Interpretable gradient boosting based ensemble learning and African vultures optimization algorithm optimization for estimating deflection induced by excavation
. Key Laboratory of Urban Security and Disaster Engineering (Ministry of Education), Beijing University of Technology, Beijing 100124, China . Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University (PolyU), Hong Kong 999077, China
Intelligent construction has become an inevitable trend in the development of the construction industry. In the excavation project, using machine learning methods for early warning can improve construction efficiency and quality and reduce the chances of damage in the excavation process. An interpretable gradient boosting based ensemble learning framework enhanced by the African Vultures Optimization Algorithm (AVOA) was proposed and evaluated in estimating the diaphragm wall deflections induced by excavation. We investigated and compared the performance of machine learning models in predicting deflections induced by excavation based on a database generated by finite element simulations. First, we exploratively analyzed these data to discover the relationship between features. We used several state-of-the-art intelligent models based on gradient boosting and several simple models for model selection. The hyperparameters for all models in evaluation are optimized using AVOA, and then the optimized models are assembled into a unified framework for fairness assessment. The comprehensive evaluation results show that the AVOA-CatBoost built in this paper performs well (RMSE = 1.84, MAE = 1.18, R2 = 0.9993) and cross-validation (RMSE = 2.65 ± 1.54, MAE = 1.17 ± 0.23, R2 = 0.998 ± 0.002). In the end, in order to improve the transparency and usefulness of the model, we constructed an interpretable model from both global and local perspectives.
Fig.1 Schematic graph of data flow in the whole ML model for excavation.
Parameter
Value
B (m)
30, 40, 50, 60
T (m)
20, 30, 35
H (m)
11, 14, 17, 20
6.097, 7.313, 8.176, 8.846
(kN/m)
15, 17, 19
100, 200, 300, 400
0.21, 0.25, 0.29, 0.34
Tab.1 Settings for each parameter
Fig.2 Diaphragm wall deflection induced by braced excavations.
Fig.3 The box plot and the normal distribution of observation,distinguished by features: (a) ; (b) ; (c) ; (d) ; (e) ; (f) ; (g) .
Fig.4 Heatmap for mutual information.
Fig.5 Schematic diagram of GBA algorithm flow.
Model
RMSE
MAE
R2
AVOA-NGBoost
4.92
3.40
0.9953
AVOA-CatBoost
1.84
1.18
0.9993
AVOA-XGBoost
4.92
3.44
0.9953
AVOA-LightGBM
2.43
1.68
0.9989
AVOA-RF
15.17
11.88
0.9551
AVOA-LSSVM
3.97
2.80
0.9969
AVOA-LR
27.56
20.83
0.8520
AVOA-Stacking
2.11
1.39
0.9991
Tab.2 Performance of the predictive models on the test data set
Fig.6 Residuals plots for predictive models with AVOA optimization. Differentiation by model: (a) AVOA-CatBoost model; (b) AVOA-LightGBM model; (c) AVOA-SRR model; (d) AVOR-LR model.
Fig.7 Regression plots for predictive models with AVOA optimization. Differentiation by model: (a) AVOA-CatBoost model; (b) AVOA-LightGBM model; (c) AVOA-SRR model; (d) AVOR-LR model.
Model
RMSE
MAE
R2
source
HHO-MLP
4.51
3.23
0.996
[21]
WO-MLP
4.74
3.44
0.996
XGBoost
7.90
None
0.990
MARS
11.10
None
0.970
[18]
ANN
11.73
None
0.970
SVR
17.40
None
0.940
Tab.3 Model performance yielded from past literature
Model
10-repeated 10-fold cross-validation (RMSE)
Mean and variance
1
2
3
4
5
6
7
8
9
10
RMSE
MAE
R2
AVOA-NGBoost
5.11
5.35
5.36
5.38
5.32
5.39
5.56
4.88
5.31
5.07
5.27 ± 1.52
3.10 ± 0.39
0.994 ± 0.003
AVOA-CatBoost
2.61
2.66
2.76
2.58
2.58
2.72
2.68
2.59
2.73
2.57
2.65 ± 1.54
1.17 ± 0.23
0.998 ± 0.002
AVOA-XGBoost
5.30
5.00
4.96
5.16
5.38
4.98
5.41
4.71
5.69
4.63
5.12 ± 2.17
2.80 ± 0.41
0.994 ± 0.006
AVOA-LightGBM
3.19
3.17
3.20
3.14
3.28
3.14
3.34
2.98
3.02
3.14
3.16 ± 1.31
1.68 ± 0.25
0.998 ± 0.002
AVOA-RF
15.86
15.59
15.89
15.58
15.76
15.46
16.11
15.53
15.65
15.63
15.71 ± 2.19
11.31 ± 1.05
0.948 ± 0.012
AVOA-LSSVM
4.53
4.56
4.57
4.49
4.55
4.48
4.57
4.49
4.50
4.50
4.52 ± 1.60
2.77 ± 0.37
0.995 ± 0.003
AVOA-LR
28.78
28.78
28.82
28.77
28.85
28.75
28.82
28.73
28.74
28.71
28.77 ± 1.97
20.62 ± 1.45
0.827 ± 0.027
AVOA-Stacking
2.88
2.92
3.00
2.82
2.98
2.87
2.99
2.76
3.09
2.74
2.90 ± 1.73
1.31 ± 0.26
0.998 ± 0.003
Tab.4 10-repeated 10-fold cross-validation (RMSE)
Fig.8 and of the AVOA-CatBoost model.
Fig.9 Global Tree SHAP value of AVOA-CatBoost.
Location of the data in the dataset
Features
Wall deflection
B
T
H
468
30
30
20
0.25
300
7.313
15
174
Tree SHAP values
−11.36
−5.08
22.85
27.06
−25.14
−13.89
43.13
174.06
Tab.5 Details about the 468th sample and Tree SHAP explanation results
Fig.10 Local Tree SHAP Value of AVOA-CatBoost in 468th sample.
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