# A Cascaded Adaptive Network-Based Fuzzy Inference System for Hydropower Forecasting

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

- Generally, artificial neural network-based algorithms are bulky in the complexity of the calculations.
- The methods are to use when the predictions depend on the uncertainty factors and non-linear inputs.
- The methods are not likely to generate the best possible predictions because the input factors vary depending on the different environments.
- The methods are require enormous amounts of computing power.

- This system uses fuzzy logic approach along with a neural network to address the uncertainty and the non-linearity of the inputs.
- The base algorithm of this system is two-input one-output ANFIS, and the computational power reduces dramatically.
- It is possible to generate a near-zero error in the prediction by increasing the number of levels in the Cascaded ANFIS algorithm.
- This study presents future power generation up to the year 2099 using two different climate models.
- The comparative study presented in this work provides a solid understanding of the potential regarding the Cascaded ANFIS algorithm compared to that of the cutting-edge time series prediction algorithms.

#### Hydropower in Sri Lanka

## 3. Study Area

^{2}) is midland, made of marble and quartz, and has an average altitude of around 530 m [30]. The region is located inside the rainy region of the country (wet zone), having a mean annual precipitation of around 2500 mm [35]. The southwest monsoon provides the majority of the rainfall for the catchment, though there are minor contributions from the northeast monsoon and inter-monsoon storms. The Samanalawewa Hydroelectric Project includes a U-shaped rockfill dam which is around 110 m high from its foundation. The power station is capable of producing 124 MW as per the design guidelines. Figure 1 illustrates a detailed catchment map.

^{3}/s [38].

## 4. Methodology

#### 4.1. Climate Data Extraction for Future

#### 4.1.1. Implementation of the Cascaded ANFIS Algorithm

#### 4.1.2. Parameter Settings for Each Algorithm

- Multilayer Perception (MLP)
- K-Nearest Neighbors (KNN)
- Adaptive Network-based Fuzzy Inference System (ANFIS)
- Particle Swarm Optimization with ANFIS (ANFIS-PSO (Hybrid))
- Genetic algorithms with ANFIS (ANFIS-GA (Hybrid))
- Linear regression
- Lasso regression
- Ridge regression
- Recurrent neural network (RNN)
- Long short-term memory (LSTM)
- Gated recurrent unit (GRU)
- Cascaded ANFIS

## 5. Results and Discussion

#### 5.1. Comparison of the Algorithms

^{2}which is 0.061 as in Figure 5. Here, the training and the testing of these algorithms were conducted using the same experimental conditions. The calculation of the difference between the real value and the prediction was conducted up to eight decimals. LR and Lasso Regression calculation results were almost the same except for the last few decimals. When presenting the results in this paper, the accuracies were rounded up to two decimals points, and it caused the plots of LR and Lasso Regression to be the same in this analysis.

#### 5.2. Forecasting of Hydropower Generation in the Future

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

ANFIS | Adaptive Network Based Fuzzy Inference System |

RNN | Recurrent Neural Network |

LSTM | Long Short-Term Memory |

GRU | Gated Recurrent Unit |

RCP | Representative Concentration Pathway |

SDG | Sustainable Development Goals |

GCMs/RCMs | Global/Regional Climate Models |

ANN | Artificial Neural Network |

ARIMA | Auto Regressive Integrated Moving Average |

FIS | Fuzzy Infererence System |

FL | Fuzzy Logic |

ML | Machine Learning |

PSO | Particle Swarm Optimization |

GA | Genetic Algorithms |

RMSE | Root Mean Square Error |

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**Figure 4.**Coefficients of Determination $\left({R}^{2}\right)$ of Rain Fall Test dataset for (

**a**) KNN, (

**b**) MLP, (

**c**) ANFIS (

**d**) PSO-ANFIS, and (

**e**) GA-ANFIS.

**Figure 5.**Coefficients of Determination $\left({R}^{2}\right)$ of Rain Fall Test dataset for (

**a**) linear regression, (

**b**) lasso regression, (

**c**) ridge regression (

**d**) RNN, (

**e**) LSTM, and (

**f**) GRU.

**Figure 9.**Hydropower predictions from Khaniya et al. (2020) [12].

Balangoda | Alupola | Detanagalla | Belihuloya | Nonpareil | Nagrak Estate | Power | |
---|---|---|---|---|---|---|---|

count | 127.00 | 127.00 | 127.00 | 127.00 | 127.00 | 127.00 | 127.00 |

mean | 377.88 | 190.57 | 221.81 | 240.77 | 183.42 | 187.65 | 22.86 |

std | 224.50 | 161.46 | 215.17 | 218.55 | 156.57 | 183.21 | 14.69 |

min | 27.40 | 7.50 | 0.00 | 2.70 | 0.00 | 0.67 | 1.10 |

25% | 205.35 | 61.35 | 50.55 | 83.30 | 54.54 | 40.31 | 10.72 |

50% | 348.10 | 136.60 | 144.50 | 160.20 | 132.20 | 124.95 | 21.04 |

75% | 509.05 | 308.05 | 349.90 | 353.95 | 289.53 | 282.10 | 34.00 |

max | 1159.90 | 734.70 | 926.10 | 1371.00 | 661.30 | 930.30 | 67.85 |

Algorithm | Parameters | |
---|---|---|

MLP | Hidden layer size | 50, 50, 50 |

Activation | tanh | |

Solver | adam | |

alpha | 0.05 | |

learning rate | constant | |

KNN | Weights | Uniform |

n_neighbors | 1 | |

ANFIS | Iteration | 100 |

Membership Functions | 3 | |

Step Size | 0.1 | |

Decrease rate | 0.9 | |

Increase rate | 1.1 | |

ANFIS-PSO | Inertia Weight | 1 |

Inertia weight damping ratio | 0.99 | |

Personal Learning Coefficient | 1 | |

Global Learning Coefficient | 2 | |

ANFIS-GA | Crossover Percentage | 0.7 |

Mutation Percentage | 0.5 | |

Mutation Rate | 0.1 | |

Selection Pressure | 8 | |

Gamma | 0.2 | |

RNN/LSTM/GRU | Optimizer | adam |

Learning rate | 0.0001 | |

Activation | relu | |

batch size | 30 | |

epochs | 100 | |

Cascaded ANFIS | Iteration | 100 |

Membership Functions | 3 | |

Step Size | 0.1 | |

Decrease rate | 0.9 | |

Increase rate | 1.1 |

Algorithm | RMSE (Train) | RMSE (Test) |
---|---|---|

MLP | 7.52 | 25.26 |

KNN | 9.73 | 19.33 |

ANFIS | 10.47 | 18.06 |

ANFIS-PSO | 10.99 | 16.61 |

ANFIS-GA | 11.88 | 16.87 |

Linear Regression | 13.74 | 14.85 |

Lasso Regression | 13.72 | 14.82 |

Ridge Regression | 13.70 | 14.88 |

RNN | 7.85 | 11.62 |

GRU | 6.50 | 8.33 |

LSTM | 6.03 | 6.88 |

Cascaded ANFIS | 1.01 | 1.80 |

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**MDPI and ACS Style**

Rathnayake, N.; Rathnayake, U.; Dang, T.L.; Hoshino, Y. A Cascaded Adaptive Network-Based Fuzzy Inference System for Hydropower Forecasting. *Sensors* **2022**, *22*, 2905.
https://doi.org/10.3390/s22082905

**AMA Style**

Rathnayake N, Rathnayake U, Dang TL, Hoshino Y. A Cascaded Adaptive Network-Based Fuzzy Inference System for Hydropower Forecasting. *Sensors*. 2022; 22(8):2905.
https://doi.org/10.3390/s22082905

**Chicago/Turabian Style**

Rathnayake, Namal, Upaka Rathnayake, Tuan Linh Dang, and Yukinobu Hoshino. 2022. "A Cascaded Adaptive Network-Based Fuzzy Inference System for Hydropower Forecasting" *Sensors* 22, no. 8: 2905.
https://doi.org/10.3390/s22082905