Superiority of Hybrid Soft Computing Models in Daily Suspended Sediment Estimation in Highly Dynamic Rivers
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area and Data Collection
2.2. ANN
2.3. ANFIS
2.4. Subtractive Clustering
2.5. Wavelet Transform
2.6. Mother Wavelets
2.7. Gamma Test (GT)
2.8. Data Normalization
2.9. Training and Testing of Developed Models
2.10. Performance Evaluation of Developed Models
2.10.1. Quantitative Evaluation
2.10.2. Hydrological Indices
Coefficient of Efficiency (CE)
Pooled Average Relative Error (PARE)
2.11. Qualitative Evaluation
2.12. Uncertainty Analysis
2.12.1. Width of Uncertainty Band of Error Prediction (We)
2.12.2. 95% Confidence Interval of Error Prediction (CIe)
3. Results
3.1. Data Analysis
3.2. GT for Input Selection
3.3. Hydrological Model Development
3.3.1. ANN/ANFIS Models for Daily SSC Prediction
3.3.2. WANN/WANFIS Models for Daily SSC Prediction
3.4. Quantitative Performance Evaluation of Developed Models for Daily SSC Prediction
3.5. Qualitative Performance Evaluation of Developed Models for Daily SSC Prediction
3.6. Uncertainty Analysis
3.7. Sensitivity Analysis
4. Discussion
Comparison of ANN, WANN, ANFIS, and WANFIS Models for Daily SSC Prediction
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
Appendix C
Appendix D
Appendix D.1. Root Mean Squared Error (RMSE)
Appendix D.2. The Correlation Coefficient (r)
Appendix D.3. Willmott Index (WI)
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Statistical Parameters | Whole Data | Training Data Set | Testing Data Set | ||||||
---|---|---|---|---|---|---|---|---|---|
Rt (mm) | Qt (m3/s) | SSCt (g/L) | Rt (mm) | Qt (m3/s) | SSCt (g/L) | Rt (mm) | Qt (m3/s) | SSCt (g/L) | |
Mean | 14.60 | 215.65 | 0.059 | 12.00 | 141.03 | 0.048 | 20.61 | 388.02 | 0.084 |
Standard Deviation | 22.91 | 405.67 | 0.088 | 17.33 | 191.73 | 0.069 | 31.53 | 646.81 | 0.118 |
Kurtosis | 11.85 | 41.33 | 20.03 | 7.62 | 14.54 | 17.105 | 6.81 | 15.67 | 13.261 |
Skewness | 3.01 | 5.38 | 3.643 | 2.51 | 3.41 | 3.175 | 2.47 | 3.48 | 3.180 |
Range | 193.32 | 4641 | 0.841 | 119.51 | 1397.00 | 0.717 | 193.32 | 4640.50 | 0.839 |
Minimum | 0.00 | 0.00 | 0.000 | 0.00 | 0.00 | 0.000 | 0.00 | 0.50 | 0.002 |
Maximum | 193.32 | 4641 | 0.841 | 119.51 | 1397.00 | 0.717 | 193.32 | 4641.00 | 0.841 |
Count | 854 | 854 | 854 | 596 | 596 | 596 | 258 | 258 | 258 |
Variable | St | Rt | Rt-1 | Rt-2 | Rt-3 | Qt | Qt-1 | Qt-2 | Qt-3 | St-1 | St-2 | St-3 | p-Values |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
St | 1.00 | - | |||||||||||
Rt | 0.70 | 1.00 | 5.65 × 10−26 | ||||||||||
Rt − 1 | 0.68 | 0.74 | 1.00 | 0.73 | |||||||||
Rt − 2 | 0.61 | 0.58 | 0.74 | 1.00 | 0.97 | ||||||||
Rt − 3 | 0.51 | 0.45 | 0.58 | 0.74 | 1.00 | 0.27 | |||||||
Qt | 0.62 | 0.66 | 0.68 | 0.63 | 0.56 | 1.00 | 0.04 | ||||||
Qt − 1 | 0.54 | 0.48 | 0.66 | 0.68 | 0.63 | 0.89 | 1.00 | 0.78 | |||||
Qt − 2 | 0.44 | 0.37 | 0.48 | 0.66 | 0.68 | 0.75 | 0.89 | 1.00 | 0.93 | ||||
Qt − 3 | 0.35 | 0.29 | 0.37 | 0.48 | 0.66 | 0.65 | 0.75 | 0.89 | 1.00 | 0.10 | |||
St − 1 | 0.72 | 0.51 | 0.70 | 0.68 | 0.61 | 0.59 | 0.62 | 0.54 | 0.44 | 1.00 | 1.82 × 10−27 | ||
St − 2 | 0.60 | 0.41 | 0.51 | 0.70 | 0.68 | 0.56 | 0.59 | 0.62 | 0.54 | 0.72 | 1.00 | 0.00016 | |
St − 3 | 0.49 | 0.33 | 0.41 | 0.51 | 0.70 | 0.52 | 0.56 | 0.59 | 0.62 | 0.60 | 0.72 | 1.00 | 0.18 |
Model | Model Input Combination | Mask | Gamma | V − Ratio |
---|---|---|---|---|
M1 | Rt | 10000000000 | 0.0047802000 | 0.5471600 |
M2 | Rt, Rt − 1 | 11000000000 | 0.0042625000 | 0.4879000 |
M3 | Rt, R t− 1, Rt−2 | 11100000000 | 0.0041758000 | 0.4779800 |
M4 | Rt, Rt − 1, Rt − 2, Rt − 3 | 11110000000 | 0.0032813667 | 0.4219459 |
M5 | Rt, Rt − 1, Rt − 2, Qt | 11110000000 | 0.0038298000 | 0.4383700 |
M6 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt | 11111000000 | 0.0030169776 | 0.3879486 |
M7 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1 | 11111100000 | 0.0034506204 | 0.4437100 |
M8 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1, Qt − 2 | 11111110000 | 0.0034489278 | 0.4434924 |
M9 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1, Qt − 2, Qt − 3 | 11111111000 | 0.0032920565 | 0.4233205 |
M10 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1, Qt − 2, Qt − 3, St − 1 | 11111111100 | 0.0032920565 | 0.4233205 |
M11 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1, Qt − 2, Qt − 3, St − 1, St − 2 | 11111111110 | 0.0032920306 | 0.4233172 |
M12 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1, Qt − 2, Qt − 3, St − 1, St − 2, St − 3 | 11111111111 | 0.0032920306 | 0.4233172 |
M13 | Rt, Rt − 1, Rt − 2, Qt, St − 1, St − 2 | 11101000110 | 0.0034097067 | 0.4384490 |
M14 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, St − 1 | 11111000100 | 0.0030159990 | 0.3878227 |
M15 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, St − 1, St − 2 | 11111000110 | 0.0030159998 | 0.3878228 |
M16 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, St − 1, St − 2, St − 3 | 11111000111 | 0.0030165903 | 0.3878988 |
M17 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1, St − 1, St − 2, St − 3 | 11111100111 | 0.0034493755 | 0.4435500 |
M18 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1, Qt − 2, St − 1, St − 2, St − 3 | 11111110111 | 0.0034489289 | 0.4434925 |
M19 | Rt, Rt − 1, Rt − 2, Qt, Qt − 1, Qt − 2, Qt − 3, St − 1, St − 2, St − 3 | 11101111111 | 0.0033026471 | 0.4246824 |
M20 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1, Qt − 2, Qt − 3, St − 1, St − 2 | 11111111110 | 0.0032920306 | 0.4233172 |
M21 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1, Qt − 2, St − 1, St − 2, St − 3 | 11111110111 | 0.0034489289 | 0.4434925 |
M22 | Rt, Rt − 1, Rt − 2, Qt, Qt − 1 | 11101100000 | 0.0042706000 | 0.4888370 |
M23 | Rt, Rt − 1, Rt − 2, Rt − 3, Qt, Qt − 1 | 11111100000 | 0.0034506204 | 0.4437100 |
M24 | Rt, Rt − 1, Rt − 2, Qt, Qt − 1, Qt − 2 | 11111100000 | 0.0040742000 | 0.4663550 |
M25 | Rt, Rt − 1, Rt − 2, Qt, Qt − 1, Qt − 2, St − 1 | 11101110100 | 0.0040742000 | 0.4663550 |
M26 | Rt, Rt − 1, Rt − 2, Qt, Qt − 1, Qt − 2, St − 1, St − 2 | 11101110110 | 0.0040742000 | 0.4663550 |
M27 | Rt, Rt − 1, Rt − 2, St − 2 | 11100000010 | 0.0041747000 | 0.4778580 |
M28 | Rt, Rt − 1, Rt − 2, St − 1, St − 2 | 11100000110 | 0.0041719000 | 0.4775350 |
M29 | Rt, Rt − 1, Rt − 2, Qt, St − 1 | 11101000100 | 0.0038292000 | 0.4383100 |
M30 | Rt, Rt − 1, Rt − 2, Qt, St − 1, St − 2 | 11101000110 | 0.0038289000 | 0.4382700 |
M31 | Rt, Rt − 1, Rt − 2, Qt, Qt − 1, St − 1, St − 2 | 11111100110 | 0.0042695000 | 0.4887090 |
M32 | Rt − 1 | 01000000000 | 0.0045396000 | 0.5196200 |
M33 | Rt − 1, Rt − 2 | 01100000000 | 0.0046157000 | 0.5283400 |
M34 | Rt − 1, Rt − 2, Qt | 01101000000 | 0.0048902000 | 0.5597500 |
M35 | Rt − 1, Rt − 2, Qt, St − 1 | 01101000100 | 0.0048889000 | 0.5596100 |
M36 | Rt − 1, Rt − 2, Qt, St − 1, St − 2 | 01101000110 | 0.0048885000 | 0.5595600 |
M37 | Rt − 1, Rt − 2, Qt, Qt − 1, St − 1, St − 2 | 01101100110 | 0.0045635000 | 0.5223630 |
M38 | Rt − 1, Rt − 2, Qt, Qt − 1, Qt − 2, St − 1, St − 2 | 01101110110 | 0.0044611000 | 0.5106410 |
M39 | Rt − 2 | 00100000000 | 0.0059649000 | 0.6827700 |
M40 | Rt − 2, Qt | 00101000000 | 0.0049465000 | 0.5662000 |
M41 | Rt − 2, Qt, St − 1 | 00101000100 | 0.0049457000 | 0.5661100 |
M42 | Rt − 2, Qt, St − 1, St − 2 | 00101000110 | 0.0049452000 | 0.5660450 |
M43 | Qt | 00001000000 | 0.0053284000 | 0.6099170 |
M44 | Qt, St − 1 | 00001000100 | 0.0053036000 | 0.6070760 |
M45 | Qt, St − 1, St − 2 | 00001000110 | 0.0052017000 | 0.5954070 |
M46 | St − 1 | 00000000100 | 0.0045528000 | 0.5211380 |
M47 | St − 1, St − 2 | 00000000110 | 0.0046496000 | 0.5322160 |
M48 | St − 2 | 00000000010 | 0.0060325000 | 0.6905120 |
M49 | Rt, Rt − 2, Qt, St − 1, St − 2 | 10101000110 | 0.0041118000 | 0.4706530 |
M50 | Rt, Qt, St − 1, St − 2 | 10001000110 | 0.0042217000 | 0.4832370 |
M51 | Rt, St − 1, St − 2 | 10000000110 | 0.0039567000 | 0.4529040 |
M52 | Rt, St − 2 | 10000000010 | 0.0042196000 | 0.4830030 |
M53 | Rt, Rt − 1, Qt, St − 1, St − 2 | 11001000110 | 0.0038594000 | 0.4417640 |
M54 | Rt, Rt − 1, St − 1, St − 2 | 11000000110 | 0.0042129000 | 0.4822330 |
M55 | Rt, Rt − 1, St − 2 | 11000000010 | 0.0042181000 | 0.4828270 |
M56 | Rt, Rt − 1, Rt − 2, St − 1, St − 2 | 11100000110 | 0.0041719000 | 0.4775350 |
M57 | Rt, Rt − 1, Rt − 2, St − 2 | 11100000010 | 0.0041747000 | 0.4778580 |
M58 | Rt, Rt − 1, Rt − 2, Qt, St − 2 | 11101000010 | 0.0038293000 | 0.4383140 |
Model | Architecture | Training | Testing | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
RMSE (g/L) | r | WI | CE | PARE (%) | RMSE (g/L) | r | WI | CE | PARE (%) | ||
ANN-3 | 6-3-1 | 0.040 | 0.81 | 0.78 | 0.655 | 0.0017 | 0.078 | 0.75 | 0.73 | 0.560 | −0.013 |
Haar-WANN-21 | 18-21-1 | 0.042 | 0.80 | 0.73 | 0.633 | 0.0041 | 0.069 | 0.83 | 0.74 | 0.661 | 0.006 |
db2-WANN-21 | 18-21-1 | 0.031 | 0.90 | 0.72 | 0.801 | 0.0236 | 0.061 | 0.86 | 0.75 | 0.734 | −0.012 |
coif2-WANN-11 | 18-11-1 | 0.021 | 0.95 | 0.81 | 0.903 | 0.0134 | 0.065 | 0.84 | 0.76 | 0.696 | −0.017 |
Model | Training | Testing | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
RMSE (g/L) | R | WI | CE | PARE (%) | RMSE (g/L) | r | WI | CE | PARE (%) | |
ANFIS-29 | 0.041 | 0.80 | 0.78 | 0.638 | 6.6 × 10−9 | 0.080 | 0.78 | 0.73 | 0.545 | 0.060 |
Haar-WANFIS-27 | 0.032 | 0.88 | 0.83 | 0.782 | 1.7 × 10−9 | 0.074 | 0.82 | 0.76 | 0.605 | 0.017 |
db2-WANFIS-25 | 0.023 | 0.94 | 0.85 | 0.892 | 2.1 × 10−10 | 0.068 | 0.84 | 0.77 | 0.666 | 0.051 |
coif2-WANFIS-43 | 0.029 | 0.91 | 0.83 | 0.821 | 3 × 10−11 | 0.060 | 0.87 | 0.80 | 0.745 | 0.015 |
Model | We (g/L) | CIe(g/L) |
---|---|---|
ANN-3 | ±0.0096 | −0.0125 to 0.0067 (0.0192) |
Haar-WANN-121 | ±0.0084 | −0.0071 to 0.0097 (0.0168) |
db2-WANN-21 | ±0.0074 | −0.0100 to 0.0049 (0.0149) |
coif2-WANN-11 | ±0.0080 | −0.0118 to 0.0042 (0.0160) |
ANFIS-29 | ±0.0096 | 0.0226 to 0.0034 (0.0260) |
Haar-WANFIS-27 | ±0.0091 | −0.0054 to 0.0128 (0.0182) |
db2-WANFIS-25 | ±0.0083 | 0.0028 to 0.0193 (0.0221) |
coif2-WANFIS-43 | ±0.0073 | −0.0041 to 0.0105 (0.0146) |
Inputs | Training | Testing | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
RMSE (g/L) | r | WI | CE | PARE (%) | RMSE (g/L) | r | WI | CE | PARE (%) | |
Rt, Rt − 1, Rt − 2, Rt − 3, Qt, St − 1 | 0.040 | 0.81 | 0.78 | 0.655 | 0.0017 | 0.078 | 0.75 | 0.73 | 0.560 | −0.013 |
Rt − 1, Rt − 2, Rt − 3, Qt, St − 1 | 0.043 | 0.78 | 0.72 | 0.612 | 0.0037 | 0.091 | 0.71 | 0.67 | 0.409 | 0.032 |
Rt, Rt − 2, Rt − 3, Qt, St − 1 | 0.040 | 0.82 | 0.77 | 0.666 | 0.0015 | 0.080 | 0.73 | 0.72 | 0.539 | 0.008 |
Rt, Rt − 1, Rt − 3, Qt, St − 1 | 0.043 | 0.79 | 0.68 | 0.613 | 0.0138 | 0.089 | 0.66 | 0.68 | 0.427 | −0.054 |
Rt, Rt − 1, Rt − 2, Qt, St − 1 | 0.045 | 0.77 | 0.63 | 0.570 | 0.0327 | 0.096 | 0.68 | 0.67 | 0.342 | 0.054 |
Rt, Rt − 1, Rt − 2, Rt − 3, St − 1 | 0.041 | 0.80 | 0.73 | 0.639 | 0.0207 | 0.087 | 0.69 | 0.69 | 0.455 | −0.046 |
Rt, Rt − 1, Rt − 2, Rt − 3, Qt | 0.045 | 0.75 | 0.69 | 0.563 | 0.0071 | 0.108 | 0.45 | 0.59 | 0.160 | −0.027 |
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Bajirao, T.S.; Kumar, P.; Kumar, M.; Elbeltagi, A.; Kuriqi, A. Superiority of Hybrid Soft Computing Models in Daily Suspended Sediment Estimation in Highly Dynamic Rivers. Sustainability 2021, 13, 542. https://doi.org/10.3390/su13020542
Bajirao TS, Kumar P, Kumar M, Elbeltagi A, Kuriqi A. Superiority of Hybrid Soft Computing Models in Daily Suspended Sediment Estimation in Highly Dynamic Rivers. Sustainability. 2021; 13(2):542. https://doi.org/10.3390/su13020542
Chicago/Turabian StyleBajirao, Tarate Suryakant, Pravendra Kumar, Manish Kumar, Ahmed Elbeltagi, and Alban Kuriqi. 2021. "Superiority of Hybrid Soft Computing Models in Daily Suspended Sediment Estimation in Highly Dynamic Rivers" Sustainability 13, no. 2: 542. https://doi.org/10.3390/su13020542