Prediction of Liquefaction-Induced Lateral Displacements Using Gaussian Process Regression
Abstract
:1. Introduction
1.1. Finite Element Analysis
1.2. Simplified Analytical Models
1.2.1. Sliding Block Model
1.2.2. Minimum Potential Energy Model
1.2.3. Shear Strength Loss and Strain Re-Hardening Model
1.2.4. Viscous Models
1.3. Empirical Models and Soft Computing Techniques
- Seismic parameters—seismic source distance (R, km) and earthquake magnitude, (M).
- Topographic characteristics (in percent)—gradient of ground surface (S) and free face ratio.
- Geotechnical parameters (in percent)—average mean particle size within T15 (D5015, mm) and averaged fines contents in T15 (F15)
2. Gaussian Process Regression
3. Case-History Database
4. Correlation Analysis
5. Construction and Evaluation of Prediction Model
6. Result and Discussion
6.1. Performance of GPR Model
6.2. Sensitivity Analysis
7. Conclusions
- With respect to the values of GPR with R2 = 0.9402, r = 0.9697, MAE = 0.3403, RMSE = 0.5597, RSR = 0.248 and NSE = 0.938 in training phase whereas for testing phase it performed equally well with R2 = 0.894, r = 0.9455, MAE = 0.5443, RMSE = 0.8438, RSR = 0.387 and NSE = 0.851, In comparison to the EPR, ANN, and MLR models in literature, the GPR model was found to be more accurate and stable than the other models.
- The results of sensitivity analysis show that the degree of importance of different input parameters on lateral displacement is as T15 > M > R > amax> W > F15 > D5015.
- The developed Pearson VII kernel function-based GPR model makes predictions accurate and outperforms the others for this dataset and may be applied to a range of geotechnical engineering situations involving uncertainties.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Earthquake | M | R (km) | amax (g) | F15 (%) | D5015 (mm) | T15 (m) | W (%) | DH (m) |
---|---|---|---|---|---|---|---|---|
1906, San Francisco | 7.9 | 27 | 0.24 | 23 | 0.25 | 7.2 | 22.02 | 1.84 |
1906, San Francisco | 7.9 | 24 | 0.26 | 30 | 0.16 | 1.5 | 17.76 | 0.92 |
1964, Alaska | 9.2 | 60 | 0.3 | 21 | 1.35 | 3.4 | 24.59 | 1.86 |
1964, Alaska | 9.2 | 100 | 0.2 | 13 | 1 | 10.4 | 7.03 | 1.38 |
1964, Alaska | 9.2 | 60 | 0.3 | 23 | 1.47 | 3.8 | 16.07 | 1.58 |
1964, Alaska | 9.2 | 60 | 0.3 | 66 | 0.07 | 3.1 | 48.98 | 1.92 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.35 | 12.7 | 3.06 | 1.01 |
1964, Niigata | 7.5 | 21 | 0.32 | 4 | 0.34 | 13.6 | 3.15 | 5.2 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 5.36 | 0.82 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.35 | 0.5 | 3.43 | 1.1 |
1964, Niigata | 7.5 | 21 | 0.32 | 32 | 0.1 | 2.4 | 2.03 | 0.54 |
1964, Niigata | 7.5 | 21 | 0.32 | 26 | 0.16 | 2.5 | 20.61 | 0.91 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.35 | 0.5 | 22.37 | 0.88 |
1964, Niigata | 7.5 | 21 | 0.32 | 10 | 0.25 | 11.3 | 29.7 | 5.03 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.29 | 7.5 | 7.32 | 3.75 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 8.78 | 0.93 |
1964, Niigata | 7.5 | 21 | 0.32 | 12 | 0.27 | 12.2 | 5.01 | 2.36 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 24.02 | 3.07 |
1964, Niigata | 7.5 | 21 | 0.32 | 9 | 0.26 | 11.3 | 19.62 | 10.16 |
1964, Niigata | 7.5 | 21 | 0.32 | 12 | 0.26 | 12.3 | 5.76 | 1.49 |
1964, Niigata | 7.5 | 21 | 0.32 | 31 | 0.12 | 2.4 | 3.26 | 1.25 |
1964, Niigata | 7.5 | 21 | 0.32 | 10 | 0.39 | 9 | 3.27 | 2.48 |
1964, Niigata | 7.5 | 21 | 0.32 | 32 | 0.11 | 2.4 | 2.09 | 1.32 |
1964, Niigata | 7.5 | 21 | 0.32 | 14 | 0.36 | 7.1 | 19.62 | 3.34 |
1964, Niigata | 7.5 | 21 | 0.32 | 4 | 0.57 | 8.6 | 2.82 | 1.23 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.26 | 11.9 | 5.93 | 2.97 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 15.6 | 4.94 | 7.36 |
1964, Niigata | 7.5 | 21 | 0.32 | 16 | 0.22 | 9.6 | 3.06 | 2.41 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 18.49 | 1.78 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.27 | 12 | 4.83 | 1.84 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.32 | 12.4 | 4.82 | 3.66 |
1964, Niigata | 7.5 | 21 | 0.32 | 12 | 0.26 | 12.4 | 5.01 | 1.75 |
1964, Niigata | 7.5 | 21 | 0.32 | 31 | 0.12 | 2.4 | 3.35 | 0.69 |
1964, Niigata | 7.5 | 21 | 0.32 | 7 | 0.35 | 9.8 | 4.5 | 0.53 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 15.6 | 7.86 | 8.37 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 13.9 | 5.77 | 4.58 |
1964, Niigata | 7.5 | 21 | 0.32 | 12 | 0.26 | 12 | 9.18 | 4.4 |
1964, Niigata | 7.5 | 21 | 0.32 | 12 | 0.24 | 11.8 | 5.54 | 4 |
1964, Niigata | 7.5 | 21 | 0.32 | 12 | 0.26 | 12.2 | 5.36 | 2.38 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.44 | 10.1 | 2.42 | 1.25 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.28 | 12.1 | 3.68 | 2.09 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.35 | 0.5 | 3.39 | 0.86 |
1964, Niigata | 7.5 | 21 | 0.32 | 14 | 0.25 | 12.6 | 13.73 | 6.27 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.4 | 7.9 | 3.59 | 1.46 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 15.6 | 17.75 | 9.15 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.35 | 0.5 | 4.26 | 0.72 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.29 | 14.3 | 6.51 | 3.61 |
1964, Niigata | 7.5 | 21 | 0.32 | 8 | 0.23 | 6.8 | 1.85 | 0.91 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 5.29 | 1.64 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.36 | 13.6 | 8.52 | 4.77 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.5 | 10.9 | 4.77 | 0.81 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.35 | 12.7 | 9.12 | 6 |
1964, Niigata | 7.5 | 21 | 0.32 | 15 | 0.25 | 9.6 | 2.68 | 1.89 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 8.19 | 2.2 |
1964, Niigata | 7.5 | 21 | 0.32 | 3 | 0.35 | 13.3 | 4.05 | 4.76 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.26 | 12 | 6.53 | 2.51 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 15.6 | 17.75 | 9.49 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.24 | 11.6 | 11.06 | 8.19 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.29 | 13.6 | 2.76 | 1.01 |
1964, Niigata | 7.5 | 21 | 0.32 | 7 | 0.34 | 10.5 | 6.03 | 5.43 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.45 | 10.5 | 5.84 | 1.86 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 15.5 | 9.98 | 6.02 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.39 | 9.2 | 4.87 | 1.86 |
1964, Niigata | 7.5 | 21 | 0.32 | 12 | 0.24 | 11.9 | 5.06 | 3.98 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 15.6 | 17.05 | 9.29 |
1964, Niigata | 7.5 | 21 | 0.32 | 15 | 0.32 | 11.3 | 2.86 | 1.41 |
1964, Niigata | 7.5 | 21 | 0.32 | 16 | 0.31 | 11 | 3.06 | 1.3 |
1964, Niigata | 7.5 | 21 | 0.32 | 18 | 0.21 | 6.7 | 4.45 | 0.9 |
1964, Niigata | 7.5 | 21 | 0.32 | 15 | 0.32 | 7 | 7.72 | 1.92 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.28 | 12.1 | 2.88 | 1.56 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.38 | 11.6 | 3.22 | 2.71 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 15.6 | 5.25 | 7.19 |
1964, Niigata | 7.5 | 21 | 0.32 | 16 | 0.3 | 10.8 | 3.68 | 0.71 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.38 | 7.2 | 20.55 | 3.28 |
1964, Niigata | 7.5 | 21 | 0.32 | 9 | 0.4 | 13 | 2.05 | 1.11 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.25 | 12.5 | 16.07 | 7.4 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.37 | 12.7 | 7.05 | 3.54 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.35 | 0.5 | 2.68 | 0.82 |
1964, Niigata | 7.5 | 21 | 0.32 | 9 | 0.39 | 9.3 | 3.72 | 1.96 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.39 | 7.3 | 2.76 | 1.23 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 12.86 | 2.74 |
1964, Niigata | 7.5 | 21 | 0.32 | 12 | 0.25 | 12.1 | 16.72 | 4.88 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.27 | 12.1 | 3.38 | 1.83 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 15.6 | 5.77 | 7.21 |
1964, Niigata | 7.5 | 21 | 0.32 | 2 | 0.33 | 10.4 | 8.89 | 4.76 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.25 | 12.4 | 35 | 7.67 |
1964, Niigata | 7.5 | 21 | 0.32 | 7 | 0.32 | 9.4 | 2.99 | 1.31 |
1964, Niigata | 7.5 | 21 | 0.32 | 4 | 0.34 | 13.5 | 3.36 | 3.46 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.26 | 11.6 | 11.32 | 3.78 |
1964, Niigata | 7.5 | 21 | 0.32 | 3 | 0.44 | 11.3 | 3.82 | 1.52 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.29 | 13 | 3.1 | 0.56 |
1964, Niigata | 7.5 | 21 | 0.32 | 28 | 0.14 | 2.5 | 4.79 | 0.88 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 15.6 | 19.62 | 7.7 |
1964, Niigata | 7.5 | 21 | 0.32 | 3 | 0.44 | 11.3 | 4.87 | 1.9 |
1964, Niigata | 7.5 | 21 | 0.32 | 9 | 0.37 | 10 | 16.4 | 6.5 |
1964, Niigata | 7.5 | 21 | 0.32 | 7 | 0.35 | 9.8 | 3.9 | 2.87 |
1964, Niigata | 7.5 | 21 | 0.32 | 12 | 0.25 | 12.2 | 12.47 | 4.83 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.34 | 13.8 | 12.01 | 8.73 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 25.93 | 3.57 |
1964, Niigata | 7.5 | 21 | 0.32 | 14 | 0.25 | 12.6 | 11.32 | 3.51 |
1964, Niigata | 7.5 | 21 | 0.32 | 17 | 0.24 | 6.8 | 4.26 | 1.37 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.25 | 11.6 | 17.05 | 8.29 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.31 | 14.1 | 16.4 | 8.52 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 5.76 | 1.27 |
1964, Niigata | 7.5 | 21 | 0.32 | 15 | 0.25 | 9.5 | 3.04 | 2.68 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.27 | 11.8 | 2.27 | 1.56 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.25 | 12.4 | 12.47 | 3.21 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 7.14 | 2.15 |
1964, Niigata | 7.5 | 21 | 0.32 | 24 | 0.19 | 8.6 | 5.15 | 1.06 |
1964, Niigata | 7.5 | 21 | 0.32 | 7 | 0.43 | 10.4 | 15.25 | 2.25 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.35 | 16.7 | 11.06 | 2.91 |
1964, Niigata | 7.5 | 21 | 0.32 | 8 | 0.15 | 3.7 | 1.64 | 0.62 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.32 | 15.6 | 7.72 | 7.31 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.25 | 12.5 | 55.68 | 7.13 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.31 | 15.2 | 12.44 | 6.3 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.35 | 11.9 | 2.86 | 1.11 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.25 | 11.6 | 19.37 | 4.28 |
1964, Niigata | 7.5 | 21 | 0.32 | 10 | 0.28 | 12.1 | 3.09 | 1.66 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.36 | 9.6 | 3.72 | 3.26 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.25 | 12.3 | 16.07 | 7.06 |
1964, Niigata | 7.5 | 21 | 0.32 | 2 | 0.33 | 10.4 | 13.65 | 5.35 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.26 | 12.6 | 6.23 | 1.87 |
1964, Niigata | 7.5 | 21 | 0.32 | 3 | 0.44 | 11.3 | 3.27 | 0.96 |
1964, Niigata | 7.5 | 21 | 0.32 | 7 | 0.33 | 10.6 | 12.01 | 7.95 |
1964, Niigata | 7.5 | 21 | 0.32 | 3 | 0.44 | 11.3 | 5.12 | 1.36 |
1964, Niigata | 7.5 | 21 | 0.32 | 30 | 0.13 | 2.4 | 4.18 | 0.68 |
1964, Niigata | 7.5 | 21 | 0.32 | 4 | 0.34 | 13.6 | 2.99 | 4.85 |
1964, Niigata | 7.5 | 21 | 0.32 | 28 | 0.14 | 2.5 | 20.61 | 1.06 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.28 | 12.1 | 3.86 | 1.93 |
1964, Niigata | 7.5 | 21 | 0.32 | 2 | 0.33 | 10.4 | 7.58 | 4.57 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.28 | 12.2 | 2.9 | 1.65 |
1964, Niigata | 7.5 | 21 | 0.32 | 8 | 0.34 | 11.4 | 3.1 | 2.09 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.45 | 10 | 2.86 | 1.82 |
1964, Niigata | 7.5 | 21 | 0.32 | 12 | 0.24 | 11.9 | 4.45 | 3.38 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.35 | 12.7 | 2.79 | 1.01 |
1964, Niigata | 7.5 | 21 | 0.32 | 13 | 0.29 | 12.9 | 3.04 | 0.42 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.31 | 14.1 | 17.75 | 8.39 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.24 | 12.1 | 2.11 | 1.27 |
1964, Niigata | 7.5 | 21 | 0.32 | 7 | 0.28 | 8.1 | 17.05 | 6.18 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.35 | 0.5 | 5.96 | 0.77 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.35 | 0.5 | 2.29 | 1.38 |
1964, Niigata | 7.5 | 21 | 0.32 | 5 | 0.31 | 14.1 | 4.55 | 6.67 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.27 | 12 | 3.98 | 1.83 |
1964, Niigata | 7.5 | 21 | 0.32 | 6 | 0.29 | 7.9 | 17.05 | 5.39 |
1964, Niigata | 7.5 | 21 | 0.32 | 11 | 0.27 | 12.1 | 2.97 | 1.49 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 5.3 | 19.96 | 2.93 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 5.6 | 4.7 | 0.47 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 6.5 | 5.08 | 0.52 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 4.6 | 20.3 | 3.16 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 3.6 | 20.34 | 3.18 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 3 | 17.07 | 1.81 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 2.3 | 13.59 | 2.14 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 1.6 | 20.41 | 2.45 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 4.8 | 19.61 | 2.78 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 2.7 | 15.43 | 2.02 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 2 | 13.59 | 1.46 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 4 | 18.87 | 3.26 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 2.7 | 20.47 | 3.16 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 5.9 | 4.89 | 0.54 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 4.5 | 19.26 | 1.99 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 1 | 20.27 | 1 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 3.1 | 18.26 | 2.04 |
1971, San Fernando | 6.4 | 0.5 | 0.68 | 47 | 0.08 | 5.2 | 19.96 | 2.63 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 20 | 0.12 | 3 | 8.57 | 2.63 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 32 | 0.09 | 1.5 | 6.25 | 0.37 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 23 | 0.11 | 2 | 7.89 | 2.04 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 17 | 0.12 | 3.6 | 3.08 | 0.92 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 15 | 0.12 | 3.8 | 6.56 | 2.02 |
1979, Imperial Valley | 6.6 | 6 | 0.36 | 70 | 0.04 | 0.2 | 4.26 | 0.01 |
1979, Imperial Valley | 6.6 | 6 | 0.36 | 54 | 0.12 | 1.8 | 10.66 | 0.01 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 17 | 0.12 | 3.7 | 9.6 | 4 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 22 | 0.11 | 2.6 | 3.68 | 0.31 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 23 | 0.11 | 2.4 | 6.35 | 1.41 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 23 | 0.11 | 2 | 6.15 | 1.1 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 22 | 0.11 | 2.7 | 6.45 | 1.53 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 23 | 0.11 | 2.9 | 7.02 | 1.43 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 25 | 0.1 | 2.5 | 6.78 | 0.72 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 15 | 0.12 | 4 | 6.56 | 1.48 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 17 | 0.12 | 3.7 | 6.78 | 2.3 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 21 | 0.11 | 1.6 | 4.8 | 0.67 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 25 | 0.1 | 2.5 | 9.84 | 2.63 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 22 | 0.11 | 1.8 | 6.67 | 1.13 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 30 | 0.09 | 1.8 | 8.05 | 1.03 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 22 | 0.11 | 2.7 | 8.05 | 2.12 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 25 | 0.11 | 2.2 | 3.68 | 0.47 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 16 | 0.12 | 3.8 | 9.37 | 4.25 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 22 | 0.11 | 3 | 10.08 | 3.21 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 16 | 0.12 | 3.7 | 3.72 | 1.23 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 18 | 0.12 | 3.4 | 9.16 | 3.82 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 19 | 0.12 | 3.3 | 6.15 | 1.51 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 21 | 0.11 | 1.4 | 4.69 | 0.87 |
1979, Imperial Valley | 6.5 | 2 | 0.49 | 25 | 0.11 | 2.2 | 3.52 | 0.47 |
1987, Superstition Hills | 6.6 | 23 | 0.15 | 27 | 0.09 | 3.5 | 17.91 | 0.19 |
1987, Superstition Hills | 6.6 | 23 | 0.15 | 22 | 0.09 | 3.3 | 41.38 | 0.21 |
1987, Superstition Hills | 6.6 | 23 | 0.15 | 43 | 0.07 | 1.7 | 17.52 | 0.11 |
1987, Superstition Hills | 6.6 | 23 | 0.15 | 44 | 0.07 | 3.6 | 7.5 | 0.01 |
1987, Superstition Hills | 6.6 | 23 | 0.15 | 38 | 0.08 | 2.7 | 13.11 | 0.11 |
1987, Superstition Hills | 6.6 | 23 | 0.15 | 25 | 0.09 | 3.4 | 41.38 | 0.24 |
1989, Loma Prieta | 7 | 27.2 | 0.2 | 1 | 0.6 | 3.4 | 29.73 | 0.26 |
1989, Loma Prieta | 7 | 27.2 | 0.2 | 2 | 0.8 | 2.7 | 33.54 | 0.29 |
1995, Hyogo-Ken Nanbu | 6.8 | 7.5 | 0.35 | 12.6 | 0.47 | 14.2 | 13.95 | 1.18 |
1995, Hyogo-Ken Nanbu | 6.8 | 6 | 0.38 | 13.4 | 0.94 | 12.5 | 9.25 | 1.01 |
1995, Hyogo-Ken Nanbu | 6.8 | 8 | 0.34 | 14.6 | 1.98 | 16 | 6.67 | 0.45 |
1995, Hyogo-Ken Nanbu | 6.8 | 8 | 0.34 | 14.6 | 1.98 | 16 | 16.82 | 0.93 |
1995, Hyogo-Ken Nanbu | 6.8 | 7.5 | 0.35 | 12.6 | 0.47 | 14.2 | 10.4 | 0.89 |
1995, Hyogo-Ken Nanbu | 6.8 | 5.5 | 0.39 | 10 | 1.36 | 15 | 14.56 | 1.34 |
1995, Hyogo-Ken Nanbu | 6.8 | 5.5 | 0.39 | 10 | 1.36 | 15 | 30.21 | 2.83 |
1995, Hyogo-Ken Nanbu | 6.8 | 6.5 | 0.37 | 10 | 1.88 | 12.5 | 5.16 | 0.34 |
1995, Hyogo-Ken Nanbu | 6.8 | 5.5 | 0.39 | 10 | 1.36 | 15 | 56.8 | 2.48 |
1995, Hyogo-Ken Nanbu | 6.8 | 8 | 0.34 | 14.6 | 1.98 | 16 | 18 | 0.97 |
1995, Hyogo-Ken Nanbu | 6.8 | 8 | 0.34 | 14.6 | 1.98 | 16 | 20.69 | 0.9 |
1995, Hyogo-Ken Nanbu | 6.8 | 7.5 | 0.35 | 12.6 | 0.47 | 14.2 | 18.56 | 1.33 |
1995, Hyogo-Ken Nanbu | 6.8 | 8 | 0.34 | 14.6 | 1.98 | 16 | 14.63 | 0.66 |
1995, Hyogo-Ken Nanbu | 6.8 | 6.5 | 0.37 | 10 | 1.88 | 12.5 | 9.84 | 1.03 |
1995, Hyogo-Ken Nanbu | 6.8 | 5.5 | 0.39 | 10 | 1.36 | 15 | 14.34 | 1.31 |
1995, Hyogo-Ken Nanbu | 6.8 | 6.5 | 0.37 | 10 | 1.88 | 12.5 | 14.63 | 1.47 |
1995, Hyogo-Ken Nanbu | 6.8 | 6 | 0.38 | 13.4 | 0.94 | 12.5 | 15 | 1.48 |
1995, Hyogo-Ken Nanbu | 6.8 | 5.5 | 0.39 | 10 | 1.36 | 15 | 9.79 | 1.47 |
1995, Hyogo-Ken Nanbu | 6.8 | 8 | 0.34 | 14.6 | 1.98 | 16 | 8.45 | 0.41 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 20.8 | 0.11 | 0.5 | 7.4 | 0 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 20.8 | 0.11 | 0.8 | 13.7 | 0.45 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 20.8 | 0.11 | 0.8 | 18.4 | 0.55 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 20.8 | 0.11 | 0.8 | 25.2 | 0.8 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 20.8 | 0.11 | 0.8 | 37.3 | 1.05 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 20.8 | 0.11 | 0.8 | 49.9 | 2.05 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 13 | 0.18 | 0.75 | 21.2 | 0.49 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 20.8 | 0.11 | 1.1 | 11.9 | 0 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 20.8 | 0.11 | 1.1 | 26.3 | 0 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 30 | 0.13 | 0.45 | 12.2 | 0.4 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 30 | 0.13 | 0.45 | 14.3 | 0.65 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 30 | 0.13 | 0.45 | 24.6 | 1 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 30 | 0.13 | 0.45 | 57.7 | 1.24 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 31.4 | 0.1 | 1 | 8 | 0.35 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 31.4 | 0.1 | 1 | 10.5 | 0.61 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 31.4 | 0.1 | 1 | 19 | 0.96 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 31.4 | 0.1 | 1 | 31.3 | 2.96 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 48.5 | 0.1 | 1.8 | 9.6 | 0.35 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 48.5 | 0.1 | 1.8 | 11.7 | 0.52 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 48.5 | 0.1 | 1.8 | 13.3 | 0.62 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 48.5 | 0.1 | 1.8 | 23.7 | 1.62 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 13 | 0.18 | 0.5 | 5.7 | 0 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 13 | 0.18 | 0.75 | 6.6 | 0.1 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 13 | 0.18 | 0.75 | 7.9 | 0.17 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 13 | 0.18 | 0.75 | 9 | 0.23 |
1999, Chi-Chi | 7.6 | 5 | 0.67 | 13 | 0.18 | 0.75 | 15 | 0.29 |
1999, Kocaeli | 7.4 | 0.5 | 0.57 | 11 | 7.7 | 1.2 | 8 | 0.9 |
1999, Kocaeli | 7.4 | 0.5 | 0.57 | 31 | 0.55 | 1.7 | 6 | 0.1 |
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Method and Technique | Model | Reference | |
---|---|---|---|
Empirical model | Regression Analysis | Hamada et al. [11] | |
Youd and Perkins [25] | |||
Bardet et al. [21] | |||
Youd et al. [12] | |||
Jafarian and Nasri [28] | |||
Soft computing methods | ANN | Wang and Rahman [13] | |
Baziar and Ghorbani [33] | |||
GP | Javadi et al. [31] | ||
ANFIS | Javdanian [34] |
Dataset | Statistical Parameters | Seismic Parameter | Geotechnical Parameter | Topographic Parameter | Output | ||||
---|---|---|---|---|---|---|---|---|---|
M | amax | R | D5015 | F15 | T15 | W | DH | ||
- | g | km | mm | % | m | % | m | ||
Training | Minimum | 6.4 | 0.15 | 0.5 | 0.04 | 1 | 0.2 | 1.64 | 0 |
Average | 7.26 | 0.41 | 15.10 | 0.36 | 18.83 | 7.80 | 11.69 | 2.45 | |
Maximum | 9.2 | 0.68 | 100 | 7.7 | 70 | 16.7 | 57.7 | 10.16 | |
Standard deviation | 0.51 | 0.15 | 11.61 | 0.65 | 13.71 | 5.16 | 9.96 | 2.26 | |
Testing | Minimum | 6.4 | 0.15 | 0.5 | 0.07 | 2 | 0.5 | 2.11 | 0 |
Average | 7.3 | 0.38 | 16.10 | 0.39 | 13.96 | 7.98 | 10.04 | 2.17 | |
Maximum | 9.2 | 0.68 | 60 | 1.98 | 66 | 16 | 48.98 | 8.39 | |
Standard deviation | 0.49 | 0.13 | 10.61 | 0.42 | 12.14 | 5.20 | 9.78 | 2.21 |
Parameters | M | amax | R | D5015 | F15 | T15 | W | DH |
---|---|---|---|---|---|---|---|---|
M | 1.000 | |||||||
amax | −0.341 | 1.000 | ||||||
R | 0.761 | −0.722 | 1.000 | |||||
D5015 | 0.033 | −0.112 | 0.013 | 1.000 | ||||
F15 | −0.370 | 0.560 | −0.371 | −0.230 | 1.000 | |||
T15 | 0.208 | −0.573 | 0.360 | 0.237 | −0.591 | 1.000 | ||
W | 0.003 | 0.178 | −0.046 | 0.025 | 0.245 | −0.145 | 1.000 | |
DH | 0.179 | −0.250 | 0.230 | −0.078 | −0.354 | 0.518 | 0.146 | 1.000 |
Performance | RSR | NSE |
---|---|---|
Very Good | ||
Good | ||
Adequate | ||
Inadequate |
Model | Indicators | R2 | r | MAE (m) | RMSE (m) | RSR | NSE | Reference |
---|---|---|---|---|---|---|---|---|
GPR | Training model | 0.9402 | 0.9697 | 0.3403 | 0.5597 | 0.248 | 0.938 | Present study |
Testing model | 0.894 | 0.9455 | 0.544 | 0.8438 | 0.387 | 0.851 | ||
EPR | Training model | 0.913 | - | 0.537 | 1.003 | - | - | [4] |
Testing model | 0.883 | - | 0.291 | 1.158 | - | - | ||
ANN | Training model | 0.875 | - | 0.702 | 1.074 | - | - | |
Testing model | 0.872 | 0.82 | 1.21 | - | - | |||
MLR | Training model | 0.868 | - | 0.81 | 1.24 | - | - | |
Testing model | 0.875 | - | 0.43 | 1.196 | - | - |
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Ahmad, M.; Amjad, M.; Al-Mansob, R.A.; Kamiński, P.; Olczak, P.; Khan, B.J.; Alguno, A.C. Prediction of Liquefaction-Induced Lateral Displacements Using Gaussian Process Regression. Appl. Sci. 2022, 12, 1977. https://doi.org/10.3390/app12041977
Ahmad M, Amjad M, Al-Mansob RA, Kamiński P, Olczak P, Khan BJ, Alguno AC. Prediction of Liquefaction-Induced Lateral Displacements Using Gaussian Process Regression. Applied Sciences. 2022; 12(4):1977. https://doi.org/10.3390/app12041977
Chicago/Turabian StyleAhmad, Mahmood, Maaz Amjad, Ramez A. Al-Mansob, Paweł Kamiński, Piotr Olczak, Beenish Jehan Khan, and Arnold C. Alguno. 2022. "Prediction of Liquefaction-Induced Lateral Displacements Using Gaussian Process Regression" Applied Sciences 12, no. 4: 1977. https://doi.org/10.3390/app12041977
APA StyleAhmad, M., Amjad, M., Al-Mansob, R. A., Kamiński, P., Olczak, P., Khan, B. J., & Alguno, A. C. (2022). Prediction of Liquefaction-Induced Lateral Displacements Using Gaussian Process Regression. Applied Sciences, 12(4), 1977. https://doi.org/10.3390/app12041977