# Thermal Environment Prediction for Metro Stations Based on an RVFL Neural Network

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Training Principle of the RVFLNN Model

_{L}and B

_{L}are weights and biases from the input layer to the hidden layer, with ${W}_{L}\in {R}^{L}$ and ${B}_{L}\in {R}^{L}$. Here, d, N, and L are the dimension of input variables, the number of samples, and the number of hidden layer nodes, respectively. W

_{L}and B

_{L}are chosen in the beginning of the learning process, independently of the training data. In particular, W

_{L}and B

_{L}are chosen randomly from a predefined probability distribution in an RVFLNN. Hence, the input sets, weights, and biases of RVFLNN are as shown in Equations (1) and (2):

_{L,N}, for the hidden layer nodes. From Equation (3), each h

_{l}is a fixed nonlinear function known as a hidden function. In our paper, the sigmoid basis function is given by the following equation:

_{N,L}, is as shown in Equation (4):

## 3. Measurement Process

#### 3.1. Test Points in Metro Station

#### 3.2. Data Acquisition and Processing

- (1)
- The temperatures were monitored for 3 days and recorded every 2 min for a total of 2160 data points. T1, T2, T3, and T4 are temperatures at S1, S2, S3, and S4, respectively, as shown in Figure 3. They were processed from the primitive data with a Butterworth filter. The first 720 data points were measured on Sunday; the second and third lots of 720 data points were measured on Monday and Tuesday, respectively.
- (2)
- The passenger flow monitoring point was at Point R. The number of passengers, P
_{flow}, was monitored every two minutes. Figure 4 is the passenger flow curve after processing with median filtering. It is very obvious that the passenger flow data is very different between weekdays and weekends. - (3)
- Since the metro arrival frequency, F
_{train}, varies significantly with the time and the number of passengers, Figure 5 gives the change of F_{train}with time. It can be seen that F_{train}is obviously changed with the morning and evening rush hours. F_{train}is also different for weekdays and weekends.

#### 3.3. Thermal Environment Model Based on an RVFLNN for a Metro Station

#### 3.3.1. Model Input and Output

_{1}, T

_{3}, P

_{flow}, and F

_{train}. For subspace S3, the parameters of the input layer were determined as T

_{1}, T

_{2}, T

_{4}, P

_{flow}, and F

_{train}. For subspace S4, the parameters of the input layer were determined as T

_{1}, T

_{3}, P

_{flow}, and F

_{train}. Therefore, T

_{1}, P

_{flow}, and F

_{train}are the common training input variables for S2, S3, and S4. The final structures of the traditional RVFL for the temperature models of T

_{2}, T

_{3}, and T

_{4}are shown in Figure 6. The temperature prediction accuracy of S2 through S4 can be improved by establishing different neural network models.

#### 3.3.2. Input Normalization

_{min}is the minimum value of x; and x

_{max}is the maximum value of x.

#### 3.3.3. Build the Model

**Step 1:**Divide training set, validation set, and test set.

**Step 2:**Set the number of neural network nodes.

_{2}, T

_{3}, and T

_{4}, respectively. The output layer has 1 neuron. The hidden layer was initially set to 20 hidden neurons. The hidden layer used sigmoid as the transfer function.

**Step 3:**Parameter initialization.

**Step 4:**Training the RVFLNN.

**Step 5:**Training error and validation error evaluation and parameter adjustment.

**Step 6:**Test the RVFLNN performance.

#### 3.4. Results and Analysis

#### 3.4.1. Effects of Training Parameters

_{exp}

_{,i}and T

_{sim}

_{,i}are the experimental data and prediction data, respectively; and N is the total number of sampling points. Table 1 shows the error versus the number of hidden layer nodes from 20 to 1000.

_{train}and E

_{validation}are the average relative errors of the training data and the validation data. After the initialization of RVFLNN parameters, the number of hidden layer nodes was adjusted. It can be seen from Table 1 that when the number of hidden layer nodes gradually increases from 20 to 1000, the training error continuously decreases. However, when the hidden layer nodes reach about 800, 200, and 100 for model S2, S3, and S4, respectively, the test error begins to increase or fluctuate. Therefore, we can draw a conclusion that the generalization effect of RVFLNN will be good when the respective number of hidden layer nodes for the three different RVFLNN models is 800, 200, and 100. Thus, we determined the number of hidden layer nodes.

#### 3.4.2. Prediction Performance of Thermal Model Based on RVFLNN

_{exp}

_{,i}and T

_{sim}

_{,i}are the experimental data and the prediction data, respectively.

- (1)
- The temperature change in the metro station is influenced by many factors and its change rule is relatively complicated. The presented model based on the RVFLNN can reveal this rule very well: its fitting error and prediction error are both very small.
- (2)
- Comparison of the predicted data and experimental data shows that the maximum absolute error is about 0.4 °C and the maximum relative error is about 2.5%.
- (3)

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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(a) S2 | |||||||||

Number of Nodes | 20 | 50 | 100 | 200 | 300 | 400 | 600 | 800 | 1000 |

E_{train}$\times {10}^{-3}$ | 3.687 | 3.435 | 3.404 | 3.438 | 3.333 | 3.284 | 3.271 | 3.235 | 3.224 |

E_{validation}$\times {10}^{-3}$ | 4.532 | 4.201 | 4.144 | 4.119 | 4.067 | 3.991 | 3.972 | 3.910 | 3.941 |

(b) S3 | |||||||||

Number of Nodes | 20 | 50 | 100 | 200 | 300 | 400 | 600 | 800 | 1000 |

E_{train}$\times {10}^{-3}$ | 4.657 | 4.391 | 4.294 | 4.162 | 4.126 | 4.122 | 3.958 | 3.930 | 3.920 |

E_{validation}$\times {10}^{-3}$ | 6.011 | 5.807 | 5.490 | 5.452 | 5.528 | 5.613 | 5.487 | 5.502 | 5.494 |

(c) S4 | |||||||||

Number of Nodes | 20 | 50 | 100 | 200 | 300 | 400 | 600 | 800 | 1000 |

E_{train}$\times {10}^{-3}$ | 3.229 | 2.866 | 2.791 | 2.720 | 2.695 | 2.660 | 2.629 | 2.600 | 2.585 |

E_{validation}$\text{}\times {10}^{-3}$ | 6.880 | 6.760 | 6.714 | 6.824 | 6.773 | 6.846 | 6.763 | 6.821 | 6.773 |

λ | ω,b ϵ [−0.5, 0.5] | ω,b ϵ [−1, 1] | ω,b ϵ [−2, 2] |
---|---|---|---|

E_{validation}$\times {10}^{-3}$ | E_{validation}$\times {10}^{-3}$ | E_{validation}$\times {10}^{-3}$ | |

0.05 | 5.554 | 5.596 | 5.917 |

0.1 | 5.557 | 5.586 | 5.667 |

0.5 | 5.485 | 5.464 | 5.632 |

1 | 5.478 | 5.455 | 5.447 |

5 | 5.491 | 5.630 | 5.626 |

10 | 5.826 | 5.725 | 5681 |

20 | 6.683 | 6.030 | 5.691 |

S2 | S3 | S4 | |
---|---|---|---|

E_{test} | 4.124 | 5.513 | 6.925 |

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**MDPI and ACS Style**

Tian, Q.; Zhao, W.; Wei, Y.; Pang, L.
Thermal Environment Prediction for Metro Stations Based on an RVFL Neural Network. *Algorithms* **2018**, *11*, 49.
https://doi.org/10.3390/a11040049

**AMA Style**

Tian Q, Zhao W, Wei Y, Pang L.
Thermal Environment Prediction for Metro Stations Based on an RVFL Neural Network. *Algorithms*. 2018; 11(4):49.
https://doi.org/10.3390/a11040049

**Chicago/Turabian Style**

Tian, Qing, Weihang Zhao, Yun Wei, and Liping Pang.
2018. "Thermal Environment Prediction for Metro Stations Based on an RVFL Neural Network" *Algorithms* 11, no. 4: 49.
https://doi.org/10.3390/a11040049