# Comparison of Wavelet Artificial Neural Network, Wavelet Support Vector Machine, and Adaptive Neuro-Fuzzy Inference System Methods in Estimating Total Solar Radiation in Iraq

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## Abstract

**:**

^{2}, and IA criteria were used to evaluate the performance of the techniques and compare the results with the actual measured value. The results showed that the WANN and WSVM methods had similar results in solar energy modeling. However, the results of the WANN technique were slightly better than the WSVM technique. In Wasit and Dhi Qar stations, the value of R

^{2}for the WANN and WSVM methods was 0.89 and 0.86, respectively. The value of R

^{2}in the WANN and WSVM methods in Wasit and Dhi Qar stations was 0.88 and 0.87, respectively. The ANFIS technique also obtained acceptable results. However, compared to the other two techniques, the ANFIS results were lower, and the R

^{2}value was 0.84 and 0.83 in Wasit and Dhi Qar stations, respectively.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Artificial Neural Network (ANN)

#### 2.3. Support Vector Machine (SVM)

#### 2.4. Wavelet Transform

#### 2.5. Adaptive Neural Fuzzy Inference System (ANFIS)

- Layer 1: Every node in this layer is equal to a fuzzy set, Equation (8).
- Layer 2: The input signals are multiplied and create output, Equation (9).
- Layer 3: This layer calculates the proportion of the activity grade of the i-th rule to the sum of the activity degrees of all the rules, Equation (10).
- Layer 4: The result of every node in this layer is as seen in Equation (11).
- Layer 5: Each node in this layer, which is displayed as ∑, calculates the last output value in the form of Equation (12).

#### 2.6. Criteria for Evaluating

^{2}) were used.

^{2}(Equation (14)) indicates how much of the changes in the dependent variable are influenced by the corresponding independent variable, and the rest of the dependent variables are related to other factors. R

^{2}is between zero and one. Zero indicates that the model does not determine any of the variability of the response data around its average. However, a value of one indicates that all observed values will be the same as the fitted values, and all the data points will lie on the fitted line [29].

#### 2.7. Training, Validation, and Testing Sets

## 3. Results

^{2}, MEA and IA) demonstrated that these models were able to predict solar energy.

^{2}and AI were related to WANN-3. The amount of RMSE, MAE, R

^{2}, and AI in the training phase were 3.42, 1.8, 0.89, and 0.98, respectively, and for the testing phase, the amounts were 2.84, 2.05, 0.88, and 0.97. However, the results of WANN-1 for Wasit station were also somewhat acceptable, but the difference with WANN-3 is significant. In the WANN model, the results obtained for Dhi Qar station from the WANN-2 model had the best values for the RMSE, MEA, R

^{2}, and AI criteria. The criteria values were equal to 2.93, 2.09, 0.86, and 0.97 in the training phase and 2.78, 2.09, 0.85, and 0.96 in the test phase. The investigation revealed that the answers of the WANN-1 model at Dhi Qar station were also acceptable.

^{2}and AI were related to WSVM-1. The amount of RMSE, MAE, R

^{2}, and AI in the training phase were 2.67, 1.58, 0.88, and 0.97, respectively, and for the testing phase, the amount was 2.45, 1.81, 0.86, and 0.95. However, the WSVM-4 model at Wasit station had close results with the WSVM-1 model, which was the best model at this station. The results of the other two models, WSVM-2 and WSVM-3, were acceptable. In the WSVM model, the results obtained for Dhi Qar station from the WANN-3 model had the best values for the RMSE, MEA, R

^{2}, and AI criteria. The criteria values were equal to 2.45, 1.92, 0.87, and 0.97 in the training phase and 2.54, 2.18, 0.85, and 0.97 in the test phase. In this station also, the WSVM-1 model obtained good results.

^{2}, and AI were related to ANFIS-4. The amount of RMSE, MAE, R

^{2}, and AI in the training phase were 2.7, 1.91, 0.84, and 0.92, respectively, and for the testing phase, the amount was 2.69, 2.11, 0.8, and 0.92. The results of the ANFIS-1 model in this station were also good. In the ANFIS model, the results obtained for Dhi Qar station from the ANFIS-2 model had the best values for the RMSE, MEA, R

^{2}, and AI criteria. The criteria values were 2.62, 2.13, 0.83, and 0.94 in the training phase and 2.64, 1.98, 0.78, and 0.92 in the test phase. The results of other models for this station differed greatly from the best model.

^{2}values in both the training and the test phases compared to the ANFIS model in both Wasit and Dhi Qar stations. These results showed that the performance of the WANN and WSVM models was better than the ANFIS model. However, the ANFIS model recorded values higher than 0.78 in both stations for the training and testing phases, which showed that this model could also record acceptable estimation. However, if it is possible to use two other models, it is better to use the WAAN and WSVM models.

## 4. Discussion

^{2}= 0.89, and IA = 0.98 was obtained in Wasit station, and RSME = 2.84, EMA = 2.05, R

^{2}= 0.86, and IA = 0.97 was obtained in Dhi Qar station. In the WSVM method, RSME = 2.67, EMA = 1.58, R

^{2}= 0.88, and IA = 0.97 for Wasit station. In Dhi Qar station, RSME = 2.54, EMA = 1.92, R

^{2}= 0.87, and IA = 0.97. In the ANFIS method, for Wasit station, RSME = 2.7, EMA = 1.91, R

^{2}= 0.84, and IA = 0.95. In Dhi Qar station, RSME = 2.62, EMA = 1.98, R

^{2}= 0.83, and IA = 0.94. The results of this study indicated that all three used models predict the results well. WANN and WSVM methods in solar energy modeling had similar results. However, the results of the WANN model were slightly better than the WSVM model. The ANFIS method also obtained acceptable results but compared to the other two models, ANFIS results were less accurate. The better results of WANN and WSVR could be due to the use of the wavelet model in data preprocessing. The results of this research are similar to research conducted in Mexico. In the research conducted in Mexico, two ANN and SVM models had better results than an ANFIS model [31]. Additionally, a study completed in Nigeria showed that the SVM model had better results than the ANFIS model [14]. In this research, the MLP model was used for the learning process in the WANN method. It is suggested to use EFB and CFB methods in future studies and evaluate the best learning method. Additionally, using the Gene Expression Programming (GEP) black box model to estimate radiation intensity and compare it with other models can be a subject for researchers in future studies.

## 5. Conclusions

^{2}for the WANN and WSVM methods was 0.89 and 0.86, respectively. The value of R

^{2}in the WANN and WSVM methods in the Wasit and Dhi Qar stations was 0.88 and 0.87, respectively. The ANFIS technique also obtained acceptable results. However, compared to the other two techniques, the ANFIS results were lower, and the R

^{2}value was 0.84 and 0.83 in Wasit and Dhi Qar stations, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Symbols | definition | Unit |

ANN | Artificial Neural Network | - |

SVM | Support Vector Machine | - |

ANFIS | Adaptive Neuro-Fuzzy Inference System | - |

WANN | Wavelet Artificial Neural Network | - |

WSVM | Wavelet Support Vector Machine | - |

Rs | solar radiation | MJ/m^{2} d |

TWh | Terawatt-hour | - |

GIS | Geographic Information System | - |

T max | Maximum Temperature | °C |

T min | Minimum Temperature | °C |

H ave | Average Humidity | % |

T avg | Average Temperature | °C |

${W}_{i,j}$ | The Connection Weight of Neuron j to Neuron i | - |

$K\left(X.{X}_{i}\right)$ | a Kernel Function | - |

${\theta}_{i}$ | The Bias of Neuron i | - |

ψ (x) | Wavelet Function | - |

${\overline{W}}_{i}$ | The Output of The Third layer in ANFIS Model | - |

$\{{p}_{i},\text{}{q}_{i},\text{}{r}_{i}\}$ | Set of Adaptive parameters | - |

RMSE | Root Mean Square Error | - |

MAE | Mean Absolute Error | - |

IA | Index of Agreement | - |

R^{2} | Coefficient of Determination | - |

${P}_{i}$ | The Predicted Radiation Intensity | MJ/m^{2} d |

$\overline{P}$ | The Mean Predicted Radiation Intensity | MJ/m^{2} d |

${O}_{i}$ | The Measured Radiation Intensity | MJ/m^{2} d |

$\overline{O}$ | The Mean Measured Radiation Intensity | MJ/m^{2} d |

$n$ | The Number of Recorded Data | - |

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**Figure 2.**Correlation between radiation intensity (Rs) assessed by WANN, WSVM, and ANFIS methods and observed values at Wasit station in two stages of training and testing.

**Figure 3.**Correlation between radiation intensity (Rs) assessed by WANN, WSVM, and ANFIS methods and observed values at Dhi Qar station in two stages of training and testing.

Station | Wasit | Dhi Qar | ||||
---|---|---|---|---|---|---|

Max | Min | Average | Max | Min | Average | |

T max (°C) | 43.5 | 17.8 | 31.2 | 44.8 | 17.3 | 32.4 |

T min (°C) | 25.4 | 5.7 | 15.6 | 28.1 | 6.2 | 17.1 |

H avg (%) | 95.6 | 3.7 | 28.4 | 97.2 | 5.4 | 29.2 |

S (h) | 13.8 | 0.0 | 9.7 | 13.4 | 0.0 | 9.2 |

Rs (MJ/m^{2} d) | 41.7 | 3.1 | 22.8 | 40.2 | 2.7 | 21.6 |

**Table 2.**The results of statistical analysis of different input patterns of WANN model in Rs evaluation.

Station | Dhi Qar | Wasit | |||||||
---|---|---|---|---|---|---|---|---|---|

Model | WANN-1 | WANN-2 | WANN-3 | WANN-4 | WANN-1 | WANN-2 | WANN-3 | WANN-4 | |

Training phase | RMSE | 3.10 | 2.76 | 3.00 | 3.08 | 3.01 | 3.40 | 2.42 | 3.21 |

MEA | 2.24 | 2.09 | 2.20 | 2.18 | 2.02 | 2.21 | 1.80 | 2.07 | |

R^{2} | 0.82 | 0.86 | 0.77 | 0.78 | 0.82 | 0.76 | 0.89 | 0.79 | |

IA | 0.96 | 0.97 | 0.96 | 0.95 | 0.95 | 0.95 | 0.98 | 0.96 | |

Validation Phase | RMSE | 3.18 | 2.83 | 3.20 | 3.36 | 3.08 | 3.38 | 2.59 | 3.22 |

MEA | 2.28 | 2.07 | 2.28 | 2.38 | 2.15 | 2.21 | 2.04 | 2.13 | |

R^{2} | 0.80 | 0.85 | 0.77 | 0.76 | 0.79 | 0.77 | 0.88 | 0.74 | |

IA | 0.96 | 0.95 | 0.95 | 0.93 | 0.93 | 0.94 | 0.96 | 0.95 | |

Testing Phase | RMSE | 3.39 | 2.93 | 3.24 | 3.47 | 3.1 | 3.30 | 2.84 | 3.20 |

MEA | 2.33 | 2.09 | 2.31 | 2.43 | 2.14 | 2.23 | 2.05 | 2.14 | |

R^{2} | 0.79 | 0.85 | 0.76 | 0.74 | 0.80 | 0.79 | 0.88 | 0.76 | |

IA | 0.94 | 0.96 | 0.93 | 0.93 | 0.95 | 0.95 | 0.97 | 0.96 |

**Table 3.**The results of statistical analysis of different input patterns of WSVM model in Rs evaluation.

Station | Dhi Qar | Wasit | |||||||
---|---|---|---|---|---|---|---|---|---|

Model | WSVM-1 | WSVM-2 | WSVM-3 | WSVM-4 | WSVM-1 | WSVM-2 | WSVM-3 | WSVM-4 | |

Training phase | RMSE | 2.88 | 3.06 | 2.45 | 3.13 | 2.67 | 3.02 | 3.00 | 2.69 |

MEA | 2.04 | 2.08 | 1.92 | 2.12 | 1.58 | 1.91 | 1.90 | 1.84 | |

R^{2} | 0.82 | 0.79 | 0.87 | 0.78 | 0.88 | 0.79 | 0.80 | 0.86 | |

IA | 0.96 | 0.96 | 0.97 | 0.95 | 0.97 | 0.96 | 0.96 | 0.96 | |

Validation Phase | RMSE | 3.07 | 3.57 | 2.49 | 3.52 | 2.45 | 3.86 | 3.38 | 2.99 |

MEA | 2.18 | 2.19 | 2.11 | 2.21 | 1.67 | 3.84 | 3.19 | 1.98 | |

R^{2} | 0.75 | 0.66 | 0.85 | 0.74 | 0.86 | 0.77 | 0.88 | 0.82 | |

IA | 0.94 | 0.94 | 0.96 | 0.94 | 0.93 | 0.95 | 0.94 | 0.95 | |

Testing Phase | RMSE | 3.37 | 3.77 | 2.54 | 3.68 | 2.45 | 3.92 | 3.42 | 3.27 |

MEA | 2.22 | 2.37 | 2.18 | 2.30 | 1.81 | 2.22 | 2.06 | 2.21 | |

R^{2} | 0.74 | 0.67 | 0.85 | 0.69 | 0.86 | 0.72 | 0.76 | 0.81 | |

IA | 0.95 | 0.92 | 0.97 | 0.93 | 0.95 | 0.93 | 0.94 | 0.96 |

**Table 4.**The results of statistical analysis of different input patterns of ANFIS model in Rs evaluation.

Station | Dhi Qar | Wasit | |||||||
---|---|---|---|---|---|---|---|---|---|

Model | ANFIS-1 | ANFIS-2 | ANFIS-3 | ANFIS-4 | ANFIS-1 | ANFIS-2 | ANFIS-3 | ANFIS-4 | |

Training phase | RMSE | 2.94 | 2.62 | 2.85 | 2.92 | 2.86 | 3.23 | 3.04 | 2.70 |

MEA | 2.12 | 1.98 | 2.09 | 2.07 | 1.91 | 2.10 | 1.96 | 1.91 | |

R^{2} | 0.74 | 0.83 | 0.73 | 0.77 | 0.80 | 0.72 | 0.75 | 0.84 | |

IA | 0.91 | 0.94 | 0.93 | 0.90 | 0.89 | 0.92 | 0.93 | 0.95 | |

Validation Phase | RMSE | 3.18 | 2.59 | 2.94 | 3.19 | 2.89 | 3.17 | 3.00 | 2.65 |

MEA | 2.14 | 2.08 | 2.11 | 2.24 | 2.00 | 2.09 | 2.17 | 2.10 | |

R^{2} | 0.71 | 0.81 | 0.73 | 0.75 | 0.84 | 0.69 | 0.71 | 0.81 | |

IA | 0.90 | 0.93 | 0.91 | 0.85 | 0.86 | 0.88 | 0.91 | 0.94 | |

Testing Phase | RMSE | 3.22 | 2.64 | 3.07 | 3.29 | 2.94 | 3.13 | 3.03 | 2.69 |

MEA | 2.21 | 2.13 | 2.19 | 2.31 | 2.03 | 2.11 | 2.15 | 2.11 | |

R^{2} | 0.70 | 0.78 | 0.72 | 0.70 | 0.76 | 0.70 | 0.72 | 0.80 | |

IA | 0.89 | 0.92 | 0.90 | 0.88 | 0.87 | 0.89 | 0.91 | 0.92 |

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## Share and Cite

**MDPI and ACS Style**

Anupong, W.; Jweeg, M.J.; Alani, S.; Al-Kharsan, I.H.; Alviz-Meza, A.; Cárdenas-Escrocia, Y.
Comparison of Wavelet Artificial Neural Network, Wavelet Support Vector Machine, and Adaptive Neuro-Fuzzy Inference System Methods in Estimating Total Solar Radiation in Iraq. *Energies* **2023**, *16*, 985.
https://doi.org/10.3390/en16020985

**AMA Style**

Anupong W, Jweeg MJ, Alani S, Al-Kharsan IH, Alviz-Meza A, Cárdenas-Escrocia Y.
Comparison of Wavelet Artificial Neural Network, Wavelet Support Vector Machine, and Adaptive Neuro-Fuzzy Inference System Methods in Estimating Total Solar Radiation in Iraq. *Energies*. 2023; 16(2):985.
https://doi.org/10.3390/en16020985

**Chicago/Turabian Style**

Anupong, Wongchai, Muhsin Jaber Jweeg, Sameer Alani, Ibrahim H. Al-Kharsan, Aníbal Alviz-Meza, and Yulineth Cárdenas-Escrocia.
2023. "Comparison of Wavelet Artificial Neural Network, Wavelet Support Vector Machine, and Adaptive Neuro-Fuzzy Inference System Methods in Estimating Total Solar Radiation in Iraq" *Energies* 16, no. 2: 985.
https://doi.org/10.3390/en16020985