Reliability Analysis of Pile Foundation Using Soft Computing Techniques: A Comparative Study
Abstract
:1. Introduction
2. Details of Present Analysis
3. Theoretical Background of the Employed Models
3.1. Details of MPMR
3.2. Details of ENN
3.3. Details of GMDH
3.4. Details of ANFIS
4. Details of Data Set
5. Models Accuracy Assessments
5.1. Statistical Parameters
5.2. Taylor Diagram
5.3. REC Curve
5.4. AD Test and M-W Test
5.5. Rank Analysis
6. Results and Discussion
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Particulars | φ (KN/m3) | γ (°) | Q (kN) |
---|---|---|---|
Mean | 17.30 | 36.44 | 3416.24 |
Standard Error | 0.22 | 0.25 | 62.05 |
Median | 17.28 | 36.28 | 3375.33 |
Standard Deviation | 1.95 | 2.24 | 554.99 |
Sample Variance | 3.81 | 5.04 | 308,019.10 |
Kurtosis | −1.16 | 0.07 | −0.77 |
Skewness | 0.03 | 0.59 | 0.31 |
Minimum | 14.00 | 33.00 | 2547.35 |
Maximum | 21.00 | 43.00 | 4766.35 |
Indices | ENN (TR) | ENN (TS) | MPMR (TR) | MPMR (TS) | GMDH (TR) | GMDH (TS) | ANFIS (TR) | ANFIS (TS) | Ideal Value |
---|---|---|---|---|---|---|---|---|---|
WMAPE | 0.005 | 0.006 | 0 | 0.001 | 0 | 0 | 0 | 0 | 0 |
NS | 0.999 | 0.999 | 0.999 | 0.999 | 1 | 1 | 1 | 1 | 1 |
RMSE | 2.03 | 31.24 | 0.32 | 8.29 | 0.6 | 2.13 | 0 | 2.13 | 0 |
VAF | 99.94 | 99.92 | 99.99 | 99.99 | 99.99 | 99.99 | 99.95 | 99.99 | 100 |
R2 | 0.999 | 0.999 | 0.999 | 0.999 | 1 | 1 | 1 | 1 | 1 |
Adj. R2 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 0.999 | 1 | 0.999 | 1 |
BF | 1.0 | 1.0 | 1.0 | 0.999 | 0.999 | 0.999 | 1 | 0.999 | 1 |
RSR | 0 | 0.01 | 0 | 0.002 | 0 | 0 | 0 | 0 | 0 |
NMBE | 0.05 | 0.16 | 0 | 0.025 | 0 | 0.012 | 0 | 0 | 0 |
MAPE | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
MBE | 0.57 | −6.9 | 0.036 | 1.09 | 0 | 0.53 | 0 | 0.53 | 0 |
LMI | 0.99 | 0.955 | 0.998 | 0.998 | 0.999 | 0.999 | 1 | 0.999 | 1 |
t-stat | 0.09 | 1.09 | 0.039 | 0.64 | 0.034 | 1.25 | 0 | 1.25 | 0 |
WI | 0.999 | 0.9996 | 0.999 | 0.999 | 0.999 | 1 | 1 | 1 | 1 |
S.No. | Parameters | ENN | MPMR | GMDH | ANFIS | ||||
---|---|---|---|---|---|---|---|---|---|
TR | TS | TR | TS | TR | TS | TR | TS | ||
1 | WMAPE | 1 | 1 | 2 | 2 | 2 | 3 | 2 | 3 |
2 | NS | 3 | 3 | 1 | 1 | 1 | 1 | 1 | 1 |
3 | RMSE | 1 | 1 | 3 | 2 | 2 | 3 | 4 | 3 |
4 | VAF | 1 | 1 | 3 | 2 | 3 | 2 | 2 | 2 |
5 | R2 | 1 | 1 | 1 | 1 | 3 | 3 | 3 | 3 |
6 | Adj. R2 | 1 | 1 | 1 | 1 | 1 | 1 | 4 | 1 |
7 | BF | 1 | 1 | 1 | 2 | 4 | 2 | 1 | 2 |
8 | RSR | 1 | 4 | 1 | 3 | 1 | 1 | 1 | 1 |
9 | NMBE | 1 | 1 | 2 | 2 | 2 | 3 | 2 | 4 |
10 | MAPE | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
11 | WI | 1 | 1 | 2 | 2 | 3 | 3 | 3 | 3 |
12 | MBE | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 3 |
13 | LMI | 4 | 2 | 3 | 1 | 2 | 3 | 1 | 3 |
14 | t-stat | 1 | 2 | 1 | 1 | 1 | 3 | 4 | 3 |
Total rank | 19 | 21 | 24 | 23 | 29 | 32 | 33 | 33 | |
Finial rank | 40 | 47 | 61 | 66 |
Models | Phase | M-W Test U Value | M-W Test p Value | AD Test U Value | AD Test p Value |
---|---|---|---|---|---|
ENN | Testing | 1570 | 0.99 | 0.04 | 1 |
Training | 1559 | 0.96 | 0.05 | 1 | |
MPMR | Testing | 1559 | 0.96 | 0.04 | 1 |
Training | 1570 | 0.99 | 0.04 | 1 | |
ANFIS | Testing | 1564 | 0.98 | 0.28 | 1 |
Training | 1564 | 0.98 | 0.28 | 1 | |
GMDH | Testing | 1568 | 1.00 | 0.04 | 1 |
Training | 1568 | 1.00 | 0.04 | 1 |
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Kumar, M.; Bardhan, A.; Samui, P.; Hu, J.W.; Kaloop, M.R. Reliability Analysis of Pile Foundation Using Soft Computing Techniques: A Comparative Study. Processes 2021, 9, 486. https://doi.org/10.3390/pr9030486
Kumar M, Bardhan A, Samui P, Hu JW, Kaloop MR. Reliability Analysis of Pile Foundation Using Soft Computing Techniques: A Comparative Study. Processes. 2021; 9(3):486. https://doi.org/10.3390/pr9030486
Chicago/Turabian StyleKumar, Manish, Abidhan Bardhan, Pijush Samui, Jong Wan Hu, and Mosbeh R. Kaloop. 2021. "Reliability Analysis of Pile Foundation Using Soft Computing Techniques: A Comparative Study" Processes 9, no. 3: 486. https://doi.org/10.3390/pr9030486