# Capability and Robustness of Novel Hybridized Artificial Intelligence Technique for Sediment Yield Modeling in Godavari River, India

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## Abstract

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## 1. Introduction

## 2. Proposed Methodology

#### 2.1. GA-ANN

^{9}) with the help of normalization. The normalization process can be carried out using the following equation:

_{norm}represents the normalized value of C

_{i}, which is the ith chromosomal 8-bit binary coded number; the constants ‘b’ and ‘a’ represents the highest and lowest values, respectively within that range ‘µ’ is normalized and therefore the values of ‘b’ and ‘a’ are 9 × 10

^{9}and 0.001, respectively; C

_{min}and C

_{max}represents the lowest and highest values in decimal of an eight-bit binary form of ‘µ’.

#### 2.2. ANN

#### 2.3. MLR Model

#### 2.4. SRC Model

## 3. Data Analysis of Study Region

#### 3.1. Study Region

#### 3.2. Statistical Data Analysis

_{min}), standard deviation (SD), mean (X

_{mean}), overall maximum (X

_{max}) values, skewness, variation coefficient (C

_{v}) and the ratio of maximum to mean. It can be observed that SSY, WL and WD are positively skewed which means relatively asymmetric. Negative skewness explains a distribution which achieves more negative (lesser than average) values, whereas positively skewed explains a distribution which attains more positive (greater than average) values. During this study, the skew value ranges from 1.476 to 4.538, this is supposed to be high because it is greater than 1. SSY has the highest skewness values. A higher skewed value has a more negative impact on the ANN’s performance [99]. It is detected that SSY has the highest coefficient of variation (C

_{v}), standard deviation (SD) and max/mean values among all parameters which show that SSY has a more scattered nature and erratic behavior as compared with WD and WL. These statistical analyses reveal that SSY has maximum variability and complex nonlinear behaviors. From Figure 3, it is noticed that the SSY varies nonlinearity in proportion to WD and WL.

#### 3.3. Data Preparation and Data Processing

_{norm}represents the normalized value, D

_{i}indicates ith original value, D

_{max}and D

_{min}represents the max and min values of the data.

## 4. Results and Discussion

#### 4.1. GA-ANN

^{2}), mean absolute error (MAE), error variance (VAR) and root mean square error (RMSE) were utilized.

^{2}value is very high. According to the statistical findings, it is demonstrated that the constructed GA-ANN model achieved a higher accuracy in predicting the SSY. Because of the low error parameters and strong R

^{2}values, the model was protected from over and underfitting. The best hybrid GA-ANN model was constructed to predict SSY utilizing with just WD and WL as input parameters. The error statistics data also reveal that MAE and RMSE had comparable types of patterns. The results reveal a direct proportional association between RMSE, variance, and MAE statistics data. These results also reveal that MAE, variance and RMSE had comparable types of patterns.

#### 4.2. ANN

^{9}; and the value of µ decreased and increased by a factor of 0.10 and 10, respectively. The proposed GA-ANN model started with an initialized µ value and changed the value for each epoch to enhance the ANN’s accuracy. The optimum value of neurons and µ value in the single hidden layer of the ANN technique is equal to 30 and 0.001, respectively.

^{2}, VAR and MSE in the validation, testing and training states. Table 5 demonstrates that the RMSE (0.0376–0.0538) and MAE (0.0207–0.237) of the ANN technique is very low and r (0.799–0.924) is very high during testing, validation, and training period. These results confirm that SSY prediction by ANN model has much more accurate performance. The lower values of RMSE, MAE, MSE, error variance and higher values of r in testing, validation and training are all nearly close to each other which shows that under-fitted or over-fitted problems were not encountered in the ANN model. After result analysis, it was also found that MAE and RMSE have similar trends. It was also observed that the RMSE varied proportionally to MAE in the ANN model.

#### 4.3. MLR

#### 4.4. SRC

#### 4.5. Comparative Assessment of Various Models on the Basis of Testing Data Set

^{2}statistical metrics were employed during testing for all ANN, GA-ANN, SRC and MLR models with optimized parameters of the models demonstrated in Table 8. Performances of the GA-ANN model were compared with SRC, MLR and ANN models. During the testing phase, all of the models utilized the identical SSY dataset. The comparison was based on estimated SSY and observed SSY of testing data. It can be observed that the proposed hybrid novel GA-ANN technique provided better results on the basis of R

^{2}and RMSE as compared with the conventional models.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Location of Polavaram site in Godavari River Basin, Andhra Pradesh, India [98].

**Figure 3.**Variations in daily mean of hydro climatic data: SSY (tons/day), WL (m) and WD (cummec) at the Polavaram in Godavari River Basin.

**Figure 6.**(

**a**) Hydrograph and (

**b**) scatter plot based on test data between the predicted GA-ANN SSY and observed SSY.

**Figure 7.**(

**a**) Hydrograph and (

**b**) scatter plot based on test data between the ANN predicted SSY and observed SSY.

**Figure 8.**(

**a**) Hydrograph and (

**b**) scatter plot based on test data between the MLR predicted SSY and observed SSY.

**Figure 9.**(

**a**) Hydrograph and (

**b**) scatter plot based on test data between the SRC predicted and observed SSY.

**Table 1.**Statistics constraints of hydrological and climatical data at Polavaram, Godavari River Basin.

Statistics | WD (m ^{3}/s) | WL (m) | SSY (tons/day) |
---|---|---|---|

Mean (X_{mean}) | 4.502 | 2850.6 | 3131 |

Standard Deviation (SD) | 2.8 | 5830.1 | 7115.9 |

Maximum (X_{max}) | 17.12 | 57,310.57 | 86,400 |

Minimum (X_{min}) | 1.18 | 46.927 | 0 |

Skewness | 1.4764 | 3.6159 | 4.5379 |

Coefficient of variation (C_{v}) | 0.622 | 2.045 | 2.272 |

X_{max}/X_{mean} | 3.802 | 20.104 | 27.60 |

WD | WL | SSY | |
---|---|---|---|

WD | 1 | ||

WL | 0.8974 | 1 | |

SSY | 0.8586 | 0.7942 | 1 |

WD | WL | SSY | |
---|---|---|---|

WD | 1 | ||

WL | 0.9389 | 1 | |

SSY | 0.7633 | 0.7967 | 1 |

SL | Statistics | Training | Testing | Validation |
---|---|---|---|---|

1. | MAE | 0.01678 | 0.020492 | 0.018921 |

2. | R | 0.873212 | 0.926835 | 0.79354 |

3. | MSE | 0.001492 | 0.002836 | 0.001786 |

4. | R^{2} | 0.7624 | 0.8589 | 0.6288 |

5. | RMSE | 0.038627 | 0.053252 | 0.042259 |

6. | Error variance | 0.001491 | 0.002779 | 0.00166 |

SL | Error Statistics | Testing | Validation | Training |
---|---|---|---|---|

1. | RMSE | 0.0538 | 0.04514 | 0.0376 |

2. | MAE | 0.237 | 0.0230 | 0.0207 |

3. | r | 0.924 | 0.799 | 0.8797 |

4. | Error variance | 0.00269 | 0.00195 | 0.00141 |

5. | MSE | 0.00289 | 0.002038 | 0.001414 |

6. | R^{2} | 0.853 | 0.638 | 0.7738 |

SL. | Error Statistics | Training | Testing | Validation |
---|---|---|---|---|

1. | MAE | 0.017119 | 0.020384 | 0.018783 |

2. | r | 0.872037 | 0.92169 | 0.791669 |

3. | MSE | 0.001499 | 0.002967 | 0.0018 |

4. | R^{2} | 0.7604 | 0.8495 | 0.6267 |

5. | RMSE | 0.038723 | 0.054473 | 0.042425 |

6. | Error variance | 0.0015 | 0.002857 | 0.001687 |

SL. | Statistics | Training | Testing | Validation |
---|---|---|---|---|

1. | MAE | 0.028542 | 0.031133 | 0.014297 |

2. | R^{2} | 0.7463 | 0.8489 | 0.5739 |

3. | Error variance | 0.003 | 0.005905 | 0.000881 |

4. | r | 0.900352 | 0.917363 | 0.99081 |

5. | MSE | 0.003814 | 0.00686 | 0.000969 |

6. | RMSE | 0.061759 | 0.082824 | 0.031131 |

**Table 8.**Performance comparison of various models with optimum parameters. Bold values show the best results.

Model | RMSE | Input | MAE | Optimum Parameters | Correlation Coefficient (r) |
---|---|---|---|---|---|

GA-ANN | 0.0533 | Q, WL | 0.0205 | TF: tan-sigmoid and pure linear, NN: 11; CP: 0.9; CC: 43; HL: 1; G: 50; PS: 50; MP: 0.05 | 0.9268 |

ANN | 0.0538 | Q, WL | 0.0237 | CC: 0.001; NN: 30; HL: 1; TF: tan-sigmoid and pure linear | 0.9240 |

MLR | 0.0545 | Q, WL | 0.0204 | a: 0.0076; b: 0.0075; c:0.681 | 0.9217 |

SRC | 0.0828 | Q | 0.0311 | a: 0.4379; b: 1.0799 | 0.9174 |

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## Share and Cite

**MDPI and ACS Style**

Yadav, A.; Joshi, D.; Kumar, V.; Mohapatra, H.; Iwendi, C.; Gadekallu, T.R.
Capability and Robustness of Novel Hybridized Artificial Intelligence Technique for Sediment Yield Modeling in Godavari River, India. *Water* **2022**, *14*, 1917.
https://doi.org/10.3390/w14121917

**AMA Style**

Yadav A, Joshi D, Kumar V, Mohapatra H, Iwendi C, Gadekallu TR.
Capability and Robustness of Novel Hybridized Artificial Intelligence Technique for Sediment Yield Modeling in Godavari River, India. *Water*. 2022; 14(12):1917.
https://doi.org/10.3390/w14121917

**Chicago/Turabian Style**

Yadav, Arvind, Devendra Joshi, Vinod Kumar, Hitesh Mohapatra, Celestine Iwendi, and Thippa Reddy Gadekallu.
2022. "Capability and Robustness of Novel Hybridized Artificial Intelligence Technique for Sediment Yield Modeling in Godavari River, India" *Water* 14, no. 12: 1917.
https://doi.org/10.3390/w14121917