# Evolving Hybrid Cascade Neural Network Genetic Algorithm Space–Time Forecasting

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## Abstract

**:**

## 1. Introduction

_{10}and PM

_{2.5}are some classes of these particulate pollutants [1,2,3,4]. Let us consider a hair: the mean diameter of a single human hair is approximately 70 micrometers. This is roughly 28 times the diameter of PM

_{2.5}. The diameter of particulate matter in PM

_{10}is 10 micrometers or below. Similarly, PM

_{2.5}is normally particles of diameter 2.5 micrometers or below. Both PM

_{10}and PM

_{2.5}are inhalable. We can thus imagine how tiny 2.5 and 10 micrometers are.

_{2}) and nitrogen oxides, originating in PM (NOx) [5,6,7]. All this can be found as a product of building materials, farms, explosions, power stations, industry, and vehicles. PM is seriously damaging, as described above, as it may be opaque and small enough to be inhaled into the lungs or even into the circulation. Therefore, PM contamination affects the cardiovascular system and can cause fatal illnesses such as cardiovascular diseases, erratic heartbeat, and worsening asthma [8,9,10].

## 2. Methods

#### 2.1. Cascade Neural Network

#### 2.2. Genetic Algorithm

Algorithm 1. Scheme of the GA | |

1: | INITIALIZE population and EVALUATE |

2: | while termination condition is not satisfied do |

3: | SELECT parents |

4: | CROSSOVER pairs of parents |

5: | MUTATE the resulting offspring |

6: | EVALUATE new candidates |

7: | REPLACE individuals for the next generation |

8: | end while |

#### 2.3. Cascade Neural Network Genetic Algorithm

Algorithm 2. Function Cascade Neural Network | |

1: | input${n}_{h},m,o$ |

2: | setk = 0 |

3: | calculate Cascade Weighted |

4: | k = 0;for i = 1:nhfor j = 1:mk = k + 1; Wi1(i,j) = W(k); endend |

5: | calculate weighted input and output |

6: | fori = 1:ofor j = 1:mk = k + 1; Wi2(i,j) = W(k); endend |

7: | calculate weighted Bias Input |

8: | fori = 1:nhk = k + 1; Wbi(i,1) = W(k); end |

9: | calculate weighted output |

10: | fori = 1:ofor j = 1:nhk = k + 1; Wo(i,j) = W(k); endend |

11: | calculate weighted Bias Output |

12: | fori = 1:ok = k + 1; Wbo(i,1) = W(k); end |

## 3. Simulation and Results

#### 3.1. Construction of VAR-Cascade

#### 3.2. Study Area

_{2.5}, atmospheric PM

_{10}, and sulfur dioxide (SO

_{2}) levels. Furthermore, the locations of these areas were as established by the Taiwan Environmental Protection Administration Executive Yuan. Table 1 shows statistical summaries of the amounts of air pollution at the four studied locations. The findings typically demonstrate that Taichung has higher concentrations of PM

_{10}, PM

_{2.5}, and NO

_{X}, but in Kaohsiung, SO

_{2}is the greatest pollutant. Figure 1 shows an overview of the genetic algorithm’s training and evaluation phases. Because each type of air pollutant has a different distribution, we trained the same models for each dataset using the same model architecture.

#### 3.3. Air Pollution Forecasting Using VAR-Cascade-GA

_{1}), Taipei (Y

_{2}), Hsinchu (Y

_{3}), and Kaohsiung (Y

_{4}) in Taiwan.

_{2.5}is represented in Figure 3, PM

_{10}is represented in Figure 4, NO

_{X}is represented in Figure 5, and SO

_{2}is represented in Figure 6. In this context, the cascade neural network genetic algorithm model can be used to study nonlinear and nonstationary data on air pollution. The metrics used to evaluate the test set’s result were the root-mean-squared error (RMSE), mean absolute error (MAE), and symmetry mean absolute percentage (sMAPE) between the actual air pollution values and the predicted values. These are metrics that are commonly used in regression problems like our air pollution prediction. If all the metric values are smaller, then the model’s performance is better [25].

#### 3.4. Does the Activation Function Provide High Accuracy and Speed Up the Time Lapse?

_{10}was logsig, that for PM

_{2.5}was SoftMax, that for NO

_{x}was radbas, and that for SO

_{2}was tribas. The SoftMax activation function provided a shorter time lapse than other activation functions.

_{x}with the radial basis activation function, Equation (22) for PM

_{2.5}with the SoftMax activation function, Equation (20) for PM

_{10}with the logsig activation function, and Equation (23) for SO

_{2}with the tribas activation function. We provide the results of forecasting in Figure 7 for the next 30 steps. The results show Taichung constantly leading with the highest pollutant score compared to other cities in Taiwan.

_{x}using the radial basis activation function:

_{2.5}using the SoftMax activation function:

_{10}using the logsig activation function:

_{10}using the tribas activation function:

## 4. Conclusions

_{2}and overall suspended particulate matter was very effective when ever-increasing cars threatened city atmospheres with NOx and particulates. A space–time air pollution analysis over the last 10 years using the monitoring data clearly showed that with urban planning and countermeasure policies, air quality has improved. The analysis should be used to make future policy decisions. Air pollution temporal features were examined herein for Taiwan. The pattern from pollutants to particulates differs in air quality for each location. In a nutshell, the PM, SO

_{2}, and NO

_{x}levels have drastically increased. Future research should examine using VAR-SARIMA, VAR-ARCH, and other traditional time series as input.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

_{2.5}: fine particulate matter with a diameter of 2.5 μm, PM

_{10}: fine particulate matter 10 micrometers or less in diameter, SO

_{2}: sulfur dioxide, NO

_{x}: nitrogen dioxide, BP: backpropagation.

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**Figure 7.**Forecasting all pollution datasets using the CFNN with a genetic algorithm and backpropagation.

Pollution | Location | N | Mean | SE Mean | StDev | Variance | Minimum | Q_{1} | Median | Q_{3} | Maximum | Range |
---|---|---|---|---|---|---|---|---|---|---|---|---|

PM_{10} | TAICHUNG | 3632 | 50.642 | 0.419 | 24.949 | 622.476 | 5 | 32 | 45.5 | 65 | 173 | 168 |

TAIPEI | 3632 | 21.244 | 0.208 | 12.412 | 154.052 | 1 | 12 | 19 | 27 | 100 | 99 | |

HSINCHU | 3632 | 22.46 | 0.219 | 13.135 | 172.521 | 1 | 13 | 19 | 29 | 103 | 102 | |

KAOHSIUNG | 3632 | 31.719 | 0.31 | 18.477 | 341.414 | 1 | 17 | 29 | 44 | 123 | 122 | |

SO_{2} | TAICHUNG | 3632 | 2.8706 | 0.017 | 1.0208 | 1.042 | 0 | 2.2 | 2.7 | 3.4 | 9.3 | 9.3 |

TAIPEI | 3632 | 2.9835 | 0.0263 | 1.5742 | 2.4781 | 0.4 | 1.9 | 2.6 | 3.7 | 16.2 | 15.8 | |

HSINCHU | 3632 | 2.6778 | 0.0186 | 1.1125 | 1.2377 | 0.1 | 1.9 | 2.5 | 3.2 | 13.2 | 13.1 | |

KAOHSIUNG | 3632 | 5.3129 | 0.0515 | 3.0833 | 9.5066 | 0 | 3.3 | 4.5 | 6.4 | 33.8 | 33.8 | |

PM_{2.5} | TAICHUNG | 3632 | 26.623 | 0.264 | 15.66 | 245.244 | 1 | 15 | 23 | 35 | 106 | 105 |

TAIPEI | 3632 | 23.635 | 0.203 | 12.161 | 147.892 | 3.97 | 15.107 | 20.84 | 29.023 | 109.83 | 105.86 | |

HSINCHU | 3632 | 18.179 | 0.13 | 7.763 | 60.265 | 0.63 | 13.04 | 16.34 | 21.102 | 76.72 | 76.09 | |

KAOHSIUNG | 3632 | 23.854 | 0.163 | 9.747 | 95.014 | 5.27 | 16.49 | 21.495 | 29.697 | 68.96 | 63.69 | |

NO_{X} | TAICHUNG | 3632 | 22.944 | 0.171 | 10.26 | 105.269 | 4.35 | 15.23 | 20.57 | 28.63 | 81.43 | 77.08 |

TAIPEI | 3632 | 6.196 | 0.106 | 6.315 | 39.874 | 0.09 | 1.85 | 4.15 | 8.28 | 65.14 | 65.05 | |

HSINCHU | 3632 | 3.2786 | 0.0546 | 3.2643 | 10.6559 | 0 | 1.52 | 2.3 | 3.79 | 45.65 | 45.65 |

Pollution | Portion | Training | Testing | Average | Elapsed Time | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | SMAPE | RMSE | MAE | SMAPE | RMSE | MAE | SMAPE | |||

PM_{2.5} | 50:50 | 9.84 | 6.89 | 3.91 | 7.89 | 5.70 | 3.83 | 8.87 | 6.30 | 3.87 | 76.42 |

PM_{10} | 13.53 | 9.57 | 3.84 | 11.37 | 8.05 | 3.86 | 12.45 | 8.81 | 3.85 | 71.86 | |

NO_{X} | 5.53 | 3.55 | 6.94 | 4.37 | 2.73 | 6.95 | 4.95 | 3.14 | 6.95 | 74.23 | |

SO_{2} | 1.72 | 1.18 | 3.60 | 1.15 | 0.80 | 3.61 | 1.44 | 0.99 | 3.61 | 75.51 | |

PM_{2.5} | 60:40 | 9.86 | 6.88 | 3.89 | 7.41 | 5.42 | 3.57 | 8.63 | 6.15 | 3.73 | 76.56 |

PM_{10} | 13.49 | 9.54 | 3.76 | 10.67 | 7.57 | 3.56 | 12.08 | 8.55 | 3.66 | 75.24 | |

NO_{X} | 6.48 | 3.48 | 6.93 | 4.10 | 2.65 | 6.24 | 5.29 | 3.06 | 6.59 | 73.15 | |

SO_{2} | 1.65 | 1.13 | 3.48 | 1.07 | 0.80 | 3.43 | 1.36 | 0.97 | 3.46 | 76.13 | |

PM_{2.5} | 70:30 | 9.43 | 6.62 | 3.83 | 7.13 | 5.27 | 3.50 | 8.28 | 5.95 | 3.67 | 71.13 |

PM_{10} | 13.30 | 9.29 | 3.74 | 10.09 | 7.13 | 3.74 | 11.70 | 8.21 | 3.74 | 77.87 | |

NO_{X} | 5.31 | 3.36 | 6.98 | 4.01 | 2.54 | 7.12 | 4.66 | 2.95 | 7.05 | 74.41 | |

SO_{2} | 1.60 | 1.09 | 3.36 | 1.00 | 0.77 | 3.41 | 1.30 | 0.93 | 3.38 | 80.90 | |

PM_{2.5} | 80:20 | 9.25 | 6.46 | 3.81 | 6.83 | 4.99 | 3.50 | 8.04 | 5.73 | 3.65 | 74.25 |

PM_{10} | 13.10 | 9.07 | 3.74 | 9.19 | 6.56 | 4.13 | 11.14 | 7.82 | 3.93 | 74.25 | |

NO_{X} | 5.25 | 3.29 | 7.11 | 3.79 | 2.49 | 6.68 | 4.52 | 2.89 | 6.90 | 72.37 | |

SO_{2} | 1.54 | 1.05 | 3.42 | 0.92 | 0.70 | 3.36 | 1.23 | 0.88 | 3.39 | 80.24 | |

PM_{2.5} | 90:10 * | 9.03 | 6.34 | 3.77 | 6.78 | 4.94 | 3.47 | 7.90 | 5.64 | 3.62 | 83.83 |

PM_{10} | 12.77 | 8.85 | 3.77 | 8.02 | 5.93 | 4.09 | 10.40 | 7.39 | 3.93 | 75.00 | |

NO_{X} | 5.11 | 3.20 | 6.90 | 3.70 | 2.43 | 6.53 | 4.40 | 2.81 | 6.72 | 80.47 | |

SO_{2} | 1.48 | 1.10 | 3.37 | 0.80 | 0.62 | 2.77 | 1.14 | 0.86 | 3.07 | 71.71 |

**Noted:**Best simulation with low error (*) and yellow highlight represent the lowest value of each information pollution, accuracy measurement, and elapsed time.

Pollution | Activation Function | Training | Testing | Average | Elapsed Time | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

RMSE | MAE | SMAPE | RMSE | MAE | SMAPE | RMSE | MAE | SMAPE | |||

PM_{2.5} | logsig | 9.02 | 6.30 | 3.77 | 6.77 | 4.94 | 3.54 | 7.90 | 5.62 | 3.66 | 78.03 |

PM_{10} | 12.79 | 8.86 | 3.71 | 8.12 | 6.02 | 4.05 | 10.46 | 7.44 | 3.88 | 75.48 | |

NO_{X} | 5.04 | 3.15 | 6.84 | 3.79 | 2.43 | 6.62 | 4.42 | 2.79 | 6.73 | 72.43 | |

SO_{2} | 1.48 | 1.01 | 3.35 | 0.82 | 0.63 | 3.00 | 1.15 | 0.82 | 3.18 | 76.59 | |

PM_{2.5} | radbas | 9.06 | 6.37 | 3.80 | 6.80 | 5.00 | 3.51 | 7.93 | 5.69 | 3.66 | 80.97 |

PM_{10} | 12.79 | 8.85 | 3.79 | 8.11 | 6.03 | 4.19 | 10.45 | 7.44 | 3.99 | 74.77 | |

NO_{X} | 5.09 | 3.16 | 6.83 | 3.75 | 2.40 | 6.19 | 4.42 | 2.78 | 6.51 | 82.35 | |

SO_{2} | 1.49 | 1.01 | 3.36 | 0.83 | 0.64 | 2.93 | 1.16 | 0.83 | 3.15 | 73.33 | |

PM_{2.5} | SoftMax | 9.07 | 6.35 | 3.78 | 6.70 | 4.91 | 3.46 | 7.89 | 5.63 | 3.62 | 75.47 |

PM_{10} | 12.81 | 8.90 | 3.75 | 8.13 | 6.04 | 4.24 | 10.47 | 7.47 | 3.99 | 74.70 | |

NO_{X} | 5.11 | 3.19 | 7.12 | 3.64 | 2.35 | 6.23 | 4.38 | 2.77 | 6.67 | 72.11 | |

SO_{2} | 1.48 | 1.01 | 3.42 | 0.84 | 0.66 | 3.12 | 1.16 | 0.84 | 3.27 | 77.53 | |

PM_{2.5} | tribas | 9.03 | 6.34 | 3.80 | 6.81 | 4.97 | 3.52 | 7.92 | 5.66 | 3.66 | 93.20 |

PM_{10} | 12.81 | 8.90 | 3.75 | 8.13 | 6.04 | 4.24 | 10.47 | 7.47 | 3.99 | 74.70 | |

NO_{X} | 5.13 | 3.21 | 6.98 | 3.68 | 2.37 | 6.53 | 4.41 | 2.79 | 6.75 | 72.29 | |

SO_{2} | 1.49 | 1.01 | 3.36 | 0.84 | 0.65 | 2.94 | 1.16 | 0.83 | 3.15 | 80.35 |

**Noted:**Yellow highlight represent the lowest value of each information pollution, accuracy measurement, and elapsed time.

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Caraka, R.E.; Yasin, H.; Chen, R.-C.; Goldameir, N.E.; Supatmanto, B.D.; Toharudin, T.; Basyuni, M.; Gio, P.U.; Pardamean, B.
Evolving Hybrid Cascade Neural Network Genetic Algorithm Space–Time Forecasting. *Symmetry* **2021**, *13*, 1158.
https://doi.org/10.3390/sym13071158

**AMA Style**

Caraka RE, Yasin H, Chen R-C, Goldameir NE, Supatmanto BD, Toharudin T, Basyuni M, Gio PU, Pardamean B.
Evolving Hybrid Cascade Neural Network Genetic Algorithm Space–Time Forecasting. *Symmetry*. 2021; 13(7):1158.
https://doi.org/10.3390/sym13071158

**Chicago/Turabian Style**

Caraka, Rezzy Eko, Hasbi Yasin, Rung-Ching Chen, Noor Ell Goldameir, Budi Darmawan Supatmanto, Toni Toharudin, Mohammad Basyuni, Prana Ugiana Gio, and Bens Pardamean.
2021. "Evolving Hybrid Cascade Neural Network Genetic Algorithm Space–Time Forecasting" *Symmetry* 13, no. 7: 1158.
https://doi.org/10.3390/sym13071158