#### 3.1. Study Area

Mashhad -the capital of Khorasan Razavi Province- with approximately 351 km^{2} area is the second most polluted city in Iran after Tehran. Its geographic location is the Northeast of Iran in 36º 16’ North latitude and 59º 37’ East longitude (Figure 1).

Figure 1.
Study area and air quality measurement stations
#### 3.2. Study Data

The data used in the current study included the minimum and daily average temperature (ºC), minimum and maximum daily humidity (%), average wind speed (km/h), average daily precipitation (mm), wind angle (degree), average sunshine hours per day (h), average daily concentration of PM_{10} (μg/m^{3}), SO_{2} (ppb), CO (ppm), NO_{2} (ppb), and O_{3} (ppb).

As shown in Figure 1, the hourly air pollutants concentration data were collected from three stations from 2011 to 2016. The metrological data were taken from Mashhad synoptic station from 2011 to 2017. After data attainment and validation and outliers’ elimination, the daily average was calculated for each pollutant. SPSS version 16 was used to simulate multiple regression, and in order to simulate neural network models and Anfis, the MATLAB 2017 software was used. Network input data were divided into three categories to improve network prediction strength:

● Train data that contained 70% of data (from 2011 to 2014) were related to network training; the network weight was determined by them. This section data included 1555 items.

● Validation data that contained 15% of data (the year 2015) were in charge of network training monitoring; the decision to stop calculations was made through error consideration during training. This section data included 430 items.

● Test data that contained 15% of data (the year 2016) related to validation and network capabilities examination. This section data included 121 items.

#### 3.3. Multiple Regression

Multiple regressions are a method for collective and individual participation of two or more independent variables in a dependent variable changes. In this method, the variables are entered one by one. Some conditions should be met before using the regression model; first, linear relationship between independent and dependent variables; second, normal distribution of error values, and third, independence of error values.

In the current study, after accuracy verification of the above conditions, variables that had a significant correlation with PM_{2.5} (R^{2} = 0.95) were extracted as a model through multiple linear regression by a step-by-step approach and the coefficients of each were obtained.

#### 3.4. MLP Neural Network

Multi-layer feedforward networks are the most important structures of artificial neural networks. Generally, these networks include a set of sensory units (basic neurons) that form input layer, one or more hidden layers, and an output layer. The input signal is spread layer-by-layer through the network in a forward direction. This kind of network is commonly referred to as MLP. The number of hidden layers should be as low as possible. Initially, the network is trained by a hidden layer; in case of inappropriate function, the number of hidden layers will increase (13). If possible, less hidden neurons are examined (14). The current study used an input and an output layer, a hidden layer consisting of 85 neurons, tansig conversion function, and trainbr training algorithm.

#### 3.5. The PSO-Based ANFIS Network

In the current study, an adaptive type II neuro-fuzzy network was designed according to Sugeno algorithm using MATLAB 2017 fuzzy toolbox and genfis3 tool (using the FCM model for clustering). Network training was done by PSO algorithm to increase its efficiency. In order to optimize the particle swarm and find the most efficient state, the Kennedy and Eberhart algorithm was used due to its high efficiency. In the current study, 100 rounds for each network and 10 clusters were considered. These numbers were obtained by trial and error. In order to optimize membership function parameters in adaptive neuro-fuzzy inference system, ANFIS network and PSO algorithm parameters were presented; data are shown in Table 1.

Table 1.
ANFIS Network Parameters
Parameter | Value |
---|

**ANFIS network parameters** | |

Minimum improvement | 1e-5 |

Number of clusters | 10 |

Maximum iteration | 100 |

Partition matrix exponent | 2 |

**Particle swarm optimization algorithms** | |

Iteration numbers | 1000 |

Population | 500 |

Inertia weight damping ratio | 0.99 |

(C_{1}) | 1 |

(C_{2}) | 2 |

Inertia weight | 1 |

#### 3.6. Network Performance Assessment

Network performance was validated. Following equations were used to evaluate network performance.

$Meansquarederror\left(MSE\right)=\frac{{\sum}_{1}^{n}{(obs-calc)}^{2}}{N}$

$Root-mean-squarederror\left(RMSE\right)=\sqrt{{\sum}_{i=1}^{n}\frac{{(calc-obs)}^{2}}{N}}$

$Coefficientofdetermination\left({R}^{2}\right)=\frac{{\sum}_{1}^{n}{(calc-avg.obs)}^{2}}{{\sum}_{1}^{n}{(obs-avg.obs)}^{2}}$

The data were normalized by the below algorithm:

X_{norm} = (X - X_{min})/(X_{max} - X_{min})

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