Forecasting the Bearing Capacity of the Driven Piles Using Advanced Machine-Learning Techniques
Abstract
:1. Introduction
2. Materials and Methods
2.1. Overview of the Methodology
2.2. Database
2.3. Machine-Learning Methods
2.4. Statistical Performance Indicators
- Mean absolute error (MAE):
- 2.
- Root mean square error (RMSE):
- 3.
- Index of scattering (IOS):
- 4.
- Coefficient of determination (R2):
- 5.
- Pearson correlation coefficient (R):
- 6.
- Index of agreement (IOA):
2.5. Methodology
- Creating a geotechnical database, collected from different countries such as Iran, Mexico, and India. In this step, 100 static load-bearing tests on the UBC of steel- and concrete-driven piles were collected as datasets.
- Modeling the chosen inputs by means of numerous machine-learning methods. The ELM, DNN, SVR, RF, LASSO, PLS, Ridge, K Ridge, Stepwise, and GP methods have been employed in this step for suggesting 11 models.
- Defining the optimal model for estimating the pile-bearing capacity value using important statistical performance indicators such as MAE, RMSE, IOS, R2, R, and IOA.
- Evaluating the predictive capability of the optimal model to overcome under-fitting and over-fitting problems by utilizing the K-fold cross-validation approach with K = 5.
- Performing a sensitivity analysis by using the step-by-step method to define the most or least influential input on the bearing capacity via the proposed model.
- Designing a reliable, easy-to-use, and graphical interface based on our optimal model.
3. Results
3.1. Database Compilation
3.2. Correlation between Bearing Capacity and Input Parameters
3.3. Bearing Capacity Prediction through AI Models
3.4. Evaluating the Best Fitted Model Using the K-Fold Cross-Validation Approach
3.5. Comparison between the Proposed Models and Empirical Formulae
3.6. Sensitivity Analysis
3.7. Graphical User Interface (GUI) Design “BeaCa2021”
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
Appendix A
References
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Authors | Inputs | Methods | Database | References |
---|---|---|---|---|
Nawari et al. (1999) | SPT-N values and geometrical properties | Neural Network | 25 | [25] |
Mahnesh (2011) | Dynamic stress-wave data | Support Vector Machines and Generalized Regression Neural Network | 105 | [26] |
Milad et al. (2015) | Flap number, basic properties of the surrounding soil, pile geometry, and pile-soil friction angle | Artificial Neural Network, Genetic Programming and Linear Regression | 100 | [27] |
Jahed et al. (2017) | Soil length to socket length ratio, total length to diameter ratio, uniaxial compressive strength, and standard penetration test | hybrid PSO–ANN | 132 | [1] |
Moayedi and Jahed (2018) | Internal friction angle of soil located in shaft and tip, pile length, effective vertical stress at pile toe and pile area | ICA-ANN | 59 | [31] |
Yong et al. (2021) | Pile length, pile cross-sectional area, hammer weight, pile set, and drop height | ANFIS, GP, and SA–GP | 50 | [2] |
Shaik et al. (2019) | Internal friction angle of soil located in shaft and tip, effective vertical stress at pile toe, pile area, and pile length | ICA-ANN and ANFIS | 59 | [29] |
Kardani et al. (2020) | Shear resistance angle at the shaft of the pile, soil shear resistance angle at the tip of the pile, length of pile, cross-sectional area of the pile, and effective stress at the tip of the pile | Decision tree, k-nearest neighbor, Multilayer Perceptron Artificial Neural Network, Random Forest, Support Vector Regressor, and Extreme Gradient Boosting | 59 | [32] |
Harandizadeh et al. (2021) | CPT and pile loading test results | ANFIS and ANFIS–GMDH–PSO | 72 | [30] |
Moayedi et al. (2020) | Pile diameter, pile length, relative density, embedment ratio, and both the pile end resistance and base resistance | GA-ANFIS and PSO-ANFIS | 20 | [28] |
Liu et al. (2020) | Laboratory and in situ testing results | ANFIS, ANN, and GA-ANN | 43 | [33] |
Dehghanbanadaki et al. (2021) | Pile area, pile length, flap number, average cohesion and friction angle, average soil-specific weight, and average pile-soil friction angle | MLP–GWO and ANFIS–GWO | 100 | [34] |
Code | Parameter Type | Type of Variable | Subdivision | Variable |
---|---|---|---|---|
X1 | Input | Qualitative | X1 = 1 (Steel) | Pile material |
X1 = 2 (Concrete) | ||||
X2 | Input | Quantitative | Average cohesion (kN/m2) | |
X3 | Input | Quantitative | Average friction angle (°) | |
X4 | Input | Quantitative | Average soil-specific weight (kN/m3) | |
X5 | Input | Quantitative | Average pile-soil friction angle (°) | |
X6 | Input | Quantitative | Flap number | |
X7 | Input | Quantitative | Pile area (m2) | |
X8 | Input | Quantitative | Pile length (m) | |
Y | Output | Quantitative | Pile capacity (kN) |
Algorithms | Algorithm Parameters | Value |
---|---|---|
ELM | Hidden layers | H = 1 |
Hidden neurons | N = 12 | |
Activation function | ‘linear’ | |
Regulation parameter | C = 0.02 | |
DNN | Hidden layers | H = 2 |
Hidden neurons in the first layer | N1 = [1–20] | |
Hidden neurons in the second layer | N2 = [1–20] | |
Activation function in the first layer | ‘Tansig’ | |
Activation function in the second layer | ‘Tansig’ | |
SVR | Regulation parameter C | Series of C |
Regulation parameter lambda | Series of lambda | |
Kernel function | ‘rbf’ | |
RF | nTrees | nTrees = 100 |
mTrees | mTrees = 26 | |
LASSO | Lambda | series of lambda |
PLS | PLS components | NumComp = 3 for PSO NumComp = 4 for GT and FS |
Ridge | Regularization parameter lambda | lambda = 1 |
KRidge | Regularization parameter lambda | lambda = 1 |
Kernel function | ‘linear’ | |
Parameter for kernel | sigma = 2 × 10−7 | |
GP | Function set | +, −, ×, ÷, power, ln, sqrt, sin, cos, tan |
Population size | 100 up to 500 | |
Number of generations | 1000 | |
Genetic operators | Reproduction, crossover, mutation |
Range | Minimum | Maximum | Mean | SD | Variance | Skewness | Kurtosis | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
Statistic | Statistic | Statistic | Statistic | Std. Error | Statistic | Statistic | Statistic | Std. Error | Statistic | Std. Error | |
X2 | 148.00 | 0.00 | 148.00 | 32.3741 | 3.28447 | 32.84 | 1078.77 | 2.011 | 0.241 | 4.570 | 0.478 |
X3 | 36.62 | 0.00 | 36.62 | 25.5803 | 0.96535 | 9.653 | 93.191 | −1.310 | 0.241 | 0.855 | 0.478 |
X4 | 8.11 | 5.38 | 13.49 | 10.2029 | 0.18409 | 1.840 | 3.389 | −0.406 | 0.241 | 0.262 | 0.478 |
X5 | 6.86 | 10.14 | 17.00 | 13.6823 | 0.16987 | 1.698 | 2.885 | 0.073 | 0.241 | −0.076 | 0.478 |
X6 | 2277.00 | 14.00 | 2291.00 | 494.99 | 60.23 | 602.32 | 362,794.16 | 1.502 | 0.241 | 1.286 | 0.478 |
X7 | 1.52 | 0.07 | 1.59 | 0.4327 | 0.04656 | 0.46562 | 0.217 | 1.128 | 0.241 | −0.233 | 0.478 |
X8 | 83.80 | 14.20 | 98.00 | 27.1120 | 1.86024 | 18.60 | 346.048 | 2.761 | 0.241 | 6.962 | 0.478 |
Y | 51,560.00 | 540.00 | 52,100.00 | 5133.12 | 929.01 | 9290.14 | 86,306,843.19 | 4.043 | 0.241 | 16.258 | 0.478 |
X2 | X3 | X4 | X5 | X6 | X7 | X8 | Y | ||
---|---|---|---|---|---|---|---|---|---|
X2 | Pearson Correlation | 1 | −0.370 ** | −0.234 * | −0.221 * | 0.086 | 0.038 | −0.229 * | −0.229 * |
Significance | 0.000 | 0.019 | 0.027 | 0.396 | 0.707 | 0.022 | 0.022 | ||
N | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |
X3 | Pearson Correlation | −0.370 ** | 1 | 0.463 ** | 0.011 | 0.206 * | 0.259 ** | −0.063 | 0.099 |
Significance | 0.000 | 0.000 | 0.916 | 0.040 | 0.009 | 0.531 | 0.326 | ||
N | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |
X4 | Pearson Correlation | −0.234 * | 0.463 ** | 1 | 0.270 ** | 0.124 | 0.051 | −0.433 ** | −0.138 |
Significance | 0.019 | 0.000 | 0.007 | 0.218 | 0.612 | 0.000 | 0.172 | ||
N | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |
X5 | Pearson Correlation | −0.221 * | 0.011 | 0.270 ** | 1 | −0.489 ** | −0.555 ** | −0.189 | −0.142 |
Significance | 0.027 | 0.916 | 0.007 | 0.000 | 0.000 | 0.059 | 0.159 | ||
N | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |
X6 | Pearson Correlation | 0.086 | 0.206 * | 0.124 | −0.489 ** | 1 | 0.876 ** | 0.335 ** | 0.449 ** |
Significance | 0.396 | 0.040 | 0.218 | 0.000 | 0.000 | 0.001 | 0.000 | ||
N | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |
X7 | Pearson Correlation | 0.038 | 0.259 ** | 0.051 | −0.555 ** | 0.876 ** | 1 | 0.446 ** | 0.563 ** |
Significance | 0.707 | 0.009 | 0.612 | 0.000 | 0.000 | 0.000 | 0.000 | ||
N | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |
X8 | Pearson Correlation | −0.229 * | −0.063 | −0.433 ** | −0.189 | 0.335 ** | 0.446 ** | 1 | 0.866 ** |
Significance | 0.022 | 0.531 | 0.000 | 0.059 | 0.001 | 0.000 | 0.000 | ||
N | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |
Y | Pearson Correlation | −0.229 * | 0.099 | −0.138 | −0.142 | 0.449 ** | 0.563 ** | 0.866 ** | 1 |
Significance | 0.022 | 0.326 | 0.172 | 0.159 | 0.000 | 0.000 | 0.000 | ||
N | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
MAE × 103 | RMSE × 103 | IOS | R | R2 | IOA | |
---|---|---|---|---|---|---|
Concrete piles | ||||||
DNN | 0.1650 | 0.2140 | 0.0755 | 0.9977 | 0.9954 | 0.9988 |
ELM | 3.0424 | 4.2390 | 0.7737 | 0.9320 | 0.8686 | 0.9610 |
Lasso | 2.4324 | 3.5390 | 0.6637 | 0.9620 | 0.9254 | 0.9700 |
PLS | 2.5524 | 3.6390 | 0.6837 | 0.9688 | 0.9386 | 0.9700 |
RF | 1.1024 | 2.1690 | 0.3837 | 0.9880 | 0.9761 | 0.9912 |
Kridge | 2.2930 | 3.5917 | 0.6816 | 0.9433 | 0.8899 | 0.9641 |
Ridge | 2.4268 | 3.6145 | 0.6876 | 0.9409 | 0.8853 | 0.9636 |
LS | 2.3093 | 3.5867 | 0.6824 | 0.9414 | 0.8863 | 0.9656 |
Step | 2.4738 | 3.6421 | 0.6970 | 0.9352 | 0.8746 | 0.9626 |
SVR | 1.9787 | 4.0984 | 0.7734 | 0.9315 | 0.8676 | 0.9360 |
GP | 0.5966 | 0.9612 | 0.1731 | 0.9975 | 0.9951 | 0.9961 |
Steel piles | ||||||
DNN | 0.1870 | 0.3100 | 0.0448 | 0.9997 | 0.9994 | 0.9998 |
ELM | 3.1064 | 4.3966 | 0.9081 | 0.8478 | 0.7187 | 0.9118 |
Lasso | 2.7149 | 3.6962 | 0.7527 | 0.8990 | 0.8082 | 0.9437 |
PLS | 2.6329 | 3.6973 | 0.7763 | 0.8966 | 0.8038 | 0.9398 |
RF | 1.1213 | 2.3475 | 0.4893 | 0.9875 | 0.9751 | 0.9712 |
Kridge | 2.2482 | 3.6937 | 0.7342 | 0.8993 | 0.8088 | 0.9441 |
Ridge | 2.3820 | 3.7165 | 0.7402 | 0.8969 | 0.8044 | 0.9436 |
LS | 2.2646 | 3.6887 | 0.7350 | 0.8974 | 0.8054 | 0.9456 |
Step | 2.4291 | 3.7441 | 0.7496 | 0.8912 | 0.7943 | 0.9426 |
SVR | 1.9340 | 4.2004 | 0.8260 | 0.8875 | 0.7876 | 0.9160 |
GP | 0.5518 | 1.0632 | 0.2257 | 0.9975 | 0.9951 | 0.9965 |
Authors | Sample Size | Best Methods | Correlation Coefficient | References |
---|---|---|---|---|
Nawari et al. (1999) | 25 | ANN | 0.91 | [25] |
Mahnesh (2011) | 105 | Generalized Regression Neural Network | 0.977 | [26] |
Milad et al. (2015) | 100 | Neural Network | 0.9995 | [27] |
Jahed et al. (2017) | 132 | PSO–ANN | 0.9685 | [1] |
Moayedi and Jahed (2018) | 59 | ICA-ANN | 0.96369 | [31] |
Yong et al. (2021) | 50 | GP | 0.997 | [28] |
Shaik et al. (2019) | 59 | ANFIS | 0.967 | [33] |
Kardani et al. (2020) | 59 | Extreme Gradient Boosting | 0.975 | [2] |
Harandizadeh et al. (2021) | 72 | ANFIS–GMDH–PSO | 0.94 | [29] |
Moayedi et al. (2020) | 20 | GA–ANFIS | 0.9935 | [34] |
Liu et al. (2020) | 43 | GA-ANN | 0.998 | [32] |
Dehghanbanadaki et al. (2021) | 100 | MLP–GWO | 0.991 | [30] |
Our study | 100 | Deep Neural Network | 0.9996 |
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Benbouras, M.A.; Petrişor, A.-I.; Zedira, H.; Ghelani, L.; Lefilef, L. Forecasting the Bearing Capacity of the Driven Piles Using Advanced Machine-Learning Techniques. Appl. Sci. 2021, 11, 10908. https://doi.org/10.3390/app112210908
Benbouras MA, Petrişor A-I, Zedira H, Ghelani L, Lefilef L. Forecasting the Bearing Capacity of the Driven Piles Using Advanced Machine-Learning Techniques. Applied Sciences. 2021; 11(22):10908. https://doi.org/10.3390/app112210908
Chicago/Turabian StyleBenbouras, Mohammed Amin, Alexandru-Ionuţ Petrişor, Hamma Zedira, Laala Ghelani, and Lina Lefilef. 2021. "Forecasting the Bearing Capacity of the Driven Piles Using Advanced Machine-Learning Techniques" Applied Sciences 11, no. 22: 10908. https://doi.org/10.3390/app112210908
APA StyleBenbouras, M. A., Petrişor, A.-I., Zedira, H., Ghelani, L., & Lefilef, L. (2021). Forecasting the Bearing Capacity of the Driven Piles Using Advanced Machine-Learning Techniques. Applied Sciences, 11(22), 10908. https://doi.org/10.3390/app112210908