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Monitoring of PM_{2.5} Concentrations by Learning from Multi-Weather Sensors

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Machine Learning Methods

#### 2.2.1. Multivariate Linear Regression

**a**, Equation (1) can be written in vector form as an inner product

**y**is a vector of PM${}_{2.5}$ data in the training set.

#### 2.2.2. Multivariate Nonlinear Regression

Algorithm 1: Nelder–Mead simplex method for multivariate nonlinear regression |

#### 2.2.3. Neural Network

## 3. Results

#### 3.1. Models Training

#### 3.2. Predictions of PM${}_{2.5}$ Concentrations

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**This figure shows temporal variations of PM${}_{2.5}$ concentrations and meteorological parameters at the National Xiamen weather station during the period of January 2014–June 2014.

**Figure 2.**This figure shows two-dimensional temporal variations of PM${}_{2.5}$ concentrations and meteorological parameters by 24 h per day in the period of January 2014–June 2014.

**Figure 3.**This figure shows nonlinear distribution of PM${}_{2.5}$ concentrations with visibility and wind speed, respectively.

**Figure 4.**This figure shows a conceptualized diagram of a two-layer feed-forward network that is used for predicting PM concentrations.

**Figure 5.**This figure shows variations of the cost function value during the training of the multiple nonlinear regression model, using Algorithm 1. The value of the cost function is calculated by using Equation (7).

**Figure 6.**This figure shows variations of the training performance (

**a**) and the test performance (

**b**) with respect to the number of hidden neurons.

**Figure 7.**This figure shows the PM${}_{2.5}$ concentrations estimated by using the different machine learning methods.

**Figure 8.**This figure shows comparisons of PM${}_{2.5}$ concentrations estimated using different machine learning methods.

**Figure 9.**Linear regression lines with red color between estimated PM${}_{2.5}$ concentrations and the PM${}_{2.5}$ observation (reference) data. The spaces between the two green lines are the 95% prediction interval.

**Table 1.**Pearson’s linear correlation coefficient between PM${}_{2.5}$ and meteorological parameters.

Visibility | Wind Direction | Wind Speed | Relative Humidity | Temperature | Atmospheric Pressure | Rainfall Rate |
---|---|---|---|---|---|---|

−0.5639 | 0.2830 | −0.2839 | 0.1201 | −0.0424 | 0.0828 | −0.0308 |

Linear Regression | Nonlinear Regression | Neural Network | |
---|---|---|---|

Averaged RMSE ($\mathsf{\mu}$g/m${}^{3}$) | 24.6756 | 24.9191 | 15.6391 |

Correlation coefficient | 0.6281 | 0.6184 | 0.8701 |

**Table 3.**Effect of using different meteorological parameter inputs on the averaged RMSE ($\mathsf{\mu}$g/m${}^{3}$) and correlation coefficients of three machine learning model outputs.

Parameters | Linear Regression | Nonlinear Regression | Neural Network |
---|---|---|---|

visibility + wind + RH | 24.6756/0.6281 | 24.9191/0.6184 | 20.4548/0.7643 |

visibility + wind + RH + temperature | 24.6670/0.6284 | 27.5901/0.5107 | 17.2791/ 0.8387 |

visibility + wind + RH + temperature + air pressure | 24.5770/0.6319 | 30.1810/0.3093 | 17.1101/ 0.8460 |

visibility + wind + RH + temperature + air pressure + rainfall | 24.5141/0.6343 | 29.0009/ 0.4132 | 15.6391/ 0.8701 |

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Wang, Y.; Xu, Z.
Monitoring of PM_{2.5} Concentrations by Learning from Multi-Weather Sensors. *Sensors* **2020**, *20*, 6086.
https://doi.org/10.3390/s20216086

**AMA Style**

Wang Y, Xu Z.
Monitoring of PM_{2.5} Concentrations by Learning from Multi-Weather Sensors. *Sensors*. 2020; 20(21):6086.
https://doi.org/10.3390/s20216086

**Chicago/Turabian Style**

Wang, Yuexia, and Zhihuo Xu.
2020. "Monitoring of PM_{2.5} Concentrations by Learning from Multi-Weather Sensors" *Sensors* 20, no. 21: 6086.
https://doi.org/10.3390/s20216086