG	AT	500m - 1500m
AG	AU	500m - 1500m
AG	AV	500m - 1500m
AG	AW	500m - 1500m
AH	AD	500m - 1500m
AH	AE	500m - 1500m
AH	AI	500m - 1500m
AH	AJ	500m - 1500m
AH	AK	500m - 1500m
AH	AO	500m - 1500m
AH	AP	500m - 1500m
AH	AQ	500m - 1500m
AH	AR	500m - 1500m
AH	AS	500m - 1500m
AH	AT	500m - 1500m
AH	AU	500m - 1500m
AH	AV	500m - 1500m
AH	AW	500m - 1500m
AI	AF	500m - 1500m
AI	AG	500m - 1500m
AI	AH	500m - 1500m
AI	AR	500m - 1500m
AI	AS	500m - 1500m
AI	AT	500m - 1500m
AI	AU	500m - 1500m
AI	AV	500m - 1500m
AI	AW	500m - 1500m
AJ	AF	500m - 1500m
AJ	AG	500m - 1500m
AJ	AH	500m - 1500m
AJ	AR	500m - 1500m
AJ	AS	500m - 1500m
AJ	AT	500m - 1500m
AJ	AU	500m - 1500m
AJ	AV	500m - 1500m
AJ	AW	500m - 1500m
AK	AF	500m - 1500m
AK	AG	500m - 1500m
AK	AH	500m - 1500m
AK	AR	500m - 1500m
AK	AS	500m - 1500m
AK	AT	500m - 1500m
AK	AU	500m - 1500m
AK	AV	500m - 1500m
AK	AW	500m - 1500m
AL	AA	500m - 1500m
AL	AB	500m - 1500m
AL	AC	500m - 1500m
AL	AD	500m - 1500m
AL	AE	500m - 1500m
AL	AO	500m - 1500m
AL	AP	500m - 1500m
AL	AQ	500m - 1500m
AL	AX	500m - 1500m
AL	AY	500m - 1500m
AL	AZ	500m - 1500m
AL	BA	500m - 1500m
AL	BB	500m - 1500m
AL	BC	500m - 1500m
AM	AA	500m - 1500m
AM	AB	500m - 1500m
AM	AC	500m - 1500m
AM	AD	500m - 1500m
AM	AE	500m - 1500m
AM	AO	500m - 1500m
AM	AP	500m - 1500m
AM	AQ	500m - 1500m
AM	AX	500m - 1500m
AM	AY	500m - 1500m
AM	AZ	500m - 1500m
AM	BA	500m - 1500m
AM	BB	500m - 1500m
AM	BC	500m - 1500m
AN	AA	500m - 1500m
AN	AB	500m - 1500m
AN	AC	500m - 1500m
AN	AD	500m - 1500m
AN	AE	500m - 1500m
AN	AO	500m - 1500m
AN	AP	500m - 1500m
AN	AQ	500m - 1500m
AN	AX	500m - 1500m
AN	AY	500m - 1500m
AN	AZ	500m - 1500m
AN	BA	500m - 1500m
AN	BB	500m - 1500m
AN	BC	500m - 1500m
AO	AA	500m - 1500m
AO	AB	500m - 1500m
AO	AC	500m - 1500m
AO	AD	500m - 1500m
AO	AE	500m - 1500m
AO	AF	500m - 1500m
AO	AG	500m - 1500m
AO	AH	500m - 1500m
AO	AL	500m - 1500m
AO	AM	500m - 1500m
AO	AN	500m - 1500m
AO	AR	500m - 1500m
AO	AS	500m - 1500m
AO	AT	500m - 1500m
AO	AX	500m - 1500m
AO	AY	500m - 1500m
AO	AZ	500m - 1500m
AO	BA	500m - 1500m
AO	BB	500m - 1500m
AO	BC	500m - 1500m
AO	BD	500m - 1500m
AO	BE	500m - 1500m
AO	BF	500m - 1500m
AP	AA	500m - 1500m
AP	AB	500m - 1500m
AP	AC	500m - 1500m
AP	AD	500m - 1500m
AP	AE	500m - 1500m
AP	AF	500m - 1500m
AP	AG	500m - 1500m
AP	AH	500m - 1500m
AP	AL	500m - 1500m
AP	AM	500m - 1500m
AP	AN	500m - 1500m
AP	AR	500m - 1500m
AP	AS	500m - 1500m
AP	AT	500m - 1500m
AP	AX	500m - 1500m
AP	AY	500m - 1500m
AP	AZ	500m - 1500m
AP	BA	500m - 1500m
AP	BB	500m - 1500m
AP	BC	500m - 1500m
AP	BD	500m - 1500m
AP	BE	500m - 1500m
AP	BF	500m - 1500m
AQ	AA	500m - 1500m
AQ	AB	500m - 1500m
AQ	AC	500m - 1500m
AQ	AD	500m - 1500m
AQ	AE	500m - 1500m
AQ	AF	500m - 1500m
AQ	AG	500m - 1500m
AQ	AH	500m - 1500m
AQ	AL	500m - 1500m
AQ	AM	500m - 1500m
AQ	AN	500m - 1500m
AQ	AR	500m - 1500m
AQ	AS	500m - 1500m
AQ	AT	500m - 1500m
AQ	AX	500m - 1500m
AQ	AY	500m - 1500m
AQ	AZ	500m - 1500m
AQ	BA	500m - 1500m
AQ	BB	500m - 1500m
AQ	BC	500m - 1500m
AQ	BD	500m - 1500m
AQ	BE	500m - 1500m
AQ	BF	500m - 1500m
AR	AD	500m - 1500m
AR	AE	500m - 1500m
AR	AF	500m - 1500m
AR	AG	500m - 1500m
AR	AH	500m - 1500m
AR	AI	500m - 1500m
AR	AJ	500m - 1500m
AR	AK	500m - 1500m
AR	AO	500m - 1500m
AR	AP	500m - 1500m
AR	AQ	500m - 1500m
AR	AU	500m - 1500m
AR	AV	500m - 1500m
AR	AW	500m - 1500m
AR	BA	500m - 1500m
AR	BB	500m - 1500m
AR	BC	500m - 1500m
AR	BD	500m - 1500m
AR	BE	500m - 1500m
AR	BF	500m - 1500m
AR	BG	500m - 1500m
AR	BH	500m - 1500m
AR	BI	500m - 1500m
AS	AD	500m - 1500m
AS	AE	500m - 1500m
AS	AF	500m - 1500m
AS	AG	500m - 1500m
AS	AH	500m - 1500m
AS	AI	500m - 1500m
AS	AJ	500m - 1500m
AS	AK	500m - 1500m
AS	AO	500m - 1500m
AS	AP	500m - 1500m
AS	AQ	500m - 1500m
AS	AU	500m - 1500m
AS	AV	500m - 1500m
AS	AW	500m - 1500m
AS	BA	500m - 1500m
AS	BB	500m - 1500m
AS	BC	500m - 1500m
AS	BD	500m - 1500m
AS	BE	500m - 1500m
AS	BF	500m - 1500m
AS	BG	500m - 1500m
AS	BH	500m - 1500m
AS	BI	500m - 1500m
AT	AD	500m - 1500m
AT	AE	500m - 1500m
AT	AF	500m - 1500m
AT	AG	500m - 1500m
AT	AH	500m - 1500m
AT	AI	500m - 1500m
AT	AJ	500m - 1500m
AT	AK	500m - 1500m
AT	AO	500m - 1500m
AT	AP	500m - 1500m
AT	AQ	500m - 1500m
AT	AU	500m - 1500m
AT	AV	500m - 1500m
AT	AW	500m - 1500m
AT	BA	500m - 1500m
AT	BB	500m - 1500m
AT	BC	500m - 1500m
AT	BD	500m - 1500m
AT	BE	500m - 1500m
AT	BF	500m - 1500m
AT	BG	500m - 1500m
AT	BH	500m - 1500m
AT	BI	500m - 1500m
AU	AF	500m - 1500m
AU	AG	500m - 1500m
AU	AH	500m - 1500m
AU	AI	500m - 1500m
AU	AJ	500m - 1500m
AU	AK	500m - 1500m
AU	AR	500m - 1500m
AU	AS	500m - 1500m
AU	AT	500m - 1500m
AU	BD	500m - 1500m
AU	BE	500m - 1500m
AU	BF	500m - 1500m
AU	BG	500m - 1500m
AU	BH	500m - 1500m
AU	BI	500m - 1500m
AV	AF	500m - 1500m
AV	AG	500m - 1500m
AV	AH	500m - 1500m
AV	AI	500m - 1500m
AV	AJ	500m - 1500m
AV	AK	500m - 1500m
AV	AR	500m - 1500m
AV	AS	500m - 1500m
AV	AT	500m - 1500m
AV	BD	500m - 1500m
AV	BE	500m - 1500m
AV	BF	500m - 1500m
AV	BG	500m - 1500m
AV	BH	500m - 1500m
AV	BI	500m - 1500m
AW	AF	500m - 1500m
AW	AG	500m - 1500m
AW	AH	500m - 1500m
AW	AI	500m - 1500m
AW	AJ	500m - 1500m
AW	AK	500m - 1500m
AW	AR	500m - 1500m
AW	AS	500m - 1500m
AW	AT	500m - 1500m
AW	BD	500m - 1500m
AW	BE	500m - 1500m
AW	BF	500m - 1500m
AW	BG	500m - 1500m
AW	BH	500m - 1500m
AW	BI	500m - 1500m
AX	AL	500m - 1500m
AX	AM	500m - 1500m
AX	AN	500m - 1500m
AX	AO	500m - 1500m
AX	AP	500m - 1500m
AX	AQ	500m - 1500m
AX	BA	500m - 1500m
AX	BB	500m - 1500m
AX	BC	500m - 1500m
AX	BR	500m - 1500m
AX	BS	500m - 1500m
AX	BT	500m - 1500m
AX	BU	500m - 1500m
AX	BV	500m - 1500m
AX	BW	500m - 1500m
AY	AL	500m - 1500m
AY	AM	500m - 1500m
AY	AN	500m - 1500m
AY	AO	500m - 1500m
AY	AP	500m - 1500m
AY	AQ	500m - 1500m
AY	BA	500m - 1500m
AY	BB	500m - 1500m
AY	BC	500m - 1500m
AY	BR	500m - 1500m
AY	BS	500m - 1500m
AY	BT	500m - 1500m
AY	BU	500m - 1500m
AY	BV	500m - 1500m
AY	BW	500m - 1500m
AZ	AL	500m - 1500m
AZ	AM	500m - 1500m
AZ	AN	500m - 1500m
AZ	AO	500m - 1500m
AZ	AP	500m - 1500m
AZ	AQ	500m - 1500m
AZ	BA	500m - 1500m
AZ	BB	500m - 1500m
AZ	BC	500m - 1500m
AZ	BR	500m - 1500m
AZ	BS	500m - 1500m
AZ	BT	500m - 1500m
AZ	BU	500m - 1500m
AZ	BV	500m - 1500m
AZ	BW	500m - 1500m
BA	AL	500m - 1500m
BA	AM	500m - 1500m
BA	AN	500m - 1500m
BA	AO	500m - 1500m
BA	AP	500m - 1500m
BA	AQ	500m - 1500m
BA	AR	500m - 1500m
BA	AS	500m - 1500m
BA	AT	500m - 1500m
BA	AX	500m - 1500m
BA	AY	500m - 1500m
BA	AZ	500m - 1500m
BA	BD	500m - 1500m
BA	BE	500m - 1500m
BA	BF	500m - 1500m
BA	BR	500m - 1500m
BA	BS	500m - 1500m
BA	BT	500m - 1500m
BA	BU	500m - 1500m
BA	BV	500m - 1500m
BA	BW	500m - 1500m
BA	BX	500m - 1500m
BA	BY	500m - 1500m
BA	BZ	500m - 1500m
BB	AL	500m - 1500m
BB	AM	500m - 1500m
BB	AN	500m - 1500m
BB	AO	500m - 1500m
BB	AP	500m - 1500m
BB	AQ	500m - 1500m
BB	AR	500m - 1500m
BB	AS	500m - 1500m
BB	AT	500m - 1500m
BB	AX	500m - 1500m
BB	AY	500m - 1500m
BB	AZ	500m - 1500m
BB	BD	500m - 1500m
BB	BE	500m - 1500m
BB	BF	500m - 1500m
BB	BR	500m - 1500m
BB	BS	500m - 1500m
BB	BT	500m - 1500m
BB	BU	500m - 1500m
BB	BV	500m - 1500m
BB	BW	500m - 1500m
BB	BX	500m - 1500m
BB	BY	500m - 1500m
BB	BZ	500m - 1500m
BC	AL	500m - 1500m
BC	AM	500m - 1500m
BC	AN	500m - 1500m
BC	AO	500m - 1500m
BC	AP	500m - 1500m
BC	AQ	500m - 1500m
BC	AR	500m - 1500m
BC	AS	500m - 1500m
BC	AT	500m - 1500m
BC	AX	500m - 1500m
BC	AY	500m - 1500m
BC	AZ	500m - 1500m
BC	BD	500m - 1500m
BC	BE	500m - 1500m
BC	BF	500m - 1500m
BC	BR	500m - 1500m
BC	BS	500m - 1500m
BC	BT	500m - 1500m
BC	BU	500m - 1500m
BC	BV	500m - 1500m
BC	BW	500m - 1500m
BC	BX	500m - 1500m
BC	BY	500m - 1500m
BC	BZ	500m - 1500m
BD	AO	500m - 1500m
BD	AP	500m - 1500m
BD	AQ	500m - 1500m
BD	AR	500m - 1500m
BD	AS	500m - 1500m
BD	AT	500m - 1500m
BD	AU	500m - 1500m
BD	AV	500m - 1500m
BD	AW	500m - 1500m
BD	BA	500m - 1500m
BD	BB	500m - 1500m
BD	BC	500m - 1500m
BD	BG	500m - 1500m
BD	BH	500m - 1500m
BD	BI	500m - 1500m
BD	BU	500m - 1500m
BD	BV	500m - 1500m
BD	BW	500m - 1500m
BD	BX	500m - 1500m
BD	BY	500m - 1500m
BD	BZ	500m - 1500m
BD	CA	500m - 1500m
BD	CB	500m - 1500m
BD	CC	500m - 1500m
BE	AO	500m - 1500m
BE	AP	500m - 1500m
BE	AQ	500m - 1500m
BE	AR	500m - 1500m
BE	AS	500m - 1500m
BE	AT	500m - 1500m
BE	AU	500m - 1500m
BE	AV	500m - 1500m
BE	AW	500m - 1500m
BE	BA	500m - 1500m
BE	BB	500m - 1500m
BE	BC	500m - 1500m
BE	BG	500m - 1500m
BE	BH	500m - 1500m
BE	BI	500m - 1500m
BE	BU	500m - 1500m
BE	BV	500m - 1500m
BE	BW	500m - 1500m
BE	BX	500m - 1500m
BE	BY	500m - 1500m
BE	BZ	500m - 1500m
BE	CA	500m - 1500m
BE	CB	500m - 1500m
BE	CC	500m - 1500m
BF	AO	500m - 1500m
BF	AP	500m - 1500m
BF	AQ	500m - 1500m
BF	AR	500m - 1500m
BF	AS	500m - 1500m
BF	AT	500m - 1500m
BF	AU	500m - 1500m
BF	AV	500m - 1500m
BF	AW	500m - 1500m
BF	BA	500m - 1500m
BF	BB	500m - 1500m
BF	BC	500m - 1500m
BF	BG	500m - 1500m
BF	BH	500m - 1500m
BF	BI	500m - 1500m
BF	BU	500m - 1500m
BF	BV	500m - 1500m
BF	BW	500m - 1500m
BF	BX	500m - 1500m
BF	BY	500m - 1500m
BF	BZ	500m - 1500m
BF	CA	500m - 1500m
BF	CB	500m - 1500m
BF	CC	500m - 1500m
BG	AR	500m - 1500m
BG	AS	500m - 1500m
BG	AT	500m - 1500m
BG	AU	500m - 1500m
BG	AV	500m - 1500m
BG	AW	500m - 1500m
BG	BD	500m - 1500m
BG	BE	500m - 1500m
BG	BF	500m - 1500m
BG	BX	500m - 1500m
BG	BY	500m - 1500m
BG	BZ	500m - 1500m
BG	CA	500m - 1500m
BG	CB	500m - 1500m
BG	CC	500m - 1500m
BH	AR	500m - 1500m
BH	AS	500m - 1500m
BH	AT	500m - 1500m
BH	AU	500m - 1500m
BH	AV	500m - 1500m
BH	AW	500m - 1500m
BH	BD	500m - 1500m
BH	BE	500m - 1500m
BH	BF	500m - 1500m
BH	BX	500m - 1500m
BH	BY	500m - 1500m
BH	BZ	500m - 1500m
BH	CA	500m - 1500m
BH	CB	500m - 1500m
BH	CC	500m - 1500m
BI	AR	500m - 1500m
BI	AS	500m - 1500m
BI	AT	500m - 1500m
BI	AU	500m - 1500m
BI	AV	500m - 1500m
BI	AW	500m - 1500m
BI	BD	500m - 1500m
BI	BE	500m - 1500m
BI	BF	500m - 1500m
BI	BX	500m - 1500m
BI	BY	500m - 1500m
BI	BZ	500m - 1500m
BI	CA	500m - 1500m
BI	CB	500m - 1500m
BI	CC	500m - 1500m
BJ	BL	500m - 1500m
BJ	BM	500m - 1500m
BJ	BN	500m - 1500m
BJ	CG	500m - 1500m
BJ	CH	500m - 1500m
BJ	CI	500m - 1500m
BJ	CJ	500m - 1500m
BJ	CK	500m - 1500m
BJ	CL	500m - 1500m
BJ	CM	500m - 1500m
BJ	CN	500m - 1500m
BJ	CO	500m - 1500m
BK	BL	500m - 1500m
BK	BM	500m - 1500m
BK	BN	500m - 1500m
BK	CG	500m - 1500m
BK	CH	500m - 1500m
BK	CI	500m - 1500m
BK	CJ	500m - 1500m
BK	CK	500m - 1500m
BK	CL	500m - 1500m
BK	CM	500m - 1500m
BK	CN	500m - 1500m
BK	CO	500m - 1500m
BL	BJ	500m - 1500m
BL	BK	500m - 1500m
BL	BO	500m - 1500m
BL	BP	500m - 1500m
BL	BQ	500m - 1500m
BL	CJ	500m - 1500m
BL	CK	500m - 1500m
BL	CL	500m - 1500m
BL	CM	500m - 1500m
BL	CN	500m - 1500m
BL	CO	500m - 1500m
BL	CP	500m - 1500m
BL	CQ	500m - 1500m
BL	CR	500m - 1500m
BM	BJ	500m - 1500m
BM	BK	500m - 1500m
BM	BO	500m - 1500m
BM	BP	500m - 1500m
BM	BQ	500m - 1500m
BM	CJ	500m - 1500m
BM	CK	500m - 1500m
BM	CL	500m - 1500m
BM	CM	500m - 1500m
BM	CN	500m - 1500m
BM	CO	500m - 1500m
BM	CP	500m - 1500m
BM	CQ	500m - 1500m
BM	CR	500m - 1500m
BN	BJ	500m - 1500m
BN	BK	500m - 1500m
BN	BO	500m - 1500m
BN	BP	500m - 1500m
BN	BQ	500m - 1500m
BN	CJ	500m - 1500m
BN	CK	500m - 1500m
BN	CL	500m - 1500m
BN	CM	500m - 1500m
BN	CN	500m - 1500m
BN	CO	500m - 1500m
BN	CP	500m - 1500m
BN	CQ	500m - 1500m
BN	CR	500m - 1500m
BO	BL	500m - 1500m
BO	BM	500m - 1500m
BO	BN	500m - 1500m
BO	CM	500m - 1500m
BO	CN	500m - 1500m
BO	CO	500m - 1500m
BO	CP	500m - 1500m
BO	CQ	500m - 1500m
BO	CR	500m - 1500m
BP	BL	500m - 1500m
BP	BM	500m - 1500m
BP	BN	500m - 1500m
BP	CM	500m - 1500m
BP	CN	500m - 1500m
BP	CO	500m - 1500m
BP	CP	500m - 1500m
BP	CQ	500m - 1500m
BP	CR	500m - 1500m
BQ	BL	500m - 1500m
BQ	BM	500m - 1500m
BQ	BN	500m - 1500m
BQ	CM	500m - 1500m
BQ	CN	500m - 1500m
BQ	CO	500m - 1500m
BQ	CP	500m - 1500m
BQ	CQ	500m - 1500m
BQ	CR	500m - 1500m
BR	AX	500m - 1500m
BR	AY	500m - 1500m
BR	AZ	500m - 1500m
BR	BA	500m - 1500m
BR	BB	500m - 1500m
BR	BC	500m - 1500m
BR	BU	500m - 1500m
BR	BV	500m - 1500m
BR	BW	500m - 1500m
BR	CS	500m - 1500m
BR	CT	500m - 1500m
BR	CU	500m - 1500m
BS	AX	500m - 1500m
BS	AY	500m - 1500m
BS	AZ	500m - 1500m
BS	BA	500m - 1500m
BS	BB	500m - 1500m
BS	BC	500m - 1500m
BS	BU	500m - 1500m
BS	BV	500m - 1500m
BS	BW	500m - 1500m
BS	CS	500m - 1500m
BS	CT	500m - 1500m
BS	CU	500m - 1500m
BT	AX	500m - 1500m
BT	AY	500m - 1500m
BT	AZ	500m - 1500m
BT	BA	500m - 1500m
BT	BB	500m - 1500m
BT	BC	500m - 1500m
BT	BU	500m - 1500m
BT	BV	500m - 1500m
BT	BW	500m - 1500m
BT	CS	500m - 1500m
BT	CT	500m - 1500m
BT	CU	500m - 1500m
BU	AX	500m - 1500m
BU	AY	500m - 1500m
BU	AZ	500m - 1500m
BU	BA	500m - 1500m
BU	BB	500m - 1500m
BU	BC	500m - 1500m
BU	BD	500m - 1500m
BU	BE	500m - 1500m
BU	BF	500m - 1500m
BU	BR	500m - 1500m
BU	BS	500m - 1500m
BU	BT	500m - 1500m
BU	BX	500m - 1500m
BU	BY	500m - 1500m
BU	BZ	500m - 1500m
BU	CS	500m - 1500m
BU	CT	500m - 1500m
BU	CU	500m - 1500m
BU	CV	500m - 1500m
BU	CW	500m - 1500m
BU	CX	500m - 1500m
BV	AX	500m - 1500m
BV	AY	500m - 1500m
BV	AZ	500m - 1500m
BV	BA	500m - 1500m
BV	BB	500m - 1500m
BV	BC	500m - 1500m
BV	BD	500m - 1500m
BV	BE	500m - 1500m
BV	BF	500m - 1500m
BV	BR	500m - 1500m
BV	BS	500m - 1500m
BV	BT	500m - 1500m
BV	BX	500m - 1500m
BV	BY	500m - 1500m
BV	BZ	500m - 1500m
BV	CS	500m - 1500m
BV	CT	500m - 1500m
BV	CU	500m - 1500m
BV	CV	500m - 1500m
BV	CW	500m - 1500m
BV	CX	500m - 1500m
BW	AX	500m - 1500m
BW	AY	500m - 1500m
BW	AZ	500m - 1500m
BW	BA	500m - 1500m
BW	BB	500m - 1500m
BW	BC	500m - 1500m
BW	BD	500m - 1500m
BW	BE	500m - 1500m
BW	BF	500m - 1500m
BW	BR	500m - 1500m
BW	BS	500m - 1500m
BW	BT	500m - 1500m
BW	BX	500m - 1500m
BW	BY	500m - 1500m
BW	BZ	500m - 1500m
BW	CS	500m - 1500m
BW	CT	500m - 1500m
BW	CU	500m - 1500m
BW	CV	500m - 1500m
BW	CW	500m - 1500m
BW	CX	500m - 1500m
BX	BA	500m - 1500m
BX	BB	500m - 1500m
BX	BC	500m - 1500m
BX	BD	500m - 1500m
BX	BE	500m - 1500m
BX	BF	500m - 1500m
BX	BG	500m - 1500m
BX	BH	500m - 1500m
BX	BI	500m - 1500m
BX	BU	500m - 1500m
BX	BV	500m - 1500m
BX	BW	500m - 1500m
BX	CA	500m - 1500m
BX	CB	500m - 1500m
BX	CC	500m - 1500m
BX	CS	500m - 1500m
BX	CT	500m - 1500m
BX	CU	500m - 1500m
BX	CV	500m - 1500m
BX	CW	500m - 1500m
BX	CX	500m - 1500m
BX	CY	500m - 1500m
BX	CZ	500m - 1500m
BX	DA	500m - 1500m
BY	BA	500m - 1500m
BY	BB	500m - 1500m
BY	BC	500m - 1500m
BY	BD	500m - 1500m
BY	BE	500m - 1500m
BY	BF	500m - 1500m
BY	BG	500m - 1500m
BY	BH	500m - 1500m
BY	BI	500m - 1500m
BY	BU	500m - 1500m
BY	BV	500m - 1500m
BY	BW	500m - 1500m
BY	CA	500m - 1500m
BY	CB	500m - 1500m
BY	CC	500m - 1500m
BY	CS	500m - 1500m
BY	CT	500m - 1500m
BY	CU	500m - 1500m
BY	CV	500m - 1500m
BY	CW	500m - 1500m
BY	CX	500m - 1500m
BY	CY	500m - 1500m
BY	CZ	500m - 1500m
BY	DA	500m - 1500m
BZ	BA	500m - 1500m
BZ	BB	500m - 1500m
BZ	BC	500m - 1500m
BZ	BD	500m - 1500m
BZ	BE	500m - 1500m
BZ	BF	500m - 1500m
BZ	BG	500m - 1500m
BZ	BH	500m - 1500m
BZ	BI	500m - 1500m
BZ	BU	500m - 1500m
BZ	BV	500m - 1500m
BZ	BW	500m - 1500m
BZ	CA	500m - 1500m
BZ	CB	500m - 1500m
BZ	CC	500m - 1500m
BZ	CS	500m - 1500m
BZ	CT	500m - 1500m
BZ	CU	500m - 1500m
BZ	CV	500m - 1500m
BZ	CW	500m - 1500m
BZ	CX	500m - 1500m
BZ	CY	500m - 1500m
BZ	CZ	500m - 1500m
BZ	DA	500m - 1500m
CA	BD	500m - 1500m
CA	BE	500m - 1500m
CA	BF	500m - 1500m
CA	BG	500m - 1500m
CA	BH	500m - 1500m
CA	BI	500m - 1500m
CA	BX	500m - 1500m
CA	BY	500m - 1500m
CA	BZ	500m - 1500m
CA	CV	500m - 1500m
CA	CW	500m - 1500m
CA	CX	500m - 1500m
CA	CY	500m - 1500m
CA	CZ	500m - 1500m
CA	DA	500m - 1500m
CA	DB	500m - 1500m
CA	DC	500m - 1500m
CA	DD	500m - 1500m
CB	BD	500m - 1500m
CB	BE	500m - 1500m
CB	BF	500m - 1500m
CB	BG	500m - 1500m
CB	BH	500m - 1500m
CB	BI	500m - 1500m
CB	BX	500m - 1500m
CB	BY	500m - 1500m
CB	BZ	500m - 1500m
CB	CV	500m - 1500m
CB	CW	500m - 1500m
CB	CX	500m - 1500m
CB	CY	500m - 1500m
CB	CZ	500m - 1500m
CB	DA	500m - 1500m
CB	DB	500m - 1500m
CB	DC	500m - 1500m
CB	DD	500m - 1500m
CC	BD	500m - 1500m
CC	BE	500m - 1500m
CC	BF	500m - 1500m
CC	BG	500m - 1500m
CC	BH	500m - 1500m
CC	BI	500m - 1500m
CC	BX	500m - 1500m
CC	BY	500m - 1500m
CC	BZ	500m - 1500m
CC	CV	500m - 1500m
CC	CW	500m - 1500m
CC	CX	500m - 1500m
CC	CY	500m - 1500m
CC	CZ	500m - 1500m
CC	DA	500m - 1500m
CC	DB	500m - 1500m
CC	DC	500m - 1500m
CC	DD	500m - 1500m
CD	CG	500m - 1500m
CD	CH	500m - 1500m
CD	CI	500m - 1500m
CD	DH	500m - 1500m
CD	DI	500m - 1500m
CD	DJ	500m - 1500m
CD	DK	500m - 1500m
CD	DL	500m - 1500m
CD	DM	500m - 1500m
CE	CG	500m - 1500m
CE	CH	500m - 1500m
CE	CI	500m - 1500m
CE	DH	500m - 1500m
CE	DI	500m - 1500m
CE	DJ	500m - 1500m
CE	DK	500m - 1500m
CE	DL	500m - 1500m
CE	DM	500m - 1500m
CF	CG	500m - 1500m
CF	CH	500m - 1500m
CF	CI	500m - 1500m
CF	DH	500m - 1500m
CF	DI	500m - 1500m
CF	DJ	500m - 1500m
CF	DK	500m - 1500m
CF	DL	500m - 1500m
CF	DM	500m - 1500m
CG	BJ	500m - 1500m
CG	BK	500m - 1500m
CG	CD	500m - 1500m
CG	CE	500m - 1500m
CG	CF	500m - 1500m
CG	CJ	500m - 1500m
CG	CK	500m - 1500m
CG	CL	500m - 1500m
CG	DK	500m - 1500m
CG	DL	500m - 1500m
CG	DM	500m - 1500m
CG	DN	500m - 1500m
CG	DO	500m - 1500m
CG	DP	500m - 1500m
CH	BJ	500m - 1500m
CH	BK	500m - 1500m
CH	CD	500m - 1500m
CH	CE	500m - 1500m
CH	CF	500m - 1500m
CH	CJ	500m - 1500m
CH	CK	500m - 1500m
CH	CL	500m - 1500m
CH	DK	500m - 1500m
CH	DL	500m - 1500m
CH	DM	500m - 1500m
CH	DN	500m - 1500m
CH	DO	500m - 1500m
CH	DP	500m - 1500m
CI	BJ	500m - 1500m
CI	BK	500m - 1500m
CI	CD	500m - 1500m
CI	CE	500m - 1500m
CI	CF	500m - 1500m
CI	CJ	500m - 1500m
CI	CK	500m - 1500m
CI	CL	500m - 1500m
CI	DK	500m - 1500m
CI	DL	500m - 1500m
CI	DM	500m - 1500m
CI	DN	500m - 1500m
CI	DO	500m - 1500m
CI	DP	500m - 1500m
CJ	BJ	500m - 1500m
CJ	BK	500m - 1500m
CJ	BL	500m - 1500m
CJ	BM	500m - 1500m
CJ	BN	500m - 1500m
CJ	CG	500m - 1500m
CJ	CH	500m - 1500m
CJ	CI	500m - 1500m
CJ	CM	500m - 1500m
CJ	CN	500m - 1500m
CJ	CO	500m - 1500m
CJ	DN	500m - 1500m
CJ	DO	500m - 1500m
CJ	DP	500m - 1500m
CJ	DQ	500m - 1500m
CJ	DR	500m - 1500m
CJ	DS	500m - 1500m
CK	BJ	500m - 1500m
CK	BK	500m - 1500m
CK	BL	500m - 1500m
CK	BM	500m - 1500m
CK	BN	500m - 1500m
CK	CG	500m - 1500m
CK	CH	500m - 1500m
CK	CI	500m - 1500m
CK	CM	500m - 1500m
CK	CN	500m - 1500m
CK	CO	500m - 1500m
CK	DN	500m - 1500m
CK	DO	500m - 1500m
CK	DP	500m - 1500m
CK	DQ	500m - 1500m
CK	DR	500m - 1500m
CK	DS	500m - 1500m
CL	BJ	500m - 1500m
CL	BK	500m - 1500m
CL	BL	500m - 1500m
CL	BM	500m - 1500m
CL	BN	500m - 1500m
CL	CG	500m - 1500m
CL	CH	500m - 1500m
CL	CI	500m - 1500m
CL	CM	500m - 1500m
CL	CN	500m - 1500m
CL	CO	500m - 1500m
CL	DN	500m - 1500m
CL	DO	500m - 1500m
CL	DP	500m - 1500m
CL	DQ	500m - 1500m
CL	DR	500m - 1500m
CL	DS	500m - 1500m
CM	BJ	500m - 1500m
CM	BK	500m - 1500m
CM	BL	500m - 1500m
CM	BM	500m - 1500m
CM	BN	500m - 1500m
CM	BO	500m - 1500m
CM	BP	500m - 1500m
CM	BQ	500m - 1500m
CM	CJ	500m - 1500m
CM	CK	500m - 1500m
CM	CL	500m - 1500m
CM	CP	500m - 1500m
CM	CQ	500m - 1500m
CM	CR	500m - 1500m
CM	DN	500m - 1500m
CM	DO	500m - 1500m
CM	DP	500m - 1500m
CM	DQ	500m - 1500m
CM	DR	500m - 1500m
CM	DS	500m - 1500m
CM	DT	500m - 1500m
CM	DU	500m - 1500m
CM	DV	500m - 1500m
CN	BJ	500m - 1500m
CN	BK	500m - 1500m
CN	BL	500m - 1500m
CN	BM	500m - 1500m
CN	BN	500m - 1500m
CN	BO	500m - 1500m
CN	BP	500m - 1500m
CN	BQ	500m - 1500m
CN	CJ	500m - 1500m
CN	CK	500m - 1500m
CN	CL	500m - 1500m
CN	CP	500m - 1500m
CN	CQ	500m - 1500m
CN	CR	500m - 1500m
CN	DN	500m - 1500m
CN	DO	500m - 1500m
CN	DP	500m - 1500m
CN	DQ	500m - 1500m
CN	DR	500m - 1500m
CN	DS	500m - 1500m
CN	DT	500m - 1500m
CN	DU	500m - 1500m
CN	DV	500m - 1500m
CO	BJ	500m - 1500m
CO	BK	500m - 1500m
CO	BL	500m - 1500m
CO	BM	500m - 1500m
CO	BN	500m - 1500m
CO	BO	500m - 1500m
CO	BP	500m - 1500m
CO	BQ	500m - 1500m
CO	CJ	500m - 1500m
CO	CK	500m - 1500m
CO	CL	500m - 1500m
CO	CP	500m - 1500m
CO	CQ	500m - 1500m
CO	CR	500m - 1500m
CO	DN	500m - 1500m
CO	DO	500m - 1500m
CO	DP	500m - 1500m
CO	DQ	500m - 1500m
CO	DR	500m - 1500m
CO	DS	500m - 1500m
CO	DT	500m - 1500m
CO	DU	500m - 1500m
CO	DV	500m - 1500m
CP	BL	500m - 1500m
CP	BM	500m - 1500m
CP	BN	500m - 1500m
CP	BO	500m - 1500m
CP	BP	500m - 1500m
CP	BQ	500m - 1500m
CP	CM	500m - 1500m
CP	CN	500m - 1500m
CP	CO	500m - 1500m
CP	DQ	500m - 1500m
CP	DR	500m - 1500m
CP	DS	500m - 1500m
CP	DT	500m - 1500m
CP	DU	500m - 1500m
CP	DV	500m - 1500m
CQ	BL	500m - 1500m
CQ	BM	500m - 1500m
CQ	BN	500m - 1500m
CQ	BO	500m - 1500m
CQ	BP	500m - 1500m
CQ	BQ	500m - 1500m
CQ	CM	500m - 1500m
CQ	CN	500m - 1500m
CQ	CO	500m - 1500m
CQ	DQ	500m - 1500m
CQ	DR	500m - 1500m
CQ	DS	500m - 1500m
CQ	DT	500m - 1500m
CQ	DU	500m - 1500m
CQ	DV	500m - 1500m
CR	BL	500m - 1500m
CR	BM	500m - 1500m
CR	BN	500m - 1500m
CR	BO	500m - 1500m
CR	BP	500m - 1500m
CR	BQ	500m - 1500m
CR	CM	500m - 1500m
CR	CN	500m - 1500m
CR	CO	500m - 1500m
CR	DQ	500m - 1500m
CR	DR	500m - 1500m
CR	DS	500m - 1500m
CR	DT	500m - 1500m
CR	DU	500m - 1500m
CR	DV	500m - 1500m
CS	BR	500m - 1500m
CS	BS	500m - 1500m
CS	BT	500m - 1500m
CS	BU	500m - 1500m
CS	BV	500m - 1500m
CS	BW	500m - 1500m
CS	BX	500m - 1500m
CS	BY	500m - 1500m
CS	BZ	500m - 1500m
CS	CV	500m - 1500m
CS	CW	500m - 1500m
CS	CX	500m - 1500m
CT	BR	500m - 1500m
CT	BS	500m - 1500m
CT	BT	500m - 1500m
CT	BU	500m - 1500m
CT	BV	500m - 1500m
CT	BW	500m - 1500m
CT	BX	500m - 1500m
CT	BY	500m - 1500m
CT	BZ	500m - 1500m
CT	CV	500m - 1500m
CT	CW	500m - 1500m
CT	CX	500m - 1500m
CU	BR	500m - 1500m
CU	BS	500m - 1500m
CU	BT	500m - 1500m
CU	BU	500m - 1500m
CU	BV	500m - 1500m
CU	BW	500m - 1500m
CU	BX	500m - 1500m
CU	BY	500m - 1500m
CU	BZ	500m - 1500m
CU	CV	500m - 1500m
CU	CW	500m - 1500m
CU	CX	500m - 1500m
CV	BU	500m - 1500m
CV	BV	500m - 1500m
CV	BW	500m - 1500m
CV	BX	500m - 1500m
CV	BY	500m - 1500m
CV	BZ	500m - 1500m
CV	CA	500m - 1500m
CV	CB	500m - 1500m
CV	CC	500m - 1500m
CV	CS	500m - 1500m
CV	CT	500m - 1500m
CV	CU	500m - 1500m
CV	CY	500m - 1500m
CV	CZ	500m - 1500m
CV	DA	500m - 1500m
CW	BU	500m - 1500m
CW	BV	500m - 1500m
CW	BW	500m - 1500m
CW	BX	500m - 1500m
CW	BY	500m - 1500m
CW	BZ	500m - 1500m
CW	CA	500m - 1500m
CW	CB	500m - 1500m
CW	CC	500m - 1500m
CW	CS	500m - 1500m
CW	CT	500m - 1500m
CW	CU	500m - 1500m
CW	CY	500m - 1500m
CW	CZ	500m - 1500m
CW	DA	500m - 1500m
CX	BU	500m - 1500m
CX	BV	500m - 1500m
CX	BW	500m - 1500m
CX	BX	500m - 1500m
CX	BY	500m - 1500m
CX	BZ	500m - 1500m
CX	CA	500m - 1500m
CX	CB	500m - 1500m
CX	CC	500m - 1500m
CX	CS	500m - 1500m
CX	CT	500m - 1500m
CX	CU	500m - 1500m
CX	CY	500m - 1500m
CX	CZ	500m - 1500m
CX	DA	500m - 1500m
CY	BX	500m - 1500m
CY	BY	500m - 1500m
CY	BZ	500m - 1500m
CY	CA	500m - 1500m
CY	CB	500m - 1500m
CY	CC	500m - 1500m
CY	CV	500m - 1500m
CY	CW	500m - 1500m
CY	CX	500m - 1500m
CY	DB	500m - 1500m
CY	DC	500m - 1500m
CY	DD	500m - 1500m
CZ	BX	500m - 1500m
CZ	BY	500m - 1500m
CZ	BZ	500m - 1500m
CZ	CA	500m - 1500m
CZ	CB	500m - 1500m
CZ	CC	500m - 1500m
CZ	CV	500m - 1500m
CZ	CW	500m - 1500m
CZ	CX	500m - 1500m
CZ	DB	500m - 1500m
CZ	DC	500m - 1500m
CZ	DD	500m - 1500m
DA	BX	500m - 1500m
DA	BY	500m - 1500m
DA	BZ	500m - 1500m
DA	CA	500m - 1500m
DA	CB	500m - 1500m
DA	CC	500m - 1500m
DA	CV	500m - 1500m
DA	CW	500m - 1500m
DA	CX	500m - 1500m
DA	DB	500m - 1500m
DA	DC	500m - 1500m
DA	DD	500m - 1500m
DB	CA	500m - 1500m
DB	CB	500m - 1500m
DB	CC	500m - 1500m
DB	CY	500m - 1500m
DB	CZ	500m - 1500m
DB	DA	500m - 1500m
DB	DE	500m - 1500m
DB	DF	500m - 1500m
DB	DG	500m - 1500m
DC	CA	500m - 1500m
DC	CB	500m - 1500m
DC	CC	500m - 1500m
DC	CY	500m - 1500m
DC	CZ	500m - 1500m
DC	DA	500m - 1500m
DC	DE	500m - 1500m
DC	DF	500m - 1500m
DC	DG	500m - 1500m
DD	CA	500m - 1500m
DD	CB	500m - 1500m
DD	CC	500m - 1500m
DD	CY	500m - 1500m
DD	CZ	500m - 1500m
DD	DA	500m - 1500m
DD	DE	500m - 1500m
DD	DF	500m - 1500m
DD	DG	500m - 1500m
DE	DB	500m - 1500m
DE	DC	500m - 1500m
DE	DD	500m - 1500m
DE	DH	500m - 1500m
DE	DI	500m - 1500m
DE	DJ	500m - 1500m
DE	DW	500m - 1500m
DE	DX	500m - 1500m
DE	DY	500m - 1500m
DF	DB	500m - 1500m
DF	DC	500m - 1500m
DF	DD	500m - 1500m
DF	DH	500m - 1500m
DF	DI	500m - 1500m
DF	DJ	500m - 1500m
DF	DW	500m - 1500m
DF	DX	500m - 1500m
DF	DY	500m - 1500m
DG	DB	500m - 1500m
DG	DC	500m - 1500m
DG	DD	500m - 1500m
DG	DH	500m - 1500m
DG	DI	500m - 1500m
DG	DJ	500m - 1500m
DG	DW	500m - 1500m
DG	DX	500m - 1500m
DG	DY	500m - 1500m
DH	CD	500m - 1500m
DH	CE	500m - 1500m
DH	CF	500m - 1500m
DH	DE	500m - 1500m
DH	DF	500m - 1500m
DH	DG	500m - 1500m
DH	DK	500m - 1500m
DH	DL	500m - 1500m
DH	DM	500m - 1500m
DH	DW	500m - 1500m
DH	DX	500m - 1500m
DH	DY	500m - 1500m
DH	DZ	500m - 1500m
DH	EA	500m - 1500m
DH	EB	500m - 1500m
DI	CD	500m - 1500m
DI	CE	500m - 1500m
DI	CF	500m - 1500m
DI	DE	500m - 1500m
DI	DF	500m - 1500m
DI	DG	500m - 1500m
DI	DK	500m - 1500m
DI	DL	500m - 1500m
DI	DM	500m - 1500m
DI	DW	500m - 1500m
DI	DX	500m - 1500m
DI	DY	500m - 1500m
DI	DZ	500m - 1500m
DI	EA	500m - 1500m
DI	EB	500m - 1500m
DJ	CD	500m - 1500m
DJ	CE	500m - 1500m
DJ	CF	500m - 1500m
DJ	DE	500m - 1500m
DJ	DF	500m - 1500m
DJ	DG	500m - 1500m
DJ	DK	500m - 1500m
DJ	DL	500m - 1500m
DJ	DM	500m - 1500m
DJ	DW	500m - 1500m
DJ	DX	500m - 1500m
DJ	DY	500m - 1500m
DJ	DZ	500m - 1500m
DJ	EA	500m - 1500m
DJ	EB	500m - 1500m
DK	CD	500m - 1500m
DK	CE	500m - 1500m
DK	CF	500m - 1500m
DK	CG	500m - 1500m
DK	CH	500m - 1500m
DK	CI	500m - 1500m
DK	DH	500m - 1500m
DK	DI	500m - 1500m
DK	DJ	500m - 1500m
DK	DN	500m - 1500m
DK	DO	500m - 1500m
DK	DP	500m - 1500m
DK	DZ	500m - 1500m
DK	EA	500m - 1500m
DK	EB	500m - 1500m
DK	EC	500m - 1500m
DK	ED	500m - 1500m
DL	CD	500m - 1500m
DL	CE	500m - 1500m
DL	CF	500m - 1500m
DL	CG	500m - 1500m
DL	CH	500m - 1500m
DL	CI	500m - 1500m
DL	DH	500m - 1500m
DL	DI	500m - 1500m
DL	DJ	500m - 1500m
DL	DN	500m - 1500m
DL	DO	500m - 1500m
DL	DP	500m - 1500m
DL	DZ	500m - 1500m
DL	EA	500m - 1500m
DL	EB	500m - 1500m
DL	EC	500m - 1500m
DL	ED	500m - 1500m
DM	CD	500m - 1500m
DM	CE	500m - 1500m
DM	CF	500m - 1500m
DM	CG	500m - 1500m
DM	CH	500m - 1500m
DM	CI	500m - 1500m
DM	DH	500m - 1500m
DM	DI	500m - 1500m
DM	DJ	500m - 1500m
DM	DN	500m - 1500m
DM	DO	500m - 1500m
DM	DP	500m - 1500m
DM	DZ	500m - 1500m
DM	EA	500m - 1500m
DM	EB	500m - 1500m
DM	EC	500m - 1500m
DM	ED	500m - 1500m
DN	CG	500m - 1500m
DN	CH	500m - 1500m
DN	CI	500m - 1500m
DN	CJ	500m - 1500m
DN	CK	500m - 1500m
DN	CL	500m - 1500m
DN	CM	500m - 1500m
DN	CN	500m - 1500m
DN	CO	500m - 1500m
DN	DK	500m - 1500m
DN	DL	500m - 1500m
DN	DM	500m - 1500m
DN	DQ	500m - 1500m
DN	DR	500m - 1500m
DN	DS	500m - 1500m
DN	EC	500m - 1500m
DN	ED	500m - 1500m
DN	EE	500m - 1500m
DN	EF	500m - 1500m
DN	EG	500m - 1500m
DN	EH	500m - 1500m
DN	EI	500m - 1500m
DN	EJ	500m - 1500m
DO	CG	500m - 1500m
DO	CH	500m - 1500m
DO	CI	500m - 1500m
DO	CJ	500m - 1500m
DO	CK	500m - 1500m
DO	CL	500m - 1500m
DO	CM	500m - 1500m
DO	CN	500m - 1500m
DO	CO	500m - 1500m
DO	DK	500m - 1500m
DO	DL	500m - 1500m
DO	DM	500m - 1500m
DO	DQ	500m - 1500m
DO	DR	500m - 1500m
DO	DS	500m - 1500m
DO	EC	500m - 1500m
DO	ED	500m - 1500m
DO	EE	500m - 1500m
DO	EF	500m - 1500m
DO	EG	500m - 1500m
DO	EH	500m - 1500m
DO	EI	500m - 1500m
DO	EJ	500m - 1500m
DP	CG	500m - 1500m
DP	CH	500m - 1500m
DP	CI	500m - 1500m
DP	CJ	500m - 1500m
DP	CK	500m - 1500m
DP	CL	500m - 1500m
DP	CM	500m - 1500m
DP	CN	500m - 1500m
DP	CO	500m - 1500m
DP	DK	500m - 1500m
DP	DL	500m - 1500m
DP	DM	500m - 1500m
DP	DQ	500m - 1500m
DP	DR	500m - 1500m
DP	DS	500m - 1500m
DP	EC	500m - 1500m
DP	ED	500m - 1500m
DP	EE	500m - 1500m
DP	EF	500m - 1500m
DP	EG	500m - 1500m
DP	EH	500m - 1500m
DP	EI	500m - 1500m
DP	EJ	500m - 1500m
DQ	CJ	500m - 1500m
DQ	CK	500m - 1500m
DQ	CL	500m - 1500m
DQ	CM	500m - 1500m
DQ	CN	500m - 1500m
DQ	CO	500m - 1500m
DQ	CP	500m - 1500m
DQ	CQ	500m - 1500m
DQ	CR	500m - 1500m
DQ	DN	500m - 1500m
DQ	DO	500m - 1500m
DQ	DP	500m - 1500m
DQ	DT	500m - 1500m
DQ	DU	500m - 1500m
DQ	DV	500m - 1500m
DQ	EE	500m - 1500m
DQ	EF	500m - 1500m
DQ	EG	500m - 1500m
DQ	EH	500m - 1500m
DQ	EI	500m - 1500m
DQ	EJ	500m - 1500m
DQ	EK	500m - 1500m
DQ	EL	500m - 1500m
DQ	EM	500m - 1500m
DR	CJ	500m - 1500m
DR	CK	500m - 1500m
DR	CL	500m - 1500m
DR	CM	500m - 1500m
DR	CN	500m - 1500m
DR	CO	500m - 1500m
DR	CP	500m - 1500m
DR	CQ	500m - 1500m
DR	CR	500m - 1500m
DR	DN	500m - 1500m
DR	DO	500m - 1500m
DR	DP	500m - 1500m
DR	DT	500m - 1500m
DR	DU	500m - 1500m
DR	DV	500m - 1500m
DR	EE	500m - 1500m
DR	EF	500m - 1500m
DR	EG	500m - 1500m
DR	EH	500m - 1500m
DR	EI	500m - 1500m
DR	EJ	500m - 1500m
DR	EK	500m - 1500m
DR	EL	500m - 1500m
DR	EM	500m - 1500m
DS	CJ	500m - 1500m
DS	CK	500m - 1500m
DS	CL	500m - 1500m
DS	CM	500m - 1500m
DS	CN	500m - 1500m
DS	CO	500m - 1500m
DS	CP	500m - 1500m
DS	CQ	500m - 1500m
DS	CR	500m - 1500m
DS	DN	500m - 1500m
DS	DO	500m - 1500m
DS	DP	500m - 1500m
DS	DT	500m - 1500m
DS	DU	500m - 1500m
DS	DV	500m - 1500m
DS	EE	500m - 1500m
DS	EF	500m - 1500m
DS	EG	500m - 1500m
DS	EH	500m - 1500m
DS	EI	500m - 1500m
DS	EJ	500m - 1500m
DS	EK	500m - 1500m
DS	EL	500m - 1500m
DS	EM	500m - 1500m
DT	CM	500m - 1500m
DT	CN	500m - 1500m
DT	CO	500m - 1500m
DT	CP	500m - 1500m
DT	CQ	500m - 1500m
DT	CR	500m - 1500m
DT	DQ	500m - 1500m
DT	DR	500m - 1500m
DT	DS	500m - 1500m
DT	EH	500m - 1500m
DT	EI	500m - 1500m
DT	EJ	500m - 1500m
DT	EK	500m - 1500m
DT	EL	500m - 1500m
DT	EM	500m - 1500m
DU	CM	500m - 1500m
DU	CN	500m - 1500m
DU	CO	500m - 1500m
DU	CP	500m - 1500m
DU	CQ	500m - 1500m
DU	CR	500m - 1500m
DU	DQ	500m - 1500m
DU	DR	500m - 1500m
DU	DS	500m - 1500m
DU	EH	500m - 1500m
DU	EI	500m - 1500m
DU	EJ	500m - 1500m
DU	EK	500m - 1500m
DU	EL	500m - 1500m
DU	EM	500m - 1500m
DV	CM	500m - 1500m
DV	CN	500m - 1500m
DV	CO	500m - 1500m
DV	CP	500m - 1500m
DV	CQ	500m - 1500m
DV	CR	500m - 1500m
DV	DQ	500m - 1500m
DV	DR	500m - 1500m
DV	DS	500m - 1500m
DV	EH	500m - 1500m
DV	EI	500m - 1500m
DV	EJ	500m - 1500m
DV	EK	500m - 1500m
DV	EL	500m - 1500m
DV	EM	500m - 1500m
DW	DE	500m - 1500m
DW	DF	500m - 1500m
DW	DG	500m - 1500m
DW	DH	500m - 1500m
DW	DI	500m - 1500m
DW	DJ	500m - 1500m
DW	DZ	500m - 1500m
DW	EA	500m - 1500m
DW	EB	500m - 1500m
DX	DE	500m - 1500m
DX	DF	500m - 1500m
DX	DG	500m - 1500m
DX	DH	500m - 1500m
DX	DI	500m - 1500m
DX	DJ	500m - 1500m
DX	DZ	500m - 1500m
DX	EA	500m - 1500m
DX	EB	500m - 1500m
DY	DE	500m - 1500m
DY	DF	500m - 1500m
DY	DG	500m - 1500m
DY	DH	500m - 1500m
DY	DI	500m - 1500m
DY	DJ	500m - 1500m
DY	DZ	500m - 1500m
DY	EA	500m - 1500m
DY	EB	500m - 1500m
DZ	DH	500m - 1500m
DZ	DI	500m - 1500m
DZ	DJ	500m - 1500m
DZ	DK	500m - 1500m
DZ	DL	500m - 1500m
DZ	DM	500m - 1500m
DZ	DW	500m - 1500m
DZ	DX	500m - 1500m
DZ	DY	500m - 1500m
DZ	EC	500m - 1500m
DZ	ED	500m - 1500m
EA	DH	500m - 1500m
EA	DI	500m - 1500m
EA	DJ	500m - 1500m
EA	DK	500m - 1500m
EA	DL	500m - 1500m
EA	DM	500m - 1500m
EA	DW	500m - 1500m
EA	DX	500m - 1500m
EA	DY	500m - 1500m
EA	EC	500m - 1500m
EA	ED	500m - 1500m
EB	DH	500m - 1500m
EB	DI	500m - 1500m
EB	DJ	500m - 1500m
EB	DK	500m - 1500m
EB	DL	500m - 1500m
EB	DM	500m - 1500m
EB	DW	500m - 1500m
EB	DX	500m - 1500m
EB	DY	500m - 1500m
EB	EC	500m - 1500m
EB	ED	500m - 1500m
EC	DK	500m - 1500m
EC	DL	500m - 1500m
EC	DM	500m - 1500m
EC	DN	500m - 1500m
EC	DO	500m - 1500m
EC	DP	500m - 1500m
EC	DZ	500m - 1500m
EC	EA	500m - 1500m
EC	EB	500m - 1500m
EC	EE	500m - 1500m
EC	EF	500m - 1500m
EC	EG	500m - 1500m
ED	DK	500m - 1500m
ED	DL	500m - 1500m
ED	DM	500m - 1500m
ED	DN	500m - 1500m
ED	DO	500m - 1500m
ED	DP	500m - 1500m
ED	DZ	500m - 1500m
ED	EA	500m - 1500m
ED	EB	500m - 1500m
ED	EE	500m - 1500m
ED	EF	500m - 1500m
ED	EG	500m - 1500m
EE	DN	500m - 1500m
EE	DO	500m - 1500m
EE	DP	500m - 1500m
EE	DQ	500m - 1500m
EE	DR	500m - 1500m
EE	DS	500m - 1500m
EE	EC	500m - 1500m
EE	ED	500m - 1500m
EE	EH	500m - 1500m
EE	EI	500m - 1500m
EE	EJ	500m - 1500m
EF	DN	500m - 1500m
EF	DO	500m - 1500m
EF	DP	500m - 1500m
EF	DQ	500m - 1500m
EF	DR	500m - 1500m
EF	DS	500m - 1500m
EF	EC	500m - 1500m
EF	ED	500m - 1500m
EF	EH	500m - 1500m
EF	EI	500m - 1500m
EF	EJ	500m - 1500m
EG	DN	500m - 1500m
EG	DO	500m - 1500m
EG	DP	500m - 1500m
EG	DQ	500m - 1500m
EG	DR	500m - 1500m
EG	DS	500m - 1500m
EG	EC	500m - 1500m
EG	ED	500m - 1500m
EG	EH	500m - 1500m
EG	EI	500m - 1500m
EG	EJ	500m - 1500m
EH	DN	500m - 1500m
EH	DO	500m - 1500m
EH	DP	500m - 1500m
EH	DQ	500m - 1500m
EH	DR	500m - 1500m
EH	DS	500m - 1500m
EH	DT	500m - 1500m
EH	DU	500m - 1500m
EH	DV	500m - 1500m
EH	EE	500m - 1500m
EH	EF	500m - 1500m
EH	EG	500m - 1500m
EH	EK	500m - 1500m
EH	EL	500m - 1500m
EH	EM	500m - 1500m
EI	DN	500m - 1500m
EI	DO	500m - 1500m
EI	DP	500m - 1500m
EI	DQ	500m - 1500m
EI	DR	500m - 1500m
EI	DS	500m - 1500m
EI	DT	500m - 1500m
EI	DU	500m - 1500m
EI	DV	500m - 1500m
EI	EE	500m - 1500m
EI	EF	500m - 1500m
EI	EG	500m - 1500m
EI	EK	500m - 1500m
EI	EL	500m - 1500m
EI	EM	500m - 1500m
EJ	DN	500m - 1500m
EJ	DO	500m - 1500m
EJ	DP	500m - 1500m
EJ	DQ	500m - 1500m
EJ	DR	500m - 1500m
EJ	DS	500m - 1500m
EJ	DT	500m - 1500m
EJ	DU	500m - 1500m
EJ	DV	500m - 1500m
EJ	EE	500m - 1500m
EJ	EF	500m - 1500m
EJ	EG	500m - 1500m
EJ	EK	500m - 1500m
EJ	EL	500m - 1500m
EJ	EM	500m - 1500m
EK	DQ	500m - 1500m
EK	DR	500m - 1500m
EK	DS	500m - 1500m
EK	DT	500m - 1500m
EK	DU	500m - 1500m
EK	DV	500m - 1500m
EK	EH	500m - 1500m
EK	EI	500m - 1500m
EK	EJ	500m - 1500m
EL	DQ	500m - 1500m
EL	DR	500m - 1500m
EL	DS	500m - 1500m
EL	DT	500m - 1500m
EL	DU	500m - 1500m
EL	DV	500m - 1500m
EL	EH	500m - 1500m
EL	EI	500m - 1500m
EL	EJ	500m - 1500m
EM	DQ	500m - 1500m
EM	DR	500m - 1500m
EM	DS	500m - 1500m
EM	DT	500m - 1500m
EM	DU	500m - 1500m
EM	DV	500m - 1500m
EM	EH	500m - 1500m
EM	EI	500m - 1500m
EM	EJ	500m - 1500m

You may notice that we have not been provided the coordinates of each location. Not even the actual distance between locations is provided. Rather, the interdistance between locations is given into categorized ranges, named Interdistance class. We discuss this later.

3 DATA EXPLORATION

In this section we are going to do some exploratory data analyses (EDA) on the previously-loaded datasets, so we can understand them better and get some insights.

3.1 General overview

We start with some basic plots showing CPT test registrations, for the training dataset. To improve interpretability, we have highlighted with the dark step line the data for one pile location (specifically location EK).

# grays
gray_1 <- "#2F2F2FFF"
gray_2 <- "#474747FF"
gray_3 <- "#DFDFDFFF"
gray_4 <- "#F7F7F7FF"

# update default theme
ggtheme <-
  theme_light() +
  theme(
    text = element_text(size = 8.25, color = gray_1),
    plot.title = element_text(face = "bold", size = 8.25, hjust = 0.5),
    axis.title = element_text(face = "bold", size = 8.25),
    axis.text = element_text( size = 8.25, color = gray_2),
    panel.grid.major = element_line(color = gray_3, size = 0.25),
    panel.grid.minor = element_blank(),
    axis.ticks = element_line(color = gray_2, size = 0.25),
    axis.ticks.length = unit(.25, "cm"),
    panel.border = element_rect(color = gray_2, size = 0.25),
    strip.text = element_text(size = 8.25, color = gray_1),
    legend.background = element_blank(),
    plot.background = element_blank(),
    panel.background = element_blank(),
    strip.background = element_blank(),
    legend.key = element_blank(),
    plot.margin = margin(t = 5, r = 10, b = 5, l = 10)
  )

# set theme
theme_set(ggtheme)

library(patchwork)

training_EK <- training %>%
  filter(`Location ID` == "EK")

plot1 <- training %>%
  ggplot(aes(`z [m]`, `qc [MPa]`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_step(data = training_EK, aes(`z [m]`, `qc [MPa]`),
            size = 1,
            colour = "grey20",
            alpha = 1) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 100)) +
  theme(panel.grid.minor = element_blank())

plot2 <- training %>%
ggplot(aes(`z [m]`, `fs [MPa]`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_step(data = training_EK, aes(`z [m]`, `fs [MPa]`),
            size = 1,
            colour = "grey20",
            alpha = 1) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 2)) +
  labs(x = "") +
  theme(panel.grid.minor = element_blank())

plot3 <- training %>%
ggplot(aes(`z [m]`, `u2 [MPa]`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_step(data = training_EK, aes(`z [m]`, `u2 [MPa]`),
            size = 1,
            colour = "grey20",
            alpha = 1) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(-0.5, 0.5)) +
  labs(x = "") +
  theme(panel.grid.minor = element_blank())

plot1 + plot2 + plot3

CPT test data for training (location EK with dark step line).

Next, we built similar graphs for the data related to pile installation.

plot4 <- training %>%
ggplot(aes(`z [m]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_step(data = training_EK, aes(`z [m]`, `Blowcount [Blows/m]`),
            size = 1,
            colour = "grey20",
            alpha = 1) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank())

plot5 <- training %>%
ggplot(aes(`z [m]`, `Number of blows`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_step(data = training_EK, aes(`z [m]`, `Number of blows`),
            size = 1,
            colour = "grey20",
            alpha = 1) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 2500)) +
  labs(x = "") +
  theme(panel.grid.minor = element_blank())

plot6 <- training %>%
ggplot(aes(`z [m]`, `Normalised ENTRHU [-]`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_step(data = training_EK, aes(`z [m]`, `Normalised ENTRHU [-]`),
            size = 1,
            colour = "grey20",
            alpha = 1) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 0.70)) +
  labs(x = "") +
  theme(panel.grid.minor = element_blank())

plot4 + plot5 + plot6

Pile installation data for training (location EK with dark step line).

3.2 Understanding interdistance

Now we try to explore interdistance data, in order to see if we can get an idea on the general layout or on the geometry of the site. As we previously noted, the interdistance between locations is provided in categories. Let’s see what these categories are.

interdistance <- interdistance %>%
  mutate(`Interdistance class` = as_factor(`Interdistance class`))

as_tibble(levels(interdistance$`Interdistance class`))

## # A tibble: 5 x 1
##   value        
##   <chr>        
## 1 <500m        
## 2 500m - 1500m 
## 3 1500m - 3000m
## 4 3000m - 4500m
## 5 >4500m

We have five categories. Having the pile location data in this form seems a bit unusual, since, for a project, we normally know the exact locations where we expect pile foundations to be installed. This data shortcoming most likely limits our ability to incorporate interdistance into our analysis or even to visualize it. Nonetheless, we can try different visualization layouts.

We transform the data a bit so we can express Interdistance class in numerical terms.

interdistance <- interdistance %>%
  mutate(`Interdistance cat` = case_when(`Interdistance class` == "<500m" ~ "A",
                                         `Interdistance class` == "500m - 1500m" ~ "B",
                                         `Interdistance class` == "1500m - 3000m" ~ "C",
                                         `Interdistance class` == "3000m - 4500m" ~ "D",
                                         `Interdistance class` == ">4500m" ~ "E")) %>%
  mutate(`Interdistance num` = case_when(`Interdistance cat` == "A" ~ "1.0",
                                         `Interdistance cat` == "B" ~ "0.8",
                                         `Interdistance cat` == "C" ~ "0.6",
                                         `Interdistance cat` == "D" ~ "0.4",
                                         `Interdistance cat` == "E" ~ "0.2")) %>%
  mutate(`Interdistance num` = as.double(`Interdistance num`))

kable(top_n(interdistance, 100),
      digits = 3,
      caption = "Interdistance data (edited).",
      align = "r") %>%
  kable_styling(full_width = T, font_size = 11, position = "center") %>%
  row_spec(0, color = "grey10", background = "#F4F5F6") %>%
  scroll_box(height = "300px")

Interdistance data (edited).

ID location 1	ID location 2	Interdistance class	Interdistance cat	Interdistance num
AA	AA	<500m	A	1
AA	AB	<500m	A	1
AA	AC	<500m	A	1
AB	AA	<500m	A	1
AB	AB	<500m	A	1
AB	AC	<500m	A	1
AC	AA	<500m	A	1
AC	AB	<500m	A	1
AC	AC	<500m	A	1
AD	AD	<500m	A	1
AD	AE	<500m	A	1
AE	AD	<500m	A	1
AE	AE	<500m	A	1
AF	AF	<500m	A	1
AF	AG	<500m	A	1
AF	AH	<500m	A	1
AG	AF	<500m	A	1
AG	AG	<500m	A	1
AG	AH	<500m	A	1
AH	AF	<500m	A	1
AH	AG	<500m	A	1
AH	AH	<500m	A	1
AI	AI	<500m	A	1
AI	AJ	<500m	A	1
AI	AK	<500m	A	1
AJ	AI	<500m	A	1
AJ	AJ	<500m	A	1
AJ	AK	<500m	A	1
AK	AI	<500m	A	1
AK	AJ	<500m	A	1
AK	AK	<500m	A	1
AL	AL	<500m	A	1
AL	AM	<500m	A	1
AL	AN	<500m	A	1
AM	AL	<500m	A	1
AM	AM	<500m	A	1
AM	AN	<500m	A	1
AN	AL	<500m	A	1
AN	AM	<500m	A	1
AN	AN	<500m	A	1
AO	AO	<500m	A	1
AO	AP	<500m	A	1
AO	AQ	<500m	A	1
AP	AO	<500m	A	1
AP	AP	<500m	A	1
AP	AQ	<500m	A	1
AQ	AO	<500m	A	1
AQ	AP	<500m	A	1
AQ	AQ	<500m	A	1
AR	AR	<500m	A	1
AR	AS	<500m	A	1
AR	AT	<500m	A	1
AS	AR	<500m	A	1
AS	AS	<500m	A	1
AS	AT	<500m	A	1
AT	AR	<500m	A	1
AT	AS	<500m	A	1
AT	AT	<500m	A	1
AU	AU	<500m	A	1
AU	AV	<500m	A	1
AU	AW	<500m	A	1
AV	AU	<500m	A	1
AV	AV	<500m	A	1
AV	AW	<500m	A	1
AW	AU	<500m	A	1
AW	AV	<500m	A	1
AW	AW	<500m	A	1
AX	AX	<500m	A	1
AX	AY	<500m	A	1
AX	AZ	<500m	A	1
AY	AX	<500m	A	1
AY	AY	<500m	A	1
AY	AZ	<500m	A	1
AZ	AX	<500m	A	1
AZ	AY	<500m	A	1
AZ	AZ	<500m	A	1
BA	BA	<500m	A	1
BA	BB	<500m	A	1
BA	BC	<500m	A	1
BB	BA	<500m	A	1
BB	BB	<500m	A	1
BB	BC	<500m	A	1
BC	BA	<500m	A	1
BC	BB	<500m	A	1
BC	BC	<500m	A	1
BD	BD	<500m	A	1
BD	BE	<500m	A	1
BD	BF	<500m	A	1
BE	BD	<500m	A	1
BE	BE	<500m	A	1
BE	BF	<500m	A	1
BF	BD	<500m	A	1
BF	BE	<500m	A	1
BF	BF	<500m	A	1
BG	BG	<500m	A	1
BG	BH	<500m	A	1
BG	BI	<500m	A	1
BH	BG	<500m	A	1
BH	BH	<500m	A	1
BH	BI	<500m	A	1
BI	BG	<500m	A	1
BI	BH	<500m	A	1
BI	BI	<500m	A	1
BJ	BJ	<500m	A	1
BJ	BK	<500m	A	1
BK	BJ	<500m	A	1
BK	BK	<500m	A	1
BL	BL	<500m	A	1
BL	BM	<500m	A	1
BL	BN	<500m	A	1
BM	BL	<500m	A	1
BM	BM	<500m	A	1
BM	BN	<500m	A	1
BN	BL	<500m	A	1
BN	BM	<500m	A	1
BN	BN	<500m	A	1
BO	BO	<500m	A	1
BO	BP	<500m	A	1
BO	BQ	<500m	A	1
BP	BO	<500m	A	1
BP	BP	<500m	A	1
BP	BQ	<500m	A	1
BQ	BO	<500m	A	1
BQ	BP	<500m	A	1
BQ	BQ	<500m	A	1
BR	BR	<500m	A	1
BR	BS	<500m	A	1
BR	BT	<500m	A	1
BS	BR	<500m	A	1
BS	BS	<500m	A	1
BS	BT	<500m	A	1
BT	BR	<500m	A	1
BT	BS	<500m	A	1
BT	BT	<500m	A	1
BU	BU	<500m	A	1
BU	BV	<500m	A	1
BU	BW	<500m	A	1
BV	BU	<500m	A	1
BV	BV	<500m	A	1
BV	BW	<500m	A	1
BW	BU	<500m	A	1
BW	BV	<500m	A	1
BW	BW	<500m	A	1
BX	BX	<500m	A	1
BX	BY	<500m	A	1
BX	BZ	<500m	A	1
BY	BX	<500m	A	1
BY	BY	<500m	A	1
BY	BZ	<500m	A	1
BZ	BX	<500m	A	1
BZ	BY	<500m	A	1
BZ	BZ	<500m	A	1
CA	CA	<500m	A	1
CA	CB	<500m	A	1
CA	CC	<500m	A	1
CB	CA	<500m	A	1
CB	CB	<500m	A	1
CB	CC	<500m	A	1
CC	CA	<500m	A	1
CC	CB	<500m	A	1
CC	CC	<500m	A	1
CD	CD	<500m	A	1
CD	CE	<500m	A	1
CD	CF	<500m	A	1
CE	CD	<500m	A	1
CE	CE	<500m	A	1
CE	CF	<500m	A	1
CF	CD	<500m	A	1
CF	CE	<500m	A	1
CF	CF	<500m	A	1
CG	CG	<500m	A	1
CG	CH	<500m	A	1
CG	CI	<500m	A	1
CH	CG	<500m	A	1
CH	CH	<500m	A	1
CH	CI	<500m	A	1
CI	CG	<500m	A	1
CI	CH	<500m	A	1
CI	CI	<500m	A	1
CJ	CJ	<500m	A	1
CJ	CK	<500m	A	1
CJ	CL	<500m	A	1
CK	CJ	<500m	A	1
CK	CK	<500m	A	1
CK	CL	<500m	A	1
CL	CJ	<500m	A	1
CL	CK	<500m	A	1
CL	CL	<500m	A	1
CM	CM	<500m	A	1
CM	CN	<500m	A	1
CM	CO	<500m	A	1
CN	CM	<500m	A	1
CN	CN	<500m	A	1
CN	CO	<500m	A	1
CO	CM	<500m	A	1
CO	CN	<500m	A	1
CO	CO	<500m	A	1
CP	CP	<500m	A	1
CP	CQ	<500m	A	1
CP	CR	<500m	A	1
CQ	CP	<500m	A	1
CQ	CQ	<500m	A	1
CQ	CR	<500m	A	1
CR	CP	<500m	A	1
CR	CQ	<500m	A	1
CR	CR	<500m	A	1
CS	CS	<500m	A	1
CS	CT	<500m	A	1
CS	CU	<500m	A	1
CT	CS	<500m	A	1
CT	CT	<500m	A	1
CT	CU	<500m	A	1
CU	CS	<500m	A	1
CU	CT	<500m	A	1
CU	CU	<500m	A	1
CV	CV	<500m	A	1
CV	CW	<500m	A	1
CV	CX	<500m	A	1
CW	CV	<500m	A	1
CW	CW	<500m	A	1
CW	CX	<500m	A	1
CX	CV	<500m	A	1
CX	CW	<500m	A	1
CX	CX	<500m	A	1
CY	CY	<500m	A	1
CY	CZ	<500m	A	1
CY	DA	<500m	A	1
CZ	CY	<500m	A	1
CZ	CZ	<500m	A	1
CZ	DA	<500m	A	1
DA	CY	<500m	A	1
DA	CZ	<500m	A	1
DA	DA	<500m	A	1
DB	DB	<500m	A	1
DB	DC	<500m	A	1
DB	DD	<500m	A	1
DC	DB	<500m	A	1
DC	DC	<500m	A	1
DC	DD	<500m	A	1
DD	DB	<500m	A	1
DD	DC	<500m	A	1
DD	DD	<500m	A	1
DE	DE	<500m	A	1
DE	DF	<500m	A	1
DE	DG	<500m	A	1
DF	DE	<500m	A	1
DF	DF	<500m	A	1
DF	DG	<500m	A	1
DG	DE	<500m	A	1
DG	DF	<500m	A	1
DG	DG	<500m	A	1
DH	DH	<500m	A	1
DH	DI	<500m	A	1
DH	DJ	<500m	A	1
DI	DH	<500m	A	1
DI	DI	<500m	A	1
DI	DJ	<500m	A	1
DJ	DH	<500m	A	1
DJ	DI	<500m	A	1
DJ	DJ	<500m	A	1
DK	DK	<500m	A	1
DK	DL	<500m	A	1
DK	DM	<500m	A	1
DL	DK	<500m	A	1
DL	DL	<500m	A	1
DL	DM	<500m	A	1
DM	DK	<500m	A	1
DM	DL	<500m	A	1
DM	DM	<500m	A	1
DN	DN	<500m	A	1
DN	DO	<500m	A	1
DN	DP	<500m	A	1
DO	DN	<500m	A	1
DO	DO	<500m	A	1
DO	DP	<500m	A	1
DP	DN	<500m	A	1
DP	DO	<500m	A	1
DP	DP	<500m	A	1
DQ	DQ	<500m	A	1
DQ	DR	<500m	A	1
DQ	DS	<500m	A	1
DR	DQ	<500m	A	1
DR	DR	<500m	A	1
DR	DS	<500m	A	1
DS	DQ	<500m	A	1
DS	DR	<500m	A	1
DS	DS	<500m	A	1
DT	DT	<500m	A	1
DT	DU	<500m	A	1
DT	DV	<500m	A	1
DU	DT	<500m	A	1
DU	DU	<500m	A	1
DU	DV	<500m	A	1
DV	DT	<500m	A	1
DV	DU	<500m	A	1
DV	DV	<500m	A	1
DW	DW	<500m	A	1
DW	DX	<500m	A	1
DW	DY	<500m	A	1
DX	DW	<500m	A	1
DX	DX	<500m	A	1
DX	DY	<500m	A	1
DY	DW	<500m	A	1
DY	DX	<500m	A	1
DY	DY	<500m	A	1
DZ	DZ	<500m	A	1
DZ	EA	<500m	A	1
DZ	EB	<500m	A	1
EA	DZ	<500m	A	1
EA	EA	<500m	A	1
EA	EB	<500m	A	1
EB	DZ	<500m	A	1
EB	EA	<500m	A	1
EB	EB	<500m	A	1
EC	EC	<500m	A	1
EC	ED	<500m	A	1
ED	EC	<500m	A	1
ED	ED	<500m	A	1
EE	EE	<500m	A	1
EE	EF	<500m	A	1
EE	EG	<500m	A	1
EF	EE	<500m	A	1
EF	EF	<500m	A	1
EF	EG	<500m	A	1
EG	EE	<500m	A	1
EG	EF	<500m	A	1
EG	EG	<500m	A	1
EH	EH	<500m	A	1
EH	EI	<500m	A	1
EH	EJ	<500m	A	1
EI	EH	<500m	A	1
EI	EI	<500m	A	1
EI	EJ	<500m	A	1
EJ	EH	<500m	A	1
EJ	EI	<500m	A	1
EJ	EJ	<500m	A	1
EK	EK	<500m	A	1
EK	EL	<500m	A	1
EK	EM	<500m	A	1
EL	EK	<500m	A	1
EL	EL	<500m	A	1
EL	EM	<500m	A	1
EM	EK	<500m	A	1
EM	EL	<500m	A	1
EM	EM	<500m	A	1

library(ggraph)
library(igraph)

We use the ggraph and the igraph packages to further visualize interdistance data.

interdistance %>%
  graph_from_data_frame() %>%
  ggraph() +
  geom_edge_link(alpha = 1/100) +
  geom_node_point(size = 2) +
  geom_node_text(aes(label = name), vjust = 1.25, hjust = 1.25, size = 2.5) +
  theme_void()

Relationship between all locations considering all levels of Interdistance class.

Nice viz but difficult to make any interpretation. We can get a more insightful plot by considering just interdistance of categories <500m and 500m - 1500m.

interdistance %>%
  filter(`Interdistance cat` %in% c("A", "B")) %>%
  graph_from_data_frame() %>%
  ggraph() +
  geom_edge_link(aes(alpha = `Interdistance num`)) +
  geom_node_point(size = 2) +
  geom_node_text(aes(label = name), vjust = 1.25, hjust = 1.25, size = 2.5) +
  theme_void() +
  theme(legend.position = "none")

Relationship between all locations considering Interdistance class of <500m and 500m - 1500m only.

From the above graph, we notice the creation of some “clusters”, each containing 3 piles, representing the piles used for each jacket. Within each of these clusters, the Interdistance class is equal to <500m. In other words, when the Interdistance class between piles is <500m, they are basically the same location, as they belong to the same jacket. Let’s see how the CPT and installation data differ for piles within the same jacket. Consider locations DB, DC, and DD.

training_DBDCDD <- training %>%
  filter(`Location ID` %in% c("DB", "DC", "DD"))

plot7 <- training %>%
ggplot(aes(`z [m]`, `qc [MPa]`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_step(data = training_DBDCDD, aes(`z [m]`, `qc [MPa]`, group = `Location ID`, colour = `Location ID`),
            size = 1,
            alpha = 1) +
  scale_colour_manual(values = c("tomato", "steelblue", "grey20")) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 100)) +
  theme(legend.position = "none",
        panel.grid.minor = element_blank())

plot8 <- training %>%
ggplot(aes(`z [m]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_step(data = training_DBDCDD, aes(`z [m]`, `Blowcount [Blows/m]`, group = `Location ID`, colour = `Location ID`),
            size = 1,
            alpha = 1) +
  scale_colour_manual(values = c("tomato", "steelblue", "grey20")) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 150)) +
  theme(legend.position = "none",
        panel.grid.minor = element_blank()) +
  labs(x = "")

plot9 <- training %>%
ggplot(aes(`z [m]`, `Number of blows`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_step(data = training_DBDCDD, aes(`z [m]`, `Number of blows`, group = `Location ID`, colour = `Location ID`),
            size = 1,
            alpha = 1) +
  scale_colour_manual(values = c("tomato", "steelblue", "grey20")) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 2500)) +
  theme(legend.position = c(0.75, 0.8),
        panel.grid.minor = element_blank()) +
  labs(x = "")

plot7 + plot8 + plot9

Plot of data for locations DB, DC, and DD.

From the above graphs we can infer that the same CPT test is used for the three piles of the jacket, since the CPT profiles of all three locations completely overlap. Nonetheless, noticeable differences are observed in the Blowcount [Blows/m] values. These differences represent mostly the spatial variations of the soil conditions between piles of the same jacket.

Another way of looking at this is to emphasize that, although we have data about the installation of 114 piles, the CPT data are relatively scarce. Take the validation dataset, for example. Although it contains data about 20 pile locations, only seven CPT registrations are included. It is very likely that this limits the accuracy of our hypothetical predictive models.

We build the same plot as above but with separated locations for training and validation.

interdistance_tr <- interdistance %>%
  filter(`ID location 1` %in% training$`Location ID`) %>%
  mutate(Category = "training")

interdistance_va <- interdistance %>%
  filter(`ID location 1` %in% validation$`Location ID`) %>%
  mutate(Category = "validation")

interdistance_all <- full_join(interdistance_tr, interdistance_va)

interdistance_all %>%
  filter(`Interdistance cat` %in% c("A", "B")) %>%
  graph_from_data_frame() %>%
  ggraph() +
  geom_edge_link(aes(alpha = `Interdistance num`)) +
  geom_node_point(size = 2) +
  geom_node_text(aes(label = name), vjust = 1.25, hjust = 1.25, size = 2.5) +
  theme_void() +
  facet_wrap(~ Category, nrow = 2) +
  theme(legend.position = "none")

Relationship between all locations considering Interdistance class of <500m and 500m - 1500m only (keeping training and validation separated).

The above graph gives an idea on how the locations from training and validation are related to each other, in terms of interdistance. Consider the jacket that contains locations CG, CH and CI. This jacket is part of the validation dataset (we know that from the data but we can infer it from the bottom part of the graph, since these 3 locations are connected by a dark line). We see that the only other jacket from validation, that is closer than 1500m with this jacket, is the one that contains locations BJ and BK. All the other jackets from validation, like the one with locations DT, DU and DV, is further than 1500m.

Further analyses and considerations on the interdistance data can be made and can potentially be incorporated in the model-building process.

3.3 training vs validation data

We make a simple plot of qc [MPA] vs z [m] for training and validation datasets, just to see if there are any significant differences.

plot13 <- training %>%
ggplot(aes(`z [m]`, `qc [MPa]`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_point(data = validation, aes(`z [m]`, `qc [MPa]`),
            alpha = 1/2, colour = "grey") +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 100)) +
  theme(panel.grid.minor = element_blank(),
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "training + validation")

plot14 <- training %>%
ggplot(aes(`z [m]`, `qc [MPa]`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_point(data = validation, aes(`z [m]`, `qc [MPa]`),
            alpha = 1/2, colour = "grey") +
  geom_point(data = training, aes(`z [m]`, `qc [MPa]`),
            alpha = 1,
            colour = "grey20") +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 100)) +
  labs(x = "") +
  theme(panel.grid.minor = element_blank(),
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "training")

plot15 <- training %>%
ggplot(aes(`z [m]`, `qc [MPa]`)) +
  geom_point(alpha = 1/2, colour = "grey") +
  geom_point(data = validation, aes(`z [m]`, `qc [MPa]`),
            alpha = 1/2, colour = "grey") +
  geom_point(data = validation, aes(`z [m]`, `qc [MPa]`),
            alpha = 1,
            colour = "grey20") +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 35), ylim = c(0, 100)) +
  labs(x = "") +
  theme(panel.grid.minor = element_blank(),
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "validation")

plot13 + plot14 + plot15

qc [MPA] vs z [m] for training and validation.

3.4 Relationship and correlation between parameters

For the purpose of our work, it is particularly important to understand the relationship between Blowcount [Blows/m] and all the features (i.e. predictors), so we get a better idea which features we will actually include in the model. A good starting point is to build a scatterplot matrix of the training dataset.

library(ggforce)

ggplot(training, aes(.panel_x, .panel_y)) +
  geom_point(alpha = 1/20, size = 0.5) +
  facet_matrix(vars(`Blowcount [Blows/m]`, `z [m]`, `qc [MPa]`, `fs [MPa]`, `u2 [MPa]`, `Normalised ENTRHU [-]`, `Bottom wall thickness [mm]`, `Pile penetration [m]`)) +
  theme(panel.grid.minor = element_blank(),
        strip.background = element_blank(),
        strip.text = element_text(colour = "grey20"))

Scatterplot matrix for training.

Notice that we have not included those parameters we know to not have any meaningful influence or that are duplicates. From the previous graph, we can grasp the relationship between Blowcount [Blows/m] and other parameters. For some parameters (z [m], Normalised ENTRHU [-]), some pattern is visually recognizable, while for other parameters, it is not that obvious. All this can be numerically expressed through a correlation plot.

library(corrplot)
library(RColorBrewer)

training_corr <- training %>%
  dplyr::select(`Blowcount [Blows/m]`, `z [m]`, `qc [MPa]`, `fs [MPa]`, `u2 [MPa]`, `Normalised ENTRHU [-]`, `Bottom wall thickness [mm]`, `Pile penetration [m]`)

corr_matrix <- cor(training_corr)

corrplot(corr_matrix,
         method = "color",
         type = "lower",
         tl.col = "black",
         col = brewer.pal(n = 10, name = "RdYlBu"),
         bg = "red",
         addCoef.col = "grey20",
         addgrid.col = "grey20",
         cl.cex = .75,
         tl.cex = .75,
         number.cex = 0.65,
         number.digits = 3,
         diag = FALSE)

Correlations between parameters for training.

By looking at the first column of the correlation plot, Blowcount [Blows/m] looks particularly well-correlated to both z [m] and Normalised ENTRHU [-]. Maybe surprisingly, the correlation with the CPT test parameters isn’t so strong (the coefficient of correlation barely passes the 0.5 mark, for qc [MPa]).

4 NEW FEATURES

Now we try an approach to introduce engineering/geotechnical knowledge by means of creating some additional parameter (i.e. feature) which hopefully provides engineering insights and potentially has better predictive performance. We use the available data to estimate two parameters:

• friction angle [°] - using the Kulhawy and Mayne 1990 relationship and,
• skin friction API [kPa] - which is the value of the unit skin friction according to the relationship proposed by API.

We do this for both, training and validation. The Vertical effective stress [kPa] is necessary asan input in assessments and it is provided within the normalised datasets. Some preparatory and data manipulation is needed at this point, especially considering that the normalised data contain few missing values (NA). Various approaches can be used to deal with the NA values (removing, replacing with the average value, etc) and here we choose to replace them with the next row value. Notice that the friction angle [°] is used here as an input in the estimation of skin friction API [kPa], not as a predictive feature per se.

vert_estress_tr <- training_no %>%
  mutate(`Ic [-]` = replace(`Ic [-]`, which(is.na(`Qt [-]`)), NA)) %>%
  fill(`area ratio [-]`, `qt [MPa]`, `Delta u2 [MPa]`, `Rf [%]`, `Bq [-]`, `Qt [-]`, `Fr [%]`, `qnet [MPa]`, `Ic [-]`, .direction = "up") %>%
  dplyr::select(`ID`, `Vertical effective stress [kPa]`)

training <- training %>%
  inner_join(vert_estress_tr, by = "ID") %>%
  mutate(`friction angle [°]` = 17.6 + 11 * log((`qc [MPa]`/0.1)/(sqrt(`Vertical effective stress [kPa]`/0.1))),
         `skin friction API [kPa]` = 0.8 * `Vertical effective stress [kPa]` * tan((`friction angle [°]` - 5)*3.14/180))

vert_estress_va <- validation_no %>%
  mutate(`Ic [-]` = replace(`Ic [-]`, which(is.na(`Qt [-]`)), NA)) %>%
  fill(`area ratio [-]`, `qt [MPa]`, `Delta u2 [MPa]`, `Rf [%]`, `Bq [-]`, `Qt [-]`, `Fr [%]`, `qnet [MPa]`, `Ic [-]`, .direction = "up") %>%
  dplyr::select(`ID`, `Vertical effective stress [kPa]`)

validation <- validation %>%
  inner_join(vert_estress_va, by = "ID") %>%
  mutate(`friction angle [°]` = 17.6 + 11 * log((`qc [MPa]`/0.1)/(sqrt(`Vertical effective stress [kPa]`/0.1))),
         `skin friction API [kPa]` = 0.8 * `Vertical effective stress [kPa]` * tan((`friction angle [°]` - 5)*3.14/180))

We can visualize the difference between skin friction API [kPa] and qc [MPa] in terms of their relationship with Blowcount [Blows/m]. The next graphs suggest that skin friction API [kPa] is a better predictor for `Blowcount [Blows/m], having a value of the coefficient of correlation around 0.72.

plot16 <- training %>%
ggplot(aes(`qc [MPa]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 100), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank())

plot17 <- training %>%
ggplot(aes(`fs [MPa]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 2), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank())

plot18 <- training %>%
ggplot(aes(`skin friction API [kPa]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 250), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank())

plot16 + plot17 + plot18

Comparison of Blowcount [Blows/m]’s relationship with qc [MPa], fs [MPa] and skin friction API [kPa].

training %>%
  dplyr::select(`Blowcount [Blows/m]`, `skin friction API [kPa]`) %>%
  cor() %>%
kable(digits = 3,
      align = "r") %>%
     kable_styling(full_width = F, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

	Blowcount [Blows/m]	skin friction API [kPa]
Blowcount [Blows/m]	1.000	0.717
skin friction API [kPa]	0.717	1.000

5 MODELING

We now proceed with the model-building process, starting from some simple linear models and then progressing to more advanced ones. Before that, we need to split the data.

5.1 Splitting the training data

The first thing we do is to randomly split the training data into:

• train - used to train the model/machine;
• test - used to evaluate how the model performs on new data.

Notice that we have also another set of data, validation, which is used to evaluate the model performance in the context of the competition we introduced at the top of this post.

training <- training %>%
  mutate(`Location ID` = as_factor(`Location ID`))

training_locations <- levels(training$`Location ID`)

set.seed(111)
test_locations <- sample(training_locations, 18)

test <- training %>% filter(`Location ID` %in% test_locations)
train <- training %>% filter (!(`Location ID` %in% test_locations))

5.2 Linear Regression models

Our first attempt involves considering Linear Regression models.

5.2.1 Simple Linear Regression

The idea of a Simple Linear Regression is to predict Blowcount [Blows/m] considering only one feature. We use Normalised ENTRHU [-].

library(broom)

model_slr <- lm(`Blowcount [Blows/m]` ~ `Normalised ENTRHU [-]`, data = train)

model_slr %>%
  glance() %>%
kable(digits = 8,
      align = "r") %>%
     kable_styling(full_width = T, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.4475658	0.4474183	22.19974	3034.898	0	1	-16936.28	33878.57	33897.25	1846136	3746	3748

model_slr %>%
  tidy() %>%
kable(digits = 8,
      align = "r") %>%
     kable_styling(full_width = T, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

term	estimate	std.error	statistic	p.value
(Intercept)	20.9068	0.8842616	23.64323	0
Normalised ENTRHU [-]	119.2639	2.1648957	55.08991	0

The above tables present some of the key features of the model, like adj.r.squared, p.value, Intercept’s estimate, Intercept’s std.error, etc. These values are useful to evaluate how the model performs. The reference metric, as described in the competition evaluation section, is the RMSE (Root Mean Square Error). Lower the RMSE value, the better. We can estimate RMSE as follows.

train_aug_slr <- model_slr %>%
  augment(data = train)

sqrt(sum((train_aug_slr$`Blowcount [Blows/m]` - train_aug_slr$.fitted)^2)/nrow(train_aug_slr))

## [1] 22.19382

We can also plot the model predictions and compare it to the actual data.

plot_slr1 <- train_aug_slr %>%
  ggplot(aes(`Normalised ENTRHU [-]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  geom_point(aes(y = .fitted), color = "tomato", alpha = 1) +
  expand_limits(x = 0, y = 0) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Model fit (red) vs actual data.",
       x = "Normalised ENTRHU [-]",
       y = "Blowcount [Blows/m]")

plot_slr2 <- train_aug_slr %>%
  ggplot(aes(.fitted, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  expand_limits(x = 0, y = 0) +
  geom_abline(color = "grey20", size = 1) +
  coord_fixed(xlim = c(0, 150), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Predicted vs actual Blowcount [Blows/m].",
       x = "Predicted Blowcount [Blows/m]",
       y = "Actual Blowcount [Blows/m]")

plot_slr3 <- train_aug_slr %>%
  ggplot(aes(`Normalised ENTRHU [-]`, .resid)) +
  geom_point(alpha = 1/20) +
  geom_hline(aes(yintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Scatter plot of residuals.",
       x = "Normalised ENTRHU [-]",
       y = "Residuals")

plot_slr4 <- train_aug_slr %>%
  ggplot(aes(.resid)) +
  geom_histogram(binwidth = 2, alpha = 1/4) +
  geom_vline(aes(xintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Histogram of residuals.",
       x = "Residuals",
       y = "Count") +
  coord_cartesian(xlim = c(-100, 100))

patch_slr1 <- plot_slr1 + plot_slr2
patch_slr2 <- plot_slr3 + plot_slr4

patch_slr1 / patch_slr2

Results for Simple Linear Regression.

The above plots give another overview of our model’s results and performance, in visual terms. As it was obvious, and as it is suggested by the adj.r.squared value as well, a Simple Linear Regression model is not likely to be a good fit for our data. In particular, the residuals scatter plot and histogram suggest that the residuals show some pattern (i.e. they are not random). In this context, we would like the residuals histogram to resemble a normal distribution.

5.2.2 Multiple Linear Regression

A Multiple Linear Regression is similar to the Simple Linear Regression, with the difference that, to predict Blowcount [Blows/m], we now consider more than one feature. We use:

• Normalised ENTRHU [-];
• z [m];
• skin friction API [kPa].

We choose to use these features based on their relatively good correlation with Blowcount [Blows/m]. Note that more rigorous and robust procedures for feature selection (i.e. deciding which features to include in the model) exist. One option could be to introduce a regularization technique by means of lasso regression.

The application steps of Multiple Linear Regression are in analogy of those used for Simple Linear Regression.

model_mlr <- lm(`Blowcount [Blows/m]` ~ `Normalised ENTRHU [-]` + `z [m]` + `skin friction API [kPa]`, data = train)

model_mlr %>%
  glance() %>%
kable(digits = 8,
      align = "r") %>%
     kable_styling(full_width = T, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.5365526	0.5361812	20.33873	1444.862	0	3	-16607.13	33224.26	33255.41	1548758	3744	3748

model_mlr %>%
  tidy() %>%
kable(digits = 8,
      align = "r") %>%
     kable_styling(full_width = T, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

term	estimate	std.error	statistic	p.value
(Intercept)	17.8893563	0.82998925	21.553720	0.000e+00
Normalised ENTRHU [-]	18.7555493	4.29131009	4.370588	1.273e-05
z [m]	1.2175538	0.11676109	10.427736	0.000e+00
skin friction API [kPa]	0.2475385	0.01849432	13.384571	0.000e+00

train_aug_mlr <- model_mlr %>%
  augment(data = train)

sqrt(sum((train_aug_mlr$`Blowcount [Blows/m]` - train_aug_mlr$.fitted)^2)/nrow(train_aug_mlr))

## [1] 20.32788

plot_mlr1 <- train_aug_mlr %>%
  ggplot(aes(`Normalised ENTRHU [-]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  geom_point(aes(y = .fitted), color = "tomato", alpha = 1) +
  expand_limits(x = 0, y = 0) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Model fit (red) vs actual data.",
       x = "Normalised ENTRHU [-]",
       y = "Blowcount [Blows/m]")

plot_mlr2 <- train_aug_mlr %>%
  ggplot(aes(.fitted, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  expand_limits(x = 0, y = 0) +
  geom_abline(color = "grey20", size = 1) +
  coord_fixed(xlim = c(0, 150), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Predicted vs actual Blowcount [Blows/m].",
       x = "Predicted Blowcount [Blows/m]",
       y = "Actual Blowcount [Blows/m]")

plot_mlr3 <- train_aug_mlr %>%
  ggplot(aes(`Normalised ENTRHU [-]`, .resid)) +
  geom_point(alpha = 1/20) +
  geom_hline(aes(yintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Scatter plot of residuals.",
       x = "Normalised ENTRHU [-]",
       y = "Residuals")

plot_mlr4 <- train_aug_mlr %>%
  ggplot(aes(.resid)) +
  geom_histogram(binwidth = 2, alpha = 1/4) +
  geom_vline(aes(xintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Histogram of residuals.",
       x = "Residuals",
       y = "Count") +
  coord_cartesian(xlim = c(-100, 100))

patch_mlr1 <- plot_mlr1 + plot_mlr2
patch_mlr2 <- plot_mlr3 + plot_mlr4

patch_mlr1 / patch_mlr2

Results for Multiple Linear Regression.

We see that, the Multiple Linear Regression model performs a bit better than the Simple Linear Regression model. Yet, we are far from capturing the trend of the data.

5.3 Natural splines

Since the relationship between blowcount and other parameters is obviously not perfectly linear, it’s in our interest to explore other models which account for nonlinearity. We explore Natural Splines, which model relationship of various degrees of freedom. These models are similar to Polynomial Regression models.

5.3.1 Second degree Natural Spline - one feature

We start with a Natural Spline with 2 degrees of freedom and one feature.

library(splines)

model_ns2 <- lm(`Blowcount [Blows/m]` ~ ns(`Normalised ENTRHU [-]`, 2), data = train)

model_ns2 %>%
  glance() %>%
kable(digits = 8,
      align = "r") %>%
     kable_styling(full_width = T, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.5254787	0.5252252	20.57754	2073.582	0	2	-16651.38	33310.77	33335.68	1585765	3745	3748

model_ns2 %>%
  tidy() %>%
kable(digits = 8,
      align = "r") %>%
     kable_styling(full_width = T, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

term	estimate	std.error	statistic	p.value
(Intercept)	17.73742	0.8664459	20.471466	0
ns(Normalised ENTRHU [-], 2)1	116.28418	1.8555944	62.666809	0
ns(Normalised ENTRHU [-], 2)2	15.67978	2.0841856	7.523216	0

train_aug_ns2 <- model_ns2 %>%
  augment(data = train)

sqrt(sum((train_aug_ns2$`Blowcount [Blows/m]` - train_aug_ns2$.fitted)^2)/nrow(train_aug_ns2))

## [1] 20.56931

plot_ns21 <- train_aug_ns2 %>%
  ggplot(aes(`Normalised ENTRHU [-]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  geom_point(aes(y = .fitted), color = "tomato", alpha = 1) +
  expand_limits(x = 0, y = 0) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Model fit (red) vs actual data.",
       x = "Normalised ENTRHU [-]",
       y = "Blowcount [Blows/m]")

plot_ns22 <- train_aug_ns2 %>%
  ggplot(aes(.fitted, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  expand_limits(x = 0, y = 0) +
  geom_abline(color = "grey20", size = 1) +
  coord_fixed(xlim = c(0, 150), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Predicted vs actual Blowcount [Blows/m].",
       x = "Predicted Blowcount [Blows/m]",
       y = "Actual Blowcount [Blows/m]")

plot_ns23 <- train_aug_ns2 %>%
  ggplot(aes(`Normalised ENTRHU [-]`, .resid)) +
  geom_point(alpha = 1/20) +
  geom_hline(aes(yintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Scatter plot of residuals.",
       x = "Normalised ENTRHU [-]",
       y = "Residuals")

plot_ns24 <- train_aug_ns2 %>%
  ggplot(aes(.resid)) +
  geom_histogram(binwidth = 2, alpha = 1/4) +
  geom_vline(aes(xintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Histogram of residuals.",
       x = "Residuals",
       y = "Count") +
  coord_cartesian(xlim = c(-100, 100))

patch_ns21 <- plot_ns21 + plot_ns22
patch_ns22 <- plot_ns23 + plot_ns24

patch_ns21 / patch_ns22

Results for Natural Spline with 2 degrees of freedom - one feature.

5.3.2 Second degree Natural Spline - multiple features

We explore the same model using three features.

model_mns2 <- lm(`Blowcount [Blows/m]` ~ ns(`Normalised ENTRHU [-]`, 2) + ns(`z [m]`, 2) + ns(`skin friction API [kPa]`, 2), data = train)

model_mns2 %>%
  glance() %>%
kable(digits = 8,
      align = "r") %>%
     kable_styling(full_width = T, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.6538748	0.6533197	17.58386	1177.871	0	6	-16060.13	32136.25	32186.08	1156688	3741	3748

model_mns2 %>%
  tidy() %>%
kable(digits = 8,
      align = "r") %>%
     kable_styling(full_width = T, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

term	estimate	std.error	statistic	p.value
(Intercept)	-3.479181	1.062089	-3.275789	0.00106328
ns(Normalised ENTRHU [-], 2)1	-4.445504	3.972912	-1.118954	0.26323175
ns(Normalised ENTRHU [-], 2)2	-35.723600	2.443284	-14.621142	0.00000000
ns(z [m], 2)1	60.878212	5.404193	11.264996	0.00000000
ns(z [m], 2)2	16.451251	2.789028	5.898560	0.00000000
ns(skin friction API [kPa], 2)1	110.762209	4.570665	24.233283	0.00000000
ns(skin friction API [kPa], 2)2	41.499418	3.439455	12.065695	0.00000000

train_aug_mns2 <- model_mns2 %>%
  augment(data = train)

sqrt(sum((train_aug_mns2$`Blowcount [Blows/m]` - train_aug_mns2$.fitted)^2)/nrow(train_aug_mns2))

## [1] 17.56743

plot_mns21 <- train_aug_mns2 %>%
  ggplot(aes(`Normalised ENTRHU [-]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  geom_point(aes(y = .fitted), color = "tomato", alpha = 1) +
  expand_limits(x = 0, y = 0) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Model fit (red) vs actual data.",
       x = "Normalised ENTRHU [-]",
       y = "Blowcount [Blows/m]")

plot_mns22 <- train_aug_mns2 %>%
  ggplot(aes(.fitted, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  expand_limits(x = 0, y = 0) +
  geom_abline(color = "grey20", size = 1) +
  coord_fixed(xlim = c(0, 150), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Predicted vs actual Blowcount [Blows/m].",
       x = "Predicted Blowcount [Blows/m]",
       y = "Actual Blowcount [Blows/m]")

plot_mns23 <- train_aug_mns2 %>%
  ggplot(aes(`Normalised ENTRHU [-]`, .resid)) +
  geom_point(alpha = 1/20) +
  geom_hline(aes(yintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Scatter plot of residuals.",
       x = "Normalised ENTRHU [-]",
       y = "Residuals")

plot_mns24 <- train_aug_mns2 %>%
  ggplot(aes(.resid)) +
  geom_histogram(binwidth = 2, alpha = 1/4) +
  geom_vline(aes(xintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Histogram of residuals.",
       x = "Residuals",
       y = "Count") +
  coord_cartesian(xlim = c(-100, 100))

patch_mns21 <- plot_mns21 + plot_mns22
patch_mns22 <- plot_mns23 + plot_mns24

patch_mns21 / patch_mns22

Results for Natural Spline with 2 degrees of freedom - multiple features.

This model is already an improvement from the previous ones, achieving an adj.r.squared of 0.67 and a RMSE around 17.1. The residuals histogram seems too look more like following a normal distribution and it’s also narrower, indicating smaller residual values.

5.3.3 Natural Spline of higher degrees of freedom

We expect Natural Spline models with higher degrees of freedom to perform better, considering their higher flexibility. To see how increasing the degrees of freedom impacts the model performance, we explore models with degrees of freedom ranging between 2 and 8, and compare them.

models_ns <- tibble(spline_df = 2:8) %>%
        mutate(lm_model = map(spline_df, ~ lm(`Blowcount [Blows/m]` ~ ns(`Normalised ENTRHU [-]`, df = .), data = train)))

augmented_unnested <- models_ns %>%
        mutate(augmented = map(lm_model, augment, data = train)) %>%
        unnest(augmented)

p1 <- augmented_unnested %>%
  ggplot(aes(`Normalised ENTRHU [-]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/100) +
  geom_line(aes(y = .fitted, colour = factor(spline_df)), alpha = 1, size = 1.5) +
  expand_limits(x = 0, y = 0) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Model fit vs actual data.",
       x = "Normalised ENTRHU [-]",
       y = "Blowcount [Blows/m]",
       colour = "Degrees of freedom") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(title.position = "top"))

glanced_models <- models_ns %>%
  mutate(glanced = map(lm_model, glance, data = train)) %>%
  unnest(glanced)

p2 <- glanced_models %>%
  ggplot() +
  geom_segment(aes(x = spline_df, xend = spline_df, y = 0.5, yend = adj.r.squared), size = 2, alpha = 1/2) +
  geom_point(data = glanced_models, aes(spline_df, adj.r.squared, colour = adj.r.squared), size = 5) +
  scale_color_distiller(palette = "Spectral", limits = c(0.52, 0.54)) +
  expand_limits(x = 2, y = .5) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  scale_x_continuous(breaks = c(2:10)) +
  labs(title = "Models comparison by adjusted R-squared value.",
       x = "Number of degrees of freedom",
       y = "Adjusted R-squared", 
       colour = "Adjusted R-squared") +
  theme(legend.position = "bottom",
        legend.key.width = unit(0.7, "cm")) +
  guides(color = guide_legend(title.position = "top"))

p1 + p2

Performance comparison for Natural Splines with degrees of freedom between 2 and 8.

It looks like there is no significant improvement in model’s performance after we apply 4 degrees of freedom. Thus, we continue with a Natural Spline model with 4 degrees of freedom and by using multiple features.

model_mns4 <- lm(`Blowcount [Blows/m]` ~ ns(`Normalised ENTRHU [-]`, 4) + ns(`z [m]`, 4) + ns(`skin friction API [kPa]`, 4), data = train)

model_mns4 %>%
  glance() %>%
kable(digits = 8,
      align = "r") %>%
     kable_styling(full_width = T, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

r.squared	adj.r.squared	sigma	statistic	p.value	df	logLik	AIC	BIC	deviance	df.residual	nobs
0.6772196	0.6761826	16.99416	653.0279	0	12	-15929.27	31886.53	31973.74	1078674	3735	3748

model_mns4 %>%
  tidy() %>%
kable(digits = 8,
      align = "r") %>%
     kable_styling(full_width = T, font_size = 11, position = "center") %>%
     row_spec(0, color = "grey10", background = "#F4F5F6")

term	estimate	std.error	statistic	p.value
(Intercept)	-8.548995	1.833634	-4.662323	0.00000324
ns(Normalised ENTRHU [-], 4)1	11.885604	2.500446	4.753394	0.00000208
ns(Normalised ENTRHU [-], 4)2	-21.529732	2.412246	-8.925182	0.00000000
ns(Normalised ENTRHU [-], 4)3	-10.065279	4.795385	-2.098951	0.03588818
ns(Normalised ENTRHU [-], 4)4	8.817843	4.138711	2.130577	0.03318915
ns(z [m], 4)1	37.744106	3.378004	11.173493	0.00000000
ns(z [m], 4)2	34.078242	3.019748	11.285128	0.00000000
ns(z [m], 4)3	83.329878	7.092886	11.748374	0.00000000
ns(z [m], 4)4	30.869633	3.730955	8.273922	0.00000000
ns(skin friction API [kPa], 4)1	55.549457	2.725780	20.379291	0.00000000
ns(skin friction API [kPa], 4)2	45.586043	2.814827	16.194971	0.00000000
ns(skin friction API [kPa], 4)3	84.954922	6.100541	13.925801	0.00000000
ns(skin friction API [kPa], 4)4	68.072852	4.307986	15.801548	0.00000000

train_aug_mns4 <- model_mns4 %>%
  augment(data = train)

sqrt(sum((train_aug_mns4$`Blowcount [Blows/m]` - train_aug_mns4$.fitted)^2)/nrow(train_aug_mns4))

## [1] 16.96467

plot_mns41 <- train_aug_mns4 %>%
  ggplot(aes(`Normalised ENTRHU [-]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  geom_point(aes(y = .fitted), color = "tomato", alpha = 1) +
  expand_limits(x = 0, y = 0) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Model fit (red) vs actual data.",
       x = "Normalised ENTRHU [-]",
       y = "Blowcount [Blows/m]")

plot_mns42 <- train_aug_mns4 %>%
  ggplot(aes(.fitted, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  expand_limits(x = 0, y = 0) +
  geom_abline(color = "grey20", size = 1) +
  coord_fixed(xlim = c(0, 150), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Predicted vs actual Blowcount [Blows/m].",
       x = "Predicted Blowcount [Blows/m]",
       y = "Actual Blowcount [Blows/m]")

plot_mns43 <- train_aug_mns4 %>%
  ggplot(aes(`Normalised ENTRHU [-]`, .resid)) +
  geom_point(alpha = 1/20) +
  geom_hline(aes(yintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Scatter plot of residuals.",
       x = "Normalised ENTRHU [-]",
       y = "Residuals")

plot_mns44 <- train_aug_mns4 %>%
  ggplot(aes(.resid)) +
  geom_histogram(binwidth = 2, alpha = 1/4) +
  geom_vline(aes(xintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Histogram of residuals.",
       x = "Residuals",
       y = "Count") +
  coord_cartesian(xlim = c(-100, 100))

patch_mns41 <- plot_mns41 + plot_mns42
patch_mns42 <- plot_mns43 + plot_mns44

patch_mns41 / patch_mns42

Results for Natural Spline with 4 degrees of freedom - multiple features.

5.3.4 Validate the best model against the test data

The last model we proposed, having an adj.r.squared of 0.67 and a RMSE around 16.9, seems to be the best-performing model so far. We validate it against the test data. Note that this is indeed the reason we created this dataset, separating it from the initial training data.

test$predictions <- predict(model_mns4, newdata = test)
sqrt(sum((test$'Blowcount [Blows/m]' - test$predictions)^2)/nrow(test))

## [1] 15.26106

plot_t1 <- test %>%
  ggplot(aes(`Normalised ENTRHU [-]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  geom_point(data = test, aes(`Normalised ENTRHU [-]`, predictions), color = "tomato", alpha = 1) +
  expand_limits(x = 0, y = 0) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Model fit (red) vs actual data.",
       x = "Normalised ENTRHU [-]",
       y = "Blowcount [Blows/m]")

plot_t2 <- test %>%
  ggplot(aes(predictions, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  expand_limits(x = 0, y = 0) +
  geom_abline(color = "grey20", size = 1) +
  coord_fixed(xlim = c(0, 150), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Predicted vs actual Blowcount [Blows/m].",
       x = "Predicted Blowcount [Blows/m]",
       y = "Actual Blowcount [Blows/m]")

plot_t3 <- test %>%
  ggplot(aes(`Normalised ENTRHU [-]`, predictions - `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  geom_hline(aes(yintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Scatter plot of residuals.",
       x = "Normalised ENTRHU [-]",
       y = "Residuals")

plot_t4 <- test %>%
  ggplot(aes(predictions - `Blowcount [Blows/m]`)) +
  geom_histogram(binwidth = 2, alpha = 1/4) +
  geom_vline(aes(xintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Histogram of residuals.",
       x = "Residuals",
       y = "Count") +
  coord_cartesian(xlim = c(-100, 100))

patch_t1 <- plot_t1 + plot_t2
patch_t2 <- plot_t3 + plot_t4

patch_t1 / patch_t2

Results for Natural Spline with 4 degrees of freedom - multiple features - applied to the test data.

The RMSE value of 15.2 and the above plots suggest that the model performs well and consistently against the test dataset. Let’s plot predicted vs actual Blowcount [Blows/m] for the 18 piles from test.

test %>%
  ggplot(aes(`z [m]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/5) +
  geom_step(data = test, aes(`z [m]`, predictions, group = `Location ID`),
            size = 1,
            alpha = 1,
            colour = "tomato") +
  scale_x_reverse() +
  scale_y_continuous(position = "right") +
  coord_flip(xlim = c(0, 30), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank(),
        strip.background = element_blank(),
        strip.text = element_text(colour = "grey20"),
        strip.placement = "outside") +
  facet_wrap(~`Location ID`, ncol = 6)

Predicted (red stepped line) vs actual (grey dots) Blowcount [Blows/m] for test piles.

Generally speaking, it looks like the predicted Blowcount [Blows/m] follow the actual values very well. Nonetheless, this is not the case for every Location ID. In few cases, the model considerably overestimates or underestimates the actual data. Further model improvements could address this issue.

The following table shows the relative error in predicting the total number of blows (Number of blows) for each pile.

test_error <- test %>%
  group_by(`Location ID`) %>%
  summarise(actual_blows = sum(`Blowcount [Blows/m]`),
            predicted_blows = sum(predictions),
            error = (predicted_blows - actual_blows)/actual_blows,
            abs_error = abs(error)) %>%
  arrange(desc(abs_error)) %>%
  mutate(error = round(error, 3),
         abs_error = round(abs_error, 3))

kable(top_n(test_error, 100),
      digits = 3,
      align = "r") %>%
  kable_styling(full_width = T, font_size = 11, position = "center") %>%
  row_spec(0, color = "grey10", background = "#F4F5F6")

Location ID	actual_blows	predicted_blows	error	abs_error
DA	1926	2567.084	0.333	0.333
CP	3626	2971.899	-0.180	0.180
DD	2184	2562.608	0.173	0.173
BV	2946	3309.033	0.123	0.123
AN	3066	3432.953	0.120	0.120
BS	3958	3485.130	-0.119	0.119
CT	3420	3023.141	-0.116	0.116
DS	3326	2947.367	-0.114	0.114
BM	2262	2517.060	0.113	0.113
CL	2834	3112.687	0.098	0.098
BT	3782	3434.316	-0.092	0.092
CF	3604	3837.019	0.065	0.065
DK	3514	3736.964	0.063	0.063
CA	2594	2707.734	0.044	0.044
AY	3056	2951.616	-0.034	0.034
EG	3570	3454.040	-0.032	0.032
DN	2940	2987.781	0.016	0.016
AS	3116	3129.253	0.004	0.004

library(scales)

test_error %>%
  ggplot(aes(error, `Location ID`)) +
  geom_segment(aes(x = 0, xend = error, y = `Location ID`, yend = `Location ID`), size = 2, alpha = 1/2) +
  geom_point(aes(colour = abs_error), size = 5) +
  scale_colour_distiller(palette = "Spectral", limits = c(0, 0.4)) +
  theme(panel.grid.minor = element_blank(),
        legend.key.height = unit(2.25, "cm")) +
  labs(x = "Error",
       y = "",
       colour = "Error") +
  geom_vline(xintercept = 0, color = "grey20", size = 1) +
  scale_x_continuous(labels = scales::percent_format(accuracy = .1)) +
  coord_cartesian(xlim = c(-0.2, 0.4))

Relative error in predicting the total number of blows for test piles.

We see that the relative error in predicting the total number of blows for each pile typically lies between 0% and 13%. Only one location (location DA) shows a much higher error, having an overestimation of around 33%. The mean absolute error for all locations is around 10%.

test_error %>%
  summarise(mean_error = mean(abs_error))

## # A tibble: 1 x 1
##   mean_error
##        <dbl>
## 1      0.102

5.4 Nonlinear Regression Models

In this section we investigate models that are inherently nonlinear in nature. The advantage of using these models rely on the fact that we don’t need to know or specify the nonlinearity of the data prior to model training. Among others, we consider models like neural networks, support vector machines, and random forests. The analysis is done within the framework of the caret package, which is a comprehensive and incredibly powerful machine learning tool for R. It provides a uniform interface to build predictive models and, among other, it contains tools/functions for data splitting, pre-processing, feature selection model tuning using resampling, variable importance estimation, etc. To date, 238 models are available within the caret package.

Note that we are not going into the details of the caret package. Also, not much elaboration is provided on the used models. For more on these topics please se the caret package documentation here and here.

5.4.1 Preparatory work

Before we continue with model training, we need to prepare the scene a bit by performing the following steps.

• Data splitting - we use the data splitting specified in section 5.1 (to be consistent with the previous models).
• Parallel computing - to increase the speed of computing (some of the models require considerable computing capabilities).

library(doParallel)

detectCores()
getDoParWorkers()
cl <- makePSOCKcluster(10)
registerDoParallel(cl)

• Resampling - we estimate the model performance by a technique named k-fold cross-validation. In our case, we use a 10-fold cross-validation technique, repeated 5 times. The basic idea of a k-fold cross-validation consists in using a subset of samples to fit a model and the remaining samples are used to estimate the efficacy of the model. Then, this process is repeated multiple times. This resampling process is defined through trainControl().

library(caret)

control_object <- trainControl(method = "repeatedcv",
                               repeats = 5,
                               number = 10)

5.4.2 Training models

We train the models here and then we discuss on their performance.

5.4.2.1 Boosted Trees

set.seed(111)

gbm <- train(`Blowcount [Blows/m]` ~ `Normalised ENTRHU [-]` + `z [m]` + `skin friction API [kPa]`,
             data = train,
             method = "gbm",
             tuneGrid = expand.grid(interaction.depth = seq(1, 7, by = 2),
                                    n.trees = seq(100, 1000, by = 50),
                                    shrinkage = c(0.01, 0.1),
                                    n.minobsinnode = c(2, 20)),
             verbose = FALSE,
             trControl = control_object)

5.4.2.2 Support Vector Machines

set.seed(111)

svm <- train(`Blowcount [Blows/m]` ~ `Normalised ENTRHU [-]` + `z [m]` + `skin friction API [kPa]`,
             data = train,
             method = "svmRadial",
             tuneLength = 15,
             preProc = c("center", "scale"),
             trControl = control_object)

5.4.2.3 Neural Networks

set.seed(111)

nnet <- train(`Blowcount [Blows/m]` ~ `Normalised ENTRHU [-]` + `z [m]` + `skin friction API [kPa]`,
              data = train,
              method = "avNNet",
              tuneGrid = expand.grid(decay = c(0.001, 0.01, 0.1),
                                     size = seq(1, 27, by = 2),
                                     bag = FALSE),
              preProc = c("center", "scale"),
              linout = TRUE,
              trace = FALSE,
              maxit = 1000,
              trControl = control_object)

5.4.2.4 Random Forests

set.seed(111)

rf <- train(`Blowcount [Blows/m]` ~ `Normalised ENTRHU [-]` + `z [m]` + `skin friction API [kPa]`,
            data = train,
            method = "rf",
            tuneLength = 10,
            ntrees = 1000,
            importance = TRUE,
            trControl = control_object)

## note: only 2 unique complexity parameters in default grid. Truncating the grid to 2 .

5.4.2.5 Cubist

set.seed(111)

cb <- train(`Blowcount [Blows/m]` ~ `Normalised ENTRHU [-]` + `z [m]` + `skin friction API [kPa]`,
            data = train,
            method = "cubist",
            tuneGrid = expand.grid(.committees = c(1, 5, 10, 50, 75, 100),
                                   .neighbors = c(0, 1, 3, 5, 7, 9)),
            trControl = control_object)

Stop parallel computing (we don’t need it anymore).

stopCluster(cl)

5.4.3 Model performance comparison

We put the models together and compare their performance in terms of RMSE.

all_models <- resamples(list("Boosted Trees" = gbm,
                             "Support Vector Machines" = svm,
                             "Neural Networks" = nnet,
                             "Random Forests" = rf,
                             "Cubist" = cb))

gbm_RMSE <- all_models$values %>%
  select(Resample, `Boosted Trees~RMSE`) %>%
  rename(RMSE = `Boosted Trees~RMSE`) %>%
  mutate(Model = "Boosted Trees")

svm_RMSE <- all_models$values %>%
  select(Resample, `Support Vector Machines~RMSE`) %>%
  rename(RMSE = `Support Vector Machines~RMSE`) %>%
  mutate(Model = "Support Vector Machines")

nnet_RMSE <- all_models$values %>%
  select(Resample, `Neural Networks~RMSE`) %>%
  rename(RMSE = `Neural Networks~RMSE`) %>%
  mutate(Model = "Neural Networks")

rf_RMSE <- all_models$values %>%
  select(Resample, `Random Forests~RMSE`) %>%
  rename(RMSE = `Random Forests~RMSE`) %>%
  mutate(Model = "Random Forests")

cb_RMSE <- all_models$values %>%
  select(Resample, `Cubist~RMSE`) %>%
  rename(RMSE = `Cubist~RMSE`) %>%
  mutate(Model = "Cubist")

all_RMSE <- bind_rows(gbm_RMSE, svm_RMSE, nnet_RMSE, rf_RMSE, cb_RMSE)

kable(all_RMSE,
      digits = 3,
      caption = "RMSE values for all models.",
      align = "r") %>%
  kable_styling(full_width = T, font_size = 11, position = "center") %>%
  row_spec(0, color = "grey10", background = "#F4F5F6") %>%
  scroll_box(height = "300px")

RMSE values for all models.

Resample	RMSE	Model
Fold01.Rep1	16.099	Boosted Trees
Fold01.Rep2	16.893	Boosted Trees
Fold01.Rep3	16.585	Boosted Trees
Fold01.Rep4	17.713	Boosted Trees
Fold01.Rep5	16.167	Boosted Trees
Fold02.Rep1	15.602	Boosted Trees
Fold02.Rep2	14.386	Boosted Trees
Fold02.Rep3	16.885	Boosted Trees
Fold02.Rep4	16.177	Boosted Trees
Fold02.Rep5	16.844	Boosted Trees
Fold03.Rep1	15.678	Boosted Trees
Fold03.Rep2	15.560	Boosted Trees
Fold03.Rep3	16.715	Boosted Trees
Fold03.Rep4	16.984	Boosted Trees
Fold03.Rep5	16.601	Boosted Trees
Fold04.Rep1	17.007	Boosted Trees
Fold04.Rep2	16.288	Boosted Trees
Fold04.Rep3	15.689	Boosted Trees
Fold04.Rep4	16.703	Boosted Trees
Fold04.Rep5	16.022	Boosted Trees
Fold05.Rep1	15.156	Boosted Trees
Fold05.Rep2	16.037	Boosted Trees
Fold05.Rep3	13.842	Boosted Trees
Fold05.Rep4	14.720	Boosted Trees
Fold05.Rep5	15.199	Boosted Trees
Fold06.Rep1	14.469	Boosted Trees
Fold06.Rep2	16.216	Boosted Trees
Fold06.Rep3	15.422	Boosted Trees
Fold06.Rep4	15.421	Boosted Trees
Fold06.Rep5	15.657	Boosted Trees
Fold07.Rep1	17.102	Boosted Trees
Fold07.Rep2	14.901	Boosted Trees
Fold07.Rep3	16.116	Boosted Trees
Fold07.Rep4	15.398	Boosted Trees
Fold07.Rep5	15.292	Boosted Trees
Fold08.Rep1	17.053	Boosted Trees
Fold08.Rep2	18.169	Boosted Trees
Fold08.Rep3	17.881	Boosted Trees
Fold08.Rep4	15.278	Boosted Trees
Fold08.Rep5	17.015	Boosted Trees
Fold09.Rep1	15.866	Boosted Trees
Fold09.Rep2	15.920	Boosted Trees
Fold09.Rep3	15.409	Boosted Trees
Fold09.Rep4	15.598	Boosted Trees
Fold09.Rep5	15.215	Boosted Trees
Fold10.Rep1	16.121	Boosted Trees
Fold10.Rep2	15.896	Boosted Trees
Fold10.Rep3	15.794	Boosted Trees
Fold10.Rep4	16.319	Boosted Trees
Fold10.Rep5	16.050	Boosted Trees
Fold01.Rep1	16.528	Support Vector Machines
Fold01.Rep2	17.512	Support Vector Machines
Fold01.Rep3	17.377	Support Vector Machines
Fold01.Rep4	17.636	Support Vector Machines
Fold01.Rep5	16.696	Support Vector Machines
Fold02.Rep1	15.211	Support Vector Machines
Fold02.Rep2	14.638	Support Vector Machines
Fold02.Rep3	17.494	Support Vector Machines
Fold02.Rep4	16.876	Support Vector Machines
Fold02.Rep5	17.053	Support Vector Machines
Fold03.Rep1	16.236	Support Vector Machines
Fold03.Rep2	15.947	Support Vector Machines
Fold03.Rep3	16.766	Support Vector Machines
Fold03.Rep4	17.163	Support Vector Machines
Fold03.Rep5	16.893	Support Vector Machines
Fold04.Rep1	17.762	Support Vector Machines
Fold04.Rep2	16.280	Support Vector Machines
Fold04.Rep3	15.758	Support Vector Machines
Fold04.Rep4	17.225	Support Vector Machines
Fold04.Rep5	16.387	Support Vector Machines
Fold05.Rep1	15.095	Support Vector Machines
Fold05.Rep2	16.318	Support Vector Machines
Fold05.Rep3	14.439	Support Vector Machines
Fold05.Rep4	15.100	Support Vector Machines
Fold05.Rep5	15.536	Support Vector Machines
Fold06.Rep1	14.680	Support Vector Machines
Fold06.Rep2	16.166	Support Vector Machines
Fold06.Rep3	15.621	Support Vector Machines
Fold06.Rep4	15.561	Support Vector Machines
Fold06.Rep5	16.468	Support Vector Machines
Fold07.Rep1	17.722	Support Vector Machines
Fold07.Rep2	15.570	Support Vector Machines
Fold07.Rep3	16.511	Support Vector Machines
Fold07.Rep4	15.512	Support Vector Machines
Fold07.Rep5	15.492	Support Vector Machines
Fold08.Rep1	17.612	Support Vector Machines
Fold08.Rep2	18.556	Support Vector Machines
Fold08.Rep3	18.004	Support Vector Machines
Fold08.Rep4	15.315	Support Vector Machines
Fold08.Rep5	17.318	Support Vector Machines
Fold09.Rep1	16.165	Support Vector Machines
Fold09.Rep2	15.728	Support Vector Machines
Fold09.Rep3	15.348	Support Vector Machines
Fold09.Rep4	15.760	Support Vector Machines
Fold09.Rep5	14.962	Support Vector Machines
Fold10.Rep1	16.286	Support Vector Machines
Fold10.Rep2	16.657	Support Vector Machines
Fold10.Rep3	16.292	Support Vector Machines
Fold10.Rep4	17.151	Support Vector Machines
Fold10.Rep5	16.732	Support Vector Machines
Fold01.Rep1	15.736	Neural Networks
Fold01.Rep2	17.208	Neural Networks
Fold01.Rep3	16.718	Neural Networks
Fold01.Rep4	17.040	Neural Networks
Fold01.Rep5	16.164	Neural Networks
Fold02.Rep1	15.268	Neural Networks
Fold02.Rep2	14.670	Neural Networks
Fold02.Rep3	17.005	Neural Networks
Fold02.Rep4	16.266	Neural Networks
Fold02.Rep5	17.155	Neural Networks
Fold03.Rep1	15.738	Neural Networks
Fold03.Rep2	15.997	Neural Networks
Fold03.Rep3	16.470	Neural Networks
Fold03.Rep4	16.570	Neural Networks
Fold03.Rep5	16.107	Neural Networks
Fold04.Rep1	17.436	Neural Networks
Fold04.Rep2	16.072	Neural Networks
Fold04.Rep3	15.985	Neural Networks
Fold04.Rep4	16.816	Neural Networks
Fold04.Rep5	15.538	Neural Networks
Fold05.Rep1	15.171	Neural Networks
Fold05.Rep2	16.279	Neural Networks
Fold05.Rep3	14.288	Neural Networks
Fold05.Rep4	15.002	Neural Networks
Fold05.Rep5	14.981	Neural Networks
Fold06.Rep1	14.168	Neural Networks
Fold06.Rep2	15.676	Neural Networks
Fold06.Rep3	15.463	Neural Networks
Fold06.Rep4	15.858	Neural Networks
Fold06.Rep5	15.901	Neural Networks
Fold07.Rep1	16.921	Neural Networks
Fold07.Rep2	15.037	Neural Networks
Fold07.Rep3	16.030	Neural Networks
Fold07.Rep4	15.312	Neural Networks
Fold07.Rep5	15.721	Neural Networks
Fold08.Rep1	17.165	Neural Networks
Fold08.Rep2	17.783	Neural Networks
Fold08.Rep3	17.704	Neural Networks
Fold08.Rep4	15.366	Neural Networks
Fold08.Rep5	16.683	Neural Networks
Fold09.Rep1	15.754	Neural Networks
Fold09.Rep2	15.470	Neural Networks
Fold09.Rep3	14.933	Neural Networks
Fold09.Rep4	16.166	Neural Networks
Fold09.Rep5	15.534	Neural Networks
Fold10.Rep1	16.380	Neural Networks
Fold10.Rep2	16.187	Neural Networks
Fold10.Rep3	15.924	Neural Networks
Fold10.Rep4	16.634	Neural Networks
Fold10.Rep5	16.517	Neural Networks
Fold01.Rep1	15.365	Random Forests
Fold01.Rep2	16.292	Random Forests
Fold01.Rep3	15.618	Random Forests
Fold01.Rep4	16.994	Random Forests
Fold01.Rep5	15.255	Random Forests
Fold02.Rep1	15.714	Random Forests
Fold02.Rep2	14.688	Random Forests
Fold02.Rep3	16.411	Random Forests
Fold02.Rep4	15.962	Random Forests
Fold02.Rep5	16.036	Random Forests
Fold03.Rep1	15.312	Random Forests
Fold03.Rep2	14.772	Random Forests
Fold03.Rep3	16.543	Random Forests
Fold03.Rep4	16.033	Random Forests
Fold03.Rep5	15.624	Random Forests
Fold04.Rep1	16.148	Random Forests
Fold04.Rep2	16.332	Random Forests
Fold04.Rep3	14.804	Random Forests
Fold04.Rep4	16.231	Random Forests
Fold04.Rep5	15.388	Random Forests
Fold05.Rep1	14.062	Random Forests
Fold05.Rep2	15.585	Random Forests
Fold05.Rep3	13.019	Random Forests
Fold05.Rep4	13.993	Random Forests
Fold05.Rep5	14.575	Random Forests
Fold06.Rep1	13.792	Random Forests
Fold06.Rep2	16.092	Random Forests
Fold06.Rep3	14.980	Random Forests
Fold06.Rep4	14.497	Random Forests
Fold06.Rep5	14.712	Random Forests
Fold07.Rep1	16.143	Random Forests
Fold07.Rep2	14.246	Random Forests
Fold07.Rep3	15.592	Random Forests
Fold07.Rep4	14.521	Random Forests
Fold07.Rep5	15.323	Random Forests
Fold08.Rep1	16.371	Random Forests
Fold08.Rep2	16.933	Random Forests
Fold08.Rep3	17.364	Random Forests
Fold08.Rep4	14.776	Random Forests
Fold08.Rep5	16.323	Random Forests
Fold09.Rep1	14.631	Random Forests
Fold09.Rep2	15.350	Random Forests
Fold09.Rep3	14.735	Random Forests
Fold09.Rep4	15.857	Random Forests
Fold09.Rep5	14.345	Random Forests
Fold10.Rep1	15.068	Random Forests
Fold10.Rep2	14.500	Random Forests
Fold10.Rep3	15.366	Random Forests
Fold10.Rep4	15.519	Random Forests
Fold10.Rep5	15.448	Random Forests
Fold01.Rep1	15.883	Cubist
Fold01.Rep2	16.848	Cubist
Fold01.Rep3	16.438	Cubist
Fold01.Rep4	17.456	Cubist
Fold01.Rep5	16.010	Cubist
Fold02.Rep1	15.574	Cubist
Fold02.Rep2	14.889	Cubist
Fold02.Rep3	16.890	Cubist
Fold02.Rep4	16.065	Cubist
Fold02.Rep5	17.243	Cubist
Fold03.Rep1	15.856	Cubist
Fold03.Rep2	15.958	Cubist
Fold03.Rep3	16.510	Cubist
Fold03.Rep4	16.660	Cubist
Fold03.Rep5	15.962	Cubist
Fold04.Rep1	17.266	Cubist
Fold04.Rep2	16.067	Cubist
Fold04.Rep3	15.655	Cubist
Fold04.Rep4	16.260	Cubist
Fold04.Rep5	15.647	Cubist
Fold05.Rep1	14.726	Cubist
Fold05.Rep2	16.052	Cubist
Fold05.Rep3	13.820	Cubist
Fold05.Rep4	14.646	Cubist
Fold05.Rep5	15.088	Cubist
Fold06.Rep1	14.632	Cubist
Fold06.Rep2	15.992	Cubist
Fold06.Rep3	15.044	Cubist
Fold06.Rep4	15.200	Cubist
Fold06.Rep5	15.592	Cubist
Fold07.Rep1	16.871	Cubist
Fold07.Rep2	14.986	Cubist
Fold07.Rep3	16.169	Cubist
Fold07.Rep4	15.456	Cubist
Fold07.Rep5	15.695	Cubist
Fold08.Rep1	17.076	Cubist
Fold08.Rep2	17.512	Cubist
Fold08.Rep3	17.701	Cubist
Fold08.Rep4	15.363	Cubist
Fold08.Rep5	17.108	Cubist
Fold09.Rep1	15.283	Cubist
Fold09.Rep2	15.736	Cubist
Fold09.Rep3	15.292	Cubist
Fold09.Rep4	15.804	Cubist
Fold09.Rep5	14.847	Cubist
Fold10.Rep1	15.642	Cubist
Fold10.Rep2	15.590	Cubist
Fold10.Rep3	16.190	Cubist
Fold10.Rep4	16.659	Cubist
Fold10.Rep5	15.971	Cubist

The above table contains the RMSE values for the resampling results for all models. A plot of these data is shown in the following.

median_RMSE <- all_RMSE %>%
  group_by(Model) %>%
  summarise(`median RMSE` = median(RMSE))

all_RMSE %>%
  ggplot(aes(RMSE, fct_reorder(Model, RMSE, median))) +
  geom_point(aes(fill = RMSE), size = 5, shape = 21, colour = "grey40") +
  scale_fill_distiller(palette = "Spectral") +
  labs(y = "") +
  theme(panel.grid.minor = element_blank(),
        legend.position = "none") +
  geom_point(data = median_RMSE, aes(`median RMSE`, Model), size = 1, colour = "grey20", shape = "|", stroke = 10)

RMSE values for the resampling results for all models.

5.4.4 Apply the best model to the test data

We validate the best model (Random Forests, choosed based on the median value of RMSE) by checking its performance against the test data. We get a RMSE value of around 13.5, which is a better value compared to previous less-complex models.

test$predictions <- predict(rf, newdata = test)
sqrt(sum((test$'Blowcount [Blows/m]' - test$predictions)^2)/nrow(test))

## [1] 13.57531

plot_rf1 <- test %>%
  ggplot(aes(`Normalised ENTRHU [-]`, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  geom_point(data = test, aes(`Normalised ENTRHU [-]`, predictions), color = "tomato", alpha = 1) +
  expand_limits(x = 0, y = 0) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Model fit (red) vs actual data.",
       x = "Normalised ENTRHU [-]",
       y = "Blowcount [Blows/m]")

plot_rf2 <- test %>%
  ggplot(aes(predictions, `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  expand_limits(x = 0, y = 0) +
  geom_abline(color = "grey20", size = 1) +
  coord_fixed(xlim = c(0, 150), ylim = c(0, 150)) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Predicted vs actual Blowcount [Blows/m]",
       x = "Predicted Blowcount [Blows/m]",
       y = "Actual Blowcount [Blows/m]")

plot_rf3 <- test %>%
  ggplot(aes(`Normalised ENTRHU [-]`, predictions - `Blowcount [Blows/m]`)) +
  geom_point(alpha = 1/20) +
  geom_hline(aes(yintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Scatter plot of residuals.",
       x = "Normalised ENTRHU [-]",
       y = "Residuals")

plot_rf4 <- test %>%
  ggplot(aes(predictions - `Blowcount [Blows/m]`)) +
  geom_histogram(binwidth = 2, alpha = 1/5) +
  geom_vline(aes(xintercept = 0), color = "grey20", size = 1) +
  theme(panel.grid.minor = element_blank(),
        aspect.ratio = 1,
        plot.title = element_text(size = 9, face = "italic")) +
  labs(title = "Histogram of residuals.",
       x = "Residuals",
       y = "Count") +
  coord_cartesian(xlim = c(-100, 100))

patch_rf1 <- plot_rf1 + plot_rf2
patch_rf2 <- plot_rf3 + plot_rf4

patch_rf1 / patch_rf2

Results for Random Forests model applied to the test dataset.

In analogy to what we did for the Natural Spline models, we can estimate the relative error in predicting the total number of blows for each pile.

test_error <- test %>%
  group_by(`Location ID`) %>%
  summarise(actual_blows = sum(`Blowcount [Blows/m]`),
            predicted_blows = sum(predictions),
            error = (predicted_blows - actual_blows)/actual_blows,
            abs_error = abs(error)) %>%
  arrange(desc(abs_error)) %>%
  mutate(error = round(error, 3),
         abs_error = round(abs_error, 3))

kable(top_n(test_error, 100),
      digits = 3,
      align = "r") %>%
  kable_styling(full_width = T, font_size = 11, position = "center") %>%
  row_spec(0, color = "grey10", background = "#F4F5F6")

Location ID	actual_blows	predicted_blows	error	abs_error
DA	1926	2512.189	0.304	0.304
CP	3626	3081.291	-0.150	0.150
DD	2184	2449.782	0.122	0.122
CT	3420	3063.949	-0.104	0.104
BM	2262	2495.518	0.103	0.103
BS	3958	3550.212	-0.103	0.103
DS	3326	3024.430	-0.091	0.091
BT	3782	3478.317	-0.080	0.080
BV	2946	3159.839	0.073	0.073
AN	3066	3266.817	0.065	0.065
CL	2834	2996.335	0.057	0.057
CF	3604	3779.436	0.049	0.049
DN	2940	3068.092	0.044	0.044
DK	3514	3644.969	0.037	0.037
AY	3056	2970.421	-0.028	0.028
AS	3116	3031.852	-0.027	0.027
EG	3570	3644.214	0.021	0.021
CA	2594	2603.164	0.004	0.004

test_error %>%
  ggplot(aes(error, `Location ID`)) +
  geom_segment(aes(x = 0, xend = error, y = `Location ID`, yend = `Location ID`), size = 2, alpha = 1/2) +
  geom_point(aes(colour = abs_error), size = 5) +
  scale_colour_distiller(palette = "Spectral", limits = c(0, 0.4)) +
  theme(panel.grid.minor = element_blank(),
        legend.key.height = unit(2.25, "cm")) +
  labs(x = "Error",
       y = "",
       colour = "Error") +
  geom_vline(xintercept = 0, color = "grey20", size = 1) +
  scale_x_continuous(labels = scales::percent_format(accuracy = .1)) +
  coord_cartesian(xlim = c(-0.2, 0.4))

Relative error in predicting the total number of blows for test piles.

test_error %>%
  summarise(mean_error = mean(abs_error))

## # A tibble: 1 x 1
##   mean_error
##        <dbl>
## 1     0.0812

The results for the Random Forests model are similar to the ones from Natural Splines, but slightly better. We reach an average error of around 8%.

6 SUMMARY

Let’s make a short summary of the work presented in this post, by considering few discussion points.

• Is our model’s predictive accuracy acceptable? - We were able to achieve values of RMSE as low as 13.5. This is consistent with a relative error in predicting the total number of blows for a pile as low as 8%. I assume, the best way to create a better idea on whether this error level is acceptable, is to compare it with the error in predicting pile driveability by means of other methods used in the current engineering practice.
  
• How can we improve our model? - Of course. Some points have already been emphasized along the post but let’s sum up some of the obvious ways we can improve the performance of our model:
  • we can explore other models, non-considered here;
  • a more robust feature selection method can be implemented;
  • we might insist more in introducing engineering/geotechnical knowledge, e.g. by estimating other parameters which are better predictors of the number of blows.
• What about the data? - When building our models we made use of some robust data but, as described in the start of the post, the soil data basically consist of CPT registrations. Normally, in a project, we have in our disposal much more data gained during the site investigation process. These additional data can be potentially included in our models and improve it. Some of these data are:
  • exact coordinates for each pile;
  • ground model where all soil units and their distribution along the site;
  • data from in-situ tests other than CPT;
  • data from laboratory tests;
  • data from other similar sites or nearby sites.

---

That’s it! Thanks for reading 👋

---

7 SESSION INFO

R Version

R version 4.1.3 (2022-03-10)

Packages

 package      * version    date (UTC) lib source
 assertthat     0.2.1      2019-03-21 [1] CRAN (R 4.1.3)
 backports      1.4.1      2021-12-13 [1] CRAN (R 4.1.2)
 bit            4.0.4      2020-08-04 [1] CRAN (R 4.1.3)
 bit64          4.0.5      2020-08-30 [1] CRAN (R 4.1.3)
 broom        * 0.7.12     2022-01-28 [1] CRAN (R 4.1.3)
 bslib          0.3.1      2021-10-06 [1] CRAN (R 4.1.3)
 caret        * 6.0-91     2022-03-11 [1] CRAN (R 4.1.3)
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 cli            3.2.0      2022-02-14 [1] CRAN (R 4.1.3)
 clipr          0.8.0      2022-02-22 [1] CRAN (R 4.1.3)
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 dbplyr         2.1.1      2021-04-06 [1] CRAN (R 4.1.3)
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 dplyr        * 1.0.8      2022-02-08 [1] CRAN (R 4.1.3)
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 gbm            2.1.8      2020-07-15 [1] CRAN (R 4.1.3)
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 ggforce      * 0.3.3      2021-03-05 [1] CRAN (R 4.1.3)
 ggplot2      * 3.3.5      2021-06-25 [1] CRAN (R 4.1.3)
 ggraph       * 2.0.5      2021-02-23 [1] CRAN (R 4.1.3)
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 glue           1.6.2      2022-02-24 [1] CRAN (R 4.1.3)
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 gtable         0.3.0      2019-03-25 [1] CRAN (R 4.1.3)
 hardhat        0.2.0      2022-01-24 [1] CRAN (R 4.1.3)
 haven          2.4.3      2021-08-04 [1] CRAN (R 4.1.3)
 highr          0.9        2021-04-16 [1] CRAN (R 4.1.3)
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 htmltools      0.5.2      2021-08-25 [1] CRAN (R 4.1.3)
 httr           1.4.2      2020-07-20 [1] CRAN (R 4.1.3)
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 jsonlite       1.8.0      2022-02-22 [1] CRAN (R 4.1.3)
 kableExtra   * 1.3.4      2021-02-20 [1] CRAN (R 4.1.3)
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 knitr        * 1.38       2022-03-25 [1] CRAN (R 4.1.3)
 labeling       0.4.2      2020-10-20 [1] CRAN (R 4.1.1)
 lattice      * 0.20-45    2021-09-22 [2] CRAN (R 4.1.3)
 lava           1.6.10     2021-09-02 [1] CRAN (R 4.1.3)
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 listenv        0.8.0      2019-12-05 [1] CRAN (R 4.1.3)
 lubridate      1.8.0      2021-10-07 [1] CRAN (R 4.1.3)
 magrittr       2.0.3      2022-03-30 [1] CRAN (R 4.1.3)
 MASS           7.3-55     2022-01-16 [2] CRAN (R 4.1.3)
 Matrix         1.4-0      2021-12-08 [2] CRAN (R 4.1.3)
 ModelMetrics   1.2.2.2    2020-03-17 [1] CRAN (R 4.1.3)
 modelr         0.1.8      2020-05-19 [1] CRAN (R 4.1.3)
 munsell        0.5.0      2018-06-12 [1] CRAN (R 4.1.3)
 nlme           3.1-155    2022-01-16 [2] CRAN (R 4.1.3)
 nnet           7.3-17     2022-01-16 [2] CRAN (R 4.1.3)
 parallelly     1.31.0     2022-04-07 [1] CRAN (R 4.1.3)
 patchwork    * 1.1.1      2020-12-17 [1] CRAN (R 4.1.3)
 pillar         1.7.0      2022-02-01 [1] CRAN (R 4.1.3)
 pkgconfig      2.0.3      2019-09-22 [1] CRAN (R 4.1.3)
 plyr           1.8.7      2022-03-24 [1] CRAN (R 4.1.3)
 png            0.1-7      2013-12-03 [1] CRAN (R 4.1.1)
 polyclip       1.10-0     2019-03-14 [1] CRAN (R 4.1.1)
 pROC           1.18.0     2021-09-03 [1] CRAN (R 4.1.3)
 prodlim        2019.11.13 2019-11-17 [1] CRAN (R 4.1.3)
 purrr        * 0.3.4      2020-04-17 [1] CRAN (R 4.1.3)
 R6             2.5.1      2021-08-19 [1] CRAN (R 4.1.3)
 randomForest   4.7-1      2022-02-03 [1] CRAN (R 4.1.3)
 RColorBrewer * 1.1-3      2022-04-03 [1] CRAN (R 4.1.3)
 Rcpp           1.0.8.3    2022-03-17 [1] CRAN (R 4.1.3)
 readr        * 2.1.2      2022-01-30 [1] CRAN (R 4.1.3)
 readxl         1.4.0      2022-03-28 [1] CRAN (R 4.1.3)
 recipes        0.2.0      2022-02-18 [1] CRAN (R 4.1.3)
 reprex         2.0.1      2021-08-05 [1] CRAN (R 4.1.3)
 reshape2       1.4.4      2020-04-09 [1] CRAN (R 4.1.3)
 rlang          1.0.2      2022-03-04 [1] CRAN (R 4.1.3)
 rmarkdown      2.13       2022-03-10 [1] CRAN (R 4.1.3)
 rpart          4.1.16     2022-01-24 [2] CRAN (R 4.1.3)
 rprojroot      2.0.3      2022-04-02 [1] CRAN (R 4.1.3)
 rstudioapi     0.13       2020-11-12 [1] CRAN (R 4.1.3)
 rvest          1.0.2      2021-10-16 [1] CRAN (R 4.1.3)
 sass           0.4.1      2022-03-23 [1] CRAN (R 4.1.3)
 scales       * 1.1.1      2020-05-11 [1] CRAN (R 4.1.3)
 sessioninfo    1.2.2      2021-12-06 [1] CRAN (R 4.1.3)
 stringi        1.7.6      2021-11-29 [1] CRAN (R 4.1.2)
 stringr      * 1.4.0      2019-02-10 [1] CRAN (R 4.1.3)
 survival       3.2-13     2021-08-24 [2] CRAN (R 4.1.3)
 svglite        2.1.0      2022-02-03 [1] CRAN (R 4.1.3)
 systemfonts    1.0.4      2022-02-11 [1] CRAN (R 4.1.3)
 tibble       * 3.1.6      2021-11-07 [1] CRAN (R 4.1.3)
 tidygraph      1.2.1      2022-04-05 [1] CRAN (R 4.1.3)
 tidyr        * 1.2.0      2022-02-01 [1] CRAN (R 4.1.3)
 tidyselect     1.1.2      2022-02-21 [1] CRAN (R 4.1.3)
 tidyverse    * 1.3.1      2021-04-15 [1] CRAN (R 4.1.3)
 timeDate       3043.102   2018-02-21 [1] CRAN (R 4.1.2)
 tweenr         1.0.2      2021-03-23 [1] CRAN (R 4.1.3)
 tzdb           0.3.0      2022-03-28 [1] CRAN (R 4.1.3)
 utf8           1.2.2      2021-07-24 [1] CRAN (R 4.1.3)
 vctrs          0.4.0      2022-03-30 [1] CRAN (R 4.1.3)
 viridis        0.6.2      2021-10-13 [1] CRAN (R 4.1.3)
 viridisLite    0.4.0      2021-04-13 [1] CRAN (R 4.1.3)
 vroom          1.5.7      2021-11-30 [1] CRAN (R 4.1.3)
 webshot        0.5.2      2019-11-22 [1] CRAN (R 4.1.3)
 withr          2.5.0      2022-03-03 [1] CRAN (R 4.1.3)
 xfun           0.30       2022-03-02 [1] CRAN (R 4.1.3)
 xml2           1.3.3      2021-11-30 [1] CRAN (R 4.1.3)
 yaml           2.3.5      2022-02-21 [1] CRAN (R 4.1.2)

 [1] C:/Users/User/OneDrive/Documents/R/win-library/4.1
 [2] C:/Program Files/R/R-4.1.3/library