# A Comparative Assessment of Predicting Daily Solar Radiation Using Bat Neural Network (BNN), Generalized Regression Neural Network (GRNN), and Neuro-Fuzzy (NF) System: A Case Study

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. Layer 1: Data Gathering

_{1}, x

_{2}, .., x

_{n}) and z

_{ij}is the i

^{th}normalized data for the j

^{th}feature.

#### 3.2. Layer 2: Data Mining

#### 3.3. Layer 3: Machine Learning

- The layers of input.
- The hidden layers.
- The interconnection among various layers.
- The learning procedure to optimize and update interconnections weights.
- The transformer function aimed at delivering weighted inputs to target outputs.
- The quantity of the neurons performing in each layer.
- The output layers.

_{ij}, to construct a more precise network and minimize the performance (lost) function [32]. Consequently, the performance of the network depends on the learning algorithms. Numerous successful research studies have applied metaheuristic and intelligent algorithms, like the genetic algorithm, to train ANNs [43].

_{i}, which is representative of position/solution; v

_{i}, which refers to the velocity and dimension of the searching space; and in the next stage, the initial frequency has to be determined by the following equation:

_{min}and f

_{max}stand for predefined parameters that vary depending on the problem. Then, s

_{i}and v

_{i}must be updated using the following equations:

^{t}specifies the mean loudness value at the current iteration. A

_{i}and r

_{i}stand for loudness and pulse rate, respectively. These parameters update at each stage by means of the following equations:

_{i}usually decreases and pulse rate r

_{i}usually increases one the bat reaches its target, so $\propto \in \left(0,1\right)$ and $\gamma >0$ are constant predefined values. Also, when$t\to \infty $:

## 4. Experimental Results

#### 4.1. Data

#### 4.2. Model Implementation

## 5. Conclusions

^{2}) as two evaluation criteria, the BNN model was quite promising. For example, the MAE values of the BNN model were almost a third of the values of the ANFIS model in Jask and Tehran cities. Similarly, in Kermanshah and Ramsar cities, the MAE values of the BNN model gained almost half of the MAE values of the GRNN model. Furthermore, for the nominated cities, the values of R

^{2}of the BNN model were better than the other models. In Jask city, the value of R

^{2}of the BNN model was 0.981. Therefore, the BNN possessed a better performance than ANFIS and GRNN.

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**The conceptual framework of the proposed methodology. BA: Bat Algorithm; ANN: artificial neural network.

**Figure 7.**Comparison of estimated value of models and real data for test data of Tehran (MJ/M

^{2}/day).

**Figure 8.**Comparison of estimated value of models and real data for test data of Ramsar (MJ/M

^{2}/day).

**Figure 9.**Comparison of estimated value of models and real data for test data of Kermanshah (MJ/M

^{2}/day).

**Figure 10.**Comparison of estimated value of models and real data for test data of Jask (MJ/M

^{2}/day).

Number# | Feature | Description | Selected |
---|---|---|---|

1 | Fr1 | Sunshine | Yes |

2 | Fr2 | Mean Daily Temperature | Yes |

3 | Fr3 | Mean Wind Speed | Yes |

4 | Fr4 | Mean Humidity | Yes |

5 | Fr5 | RRR | Yes |

6 | Fr6 | Mean QFE | No |

7 | Fr7 | Mean Dew | No |

8 | Fr8 | Latitude | No |

9 | Fr9 | Elevation | No |

10 | Fr10 | Longitude | No |

Model | Parameters |
---|---|

GRNN | $\mathrm{spread}=0.2$ |

ANFIS | FIS Generation Approach: Subtractive Clustering Influence Radius = 0.55 Maximum Number of Epochs = 100 Error Goal = 0 Step Size Increasing = 1.1 |

The proposed BNN | Number of Neurons = 6 Architecture of Neural Network: (5-6-1) Population Size = 5 Number of Generations = 5 F _{min} = 0F _{max} = 1Lambda = 1.5 Alpha = 0.5 |

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**MDPI and ACS Style**

Lotfinejad, M.M.; Hafezi, R.; Khanali, M.; Hosseini, S.S.; Mehrpooya, M.; Shamshirband, S. A Comparative Assessment of Predicting Daily Solar Radiation Using Bat Neural Network (BNN), Generalized Regression Neural Network (GRNN), and Neuro-Fuzzy (NF) System: A Case Study. *Energies* **2018**, *11*, 1188.
https://doi.org/10.3390/en11051188

**AMA Style**

Lotfinejad MM, Hafezi R, Khanali M, Hosseini SS, Mehrpooya M, Shamshirband S. A Comparative Assessment of Predicting Daily Solar Radiation Using Bat Neural Network (BNN), Generalized Regression Neural Network (GRNN), and Neuro-Fuzzy (NF) System: A Case Study. *Energies*. 2018; 11(5):1188.
https://doi.org/10.3390/en11051188

**Chicago/Turabian Style**

Lotfinejad, Mohammad Mehdi, Reza Hafezi, Majid Khanali, Seyed Sina Hosseini, Mehdi Mehrpooya, and Shahaboddin Shamshirband. 2018. "A Comparative Assessment of Predicting Daily Solar Radiation Using Bat Neural Network (BNN), Generalized Regression Neural Network (GRNN), and Neuro-Fuzzy (NF) System: A Case Study" *Energies* 11, no. 5: 1188.
https://doi.org/10.3390/en11051188