Abstract
The present research introduces an optimum performance soft computing model by comparing deep (multi-layer perceptron neural network, support vector machine, least square support vector machine, support vector regression, Takagi Sugeno fuzzy model, radial basis function neural network, and feed-forward neural network) and hybrid (relevance vector machine) learning models for estimating the pile group settlement. Six kernel functions have been used to develop the RVM model. For the first time, the single (mentioned by SRVM) and dual (mentioned by DRVM) kernel function-based RVM models have been employed for the reliability analysis of settlement of pile group in clay, optimized by genetic and particle swarm optimization algorithms. For that purpose, a database has been collected from the published article. Sixteen performance metrics have been implemented to record the model's performance. Based on the performance comparison and score analysis, models MS3, MS9, MS17, MS23, and MS25 have been recognized as the better-performing models. Furthermore, the regression error characteristics curve, Uncertainty analysis, cross-validation (k-fold = 10), and Anderson–Darling test reveal that model MS23 is the best architectural model in reliability analysis of pile group settlement. The comparison of model MS23 with published models shows that model MS23 has outperformed with a performance index of 1.9997, a20-index of 100, an agreement index of 0.9971, and a scatter index of 0.0013. The compression index, void ratio, and density influence the pile group settlement prediction. Also, the problematic multicollinearity level (variance inflation for > 10) significantly affects the performance and accuracy of the deep learning model.
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Data Availability
All data, models, and code generated or used during the study appear in the submitted article. The database used in this research was collected from the literature.
Abbreviations
- 3D:
-
Three-dimensional
- a20:
-
A20-index
- ACP:
-
Axial capacity for driving piles
- ANFIS:
-
Adaptive neuro-fuzzy inference system
- ANN:
-
Artificial neural network
- ANOVA:
-
Analysis of variance
- BCP:
-
Bearing capacity of pile
- BF:
-
Bias factor
- BPNN:
-
Back propagation neural network
- CAM:
-
Cosine amplitude method
- Cc:
-
Compression index
- CPT:
-
Cone penetration test
- D:
-
Footing depth
- df:
-
Degree of freedom
- DRVM:
-
Dual Kernel function-based RVM
- e:
-
Void ratio
- ED:
-
Embedment depth
- F:
-
F State value
- F crit:
-
F critical value
- FAP:
-
Footing net applied pressure
- FE:
-
Finite element
- FEM:
-
Finite element method
- FFNN:
-
Fee-forward neural network
- FN:
-
Functional network
- FOS:
-
Factor of safety
- ɣ:
-
Soil density
- GA:
-
Genetic algorithm
- GMDH:
-
Group method of data handling
- GP:
-
Genetic programming
- GPR:
-
Gaussian process regression
- H0:
-
Null hypothesis
- HR:
-
Research hypothesis
- IOA:
-
Index of agreement
- IOS:
-
Index of scatter
- L:
-
Footing width
- L/W:
-
Length-to-width ratio of footings
- LB:
-
Lower bound
- LL:
-
Lower level
- LLP:
-
Laterally loaded piles
- LMI:
-
Legate and McCabe's index
- Lp/D:
-
Total length of pile/pile diameter
- Ls/Lt:
-
Length of pile in the soil layer/length of pile in the rock layer
- Ls-SVM:
-
Least square support vector machine
- MAE:
-
Mean absolute error
- MAPE:
-
Mean absolute percentage error
- MBE:
-
Mean bias error
- ME:
-
Margin of error
- MOE:
-
Mean of error
- MS:
-
Model structure
- MS:
-
Mean of squares
- NMBE:
-
Normalized mean bias error
- NS:
-
Nash–Sutcliffe efficiency
- ɸ:
-
Angle of internal friction
- Pcyc:
-
Half amplitude of the cyclic load
- PDR:
-
Pile driving records
- PI:
-
Performance index
- PLC:
-
Pile load capacity
- PLT:
-
In-situ pile load test
- PLTC:
-
Pile load test using a calibration chamber
- Pm:
-
Mean value of cyclic load
- PSO:
-
Particle swarm optimization algorithm
- Pu:
-
Ultimate bearing capacity of pile
- R:
-
Coefficient of correlation
- R2 :
-
Coefficient of determination
- RBFNN:
-
Radial basis function neural network
- RMSE:
-
Root mean square error
- RNN:
-
Recurrent neural network
- ROC:
-
Receiver operating characteristics
- RSR:
-
Root mean square error to observation's standard deviation ratio
- RVM:
-
Relevance vector machine
- SA:
-
Actual settlement
- SE:
-
Standard error
- SPM:
-
Supplementary materials
- SPT:
-
Standard penetration test
- SRVM:
-
Single Kernel function-based RVM
- SS:
-
Sum of square
- StDev:
-
Standard deviation
- SVM:
-
Support vector machine
- SVR:
-
Support vector regression
- TSFL:
-
Takagi–Sugeno fuzzy method
- UB:
-
Upper bound
- UBC:
-
Ultimate bearing capacity
- UCS:
-
Unconfined compressive strength
- UL:
-
Upper level
- VAF:
-
Variance accounted for
- VIF:
-
Variance inflation factor
- W:
-
Footing length
- WBC:
-
Width of confidence bound
- WMAPE:
-
Weighted mean absolute percentage error
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JK: Main author, conceptualization, literature review, manuscript preparation, application of AI models, relevance vector machine model development, methodological development, statistical analysis, detailing, and overall analysis; HS: literature review, manuscript preparation, introduction and literature writing, theory of adopted methods, soft computing model development, detailing, overall analysis; KSG: conceptualization, comprehensive analysis, manuscript finalization, detailed review, and editing.
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Khatti, J., Samadi, H. & Grover, K.S. Estimation of Settlement of Pile Group in Clay Using Soft Computing Techniques. Geotech Geol Eng 42, 1729–1760 (2024). https://doi.org/10.1007/s10706-023-02643-x
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DOI: https://doi.org/10.1007/s10706-023-02643-x