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Abstract In order to solve the limitations of existing air quality evaluation system， a new air quality evaluation system was established based on FCM， the BP neural network， with the aim to provide scientific bases for the targeted and efficient control of air pollution， formulation of prevention and control strategy， and improvement of living environment. Based on the existing data of 6 air quality indices， the air quality data were reclassified by using FCM algorithm， obtaining the clustering center， which minimized the cost function of non??similar index. Then， the reclassified 6 classes of data were proceeded with BP neural network training and simulation， so as to achieve the purpose of identification， thereby forming a new air quality evaluation system.
Key words FCM clustering??BP neural network??Air quality assessment system
At present， the air quality problem has attracted much attention from the public， and many people have complained that China??s air quality report value is significantly different from the actual perception[1]， which is mainly caused by the existing air quality evaluation system. Currently， China uses AQI as the index for evaluating air quality. It is determined by the maximum air quality sub??index of each pollutant， and its evaluation results are relatively simple and cannot fully reflect the air quality. Therefore， in this paper， based on the existing data of 6 air indices， the air quality data were reclassified using FCM， and BP neural network was used to reconstruct the correspondence between the 6 air indices and air quality levels， with the aim to construct a new air quality evaluation system[2].
Clustering Classification of 6 Air Quality Indices Based on FCM Algorithm
Fuzzy c??means （FCM） clustering algorithm[3] divides n vectors into c fuzzy groups and finds the clustering center of each group to minimize the value function of the non??similar index. The clustering process is as follows：
Step 1， standardize the data matrix；
Step 2， establish a fuzzy similar matrix and initialize the membership matrix；
Step 3， start the iteration of the algorithm until the objective function converges to a minimum value；
Step 4， determine the class of the data of the final membership matrix according to the iterative result， and show the final clustering result.
Based on the above processes， MATLAB was used to conduct the FCM clustering analysis of the air quality data of 13 regions in the past three years， and the 9 174 sample data were divided into 6 classes， which provided data basis for BP neural network classification. Then 6 levels were classified according to the values of the clustering centers， namely， excellent， good， lightly polluted， medium polluted， heavily polluted， severely polluted （Table 1）. As shown in Table 1， the values of O3 did not increase with the increase of air pollution level， while the values of other indices increased with the increase of air pollution level， so that the influence of O3 on air quality pollution was not significant.
Construction of BP Neural Network Meeting the Relationship Between 6 Air Quality Indices and Air Quality Levels
BP neural network[4] can build an extremely complex and more accurate relationship network， especially for nonlinear relations[5]. And the various indices of air quality and air quality levels are not in significant linear relationship[6]， so it is believed that the relationship constructed using BP neural network is more accurate than that constructed using AQI. According to the above clustering classification method， FCM algorithm classified the data of various air quality indices in 13 regions of Beijing， Tianjin and Hebei in the past 3 years. Then， the 6 classes of data were trained and simulated using BP neural network to achieve the purpose of identification， thereby forming a new air quality evaluation system.
Brief description of BP neural network
BP neural network is a one??way forward neural network. First， BP neural network can be divided into single hidden layer and multi hidden layer. In the construction process， the proper selection of the number of hidden layers is the key， which is closely related to the output and input of the whole network. Secondly， there are selections of transfer function， output function and training function. Finally， it is also important to select the parameters in training.
Selection of various functions and parameters of BP neural network
It is generally believed that the BP neural network of single hidden layer is simple in principle， slow in convergence， and easy to result in the dilemma that the results are optimal in parts but not optimal for the whole. However， the BP neural network structure of more than 3 layers is too complicated， and the input is only 6 （the number of indices is not enough）， so BP neural network with two hidden layers is selected to construct the relationship[6].
Based on the previous experience， there were about 20 nodes in the first hidden layer， and 3-5 in the second. Through multiple debugging attempts， the results showed that the fitting degree reached the optimal state when there were 23 nodes in the first hidden layer and 5 nodes in the second.
The training function of the network was the trainbgf function， and the transfer function between each layer was the tansig function， while the final output function was the purelin function. In training， the number of training was 1 000 times， the maximum number of verification failures was 5， the minimum gradient of performance function was 1e??6， and the number of tests defaulted to 6.
Training process and simulation results of BP neural network with two layers of hidden layers
After inputting the classified 9 174 sets of data， the data were randomly divided into 3 groups of samples， namely training samples， validation samples， and test samples[7].
As shown in Fig. 1， the variation curves of the 3 groups of samples were basically consistent， showing high approximate degree.
As shown in Fig. 2， the degree of error and the convergence speed were both at low levels， achieving the desired goal. The effect reached the optimal at the 77th iteration. Mu decreased with the decrease of the error， so it was easy to see that the error became smaller and smaller with the increase of the number of iterations. When val fail reached 6， the program terminated itself， so there was no training data change after that， and the training was ended.
The value of R of each group of samples was close to 1， and the fitting effect was significant， which was believed to be the optimal situation. As shown in Fig.3， the curves of the 3 groups of samples were basically in coincidence， and the changes were basically consistent.
Conclusion
The establishment of the neural network is based on the comprehensive consideration of the 6 indices， and the final air quality level corresponds to the comprehensive consideration of the 6 indices， which makes up for the shortcomings of AQI which simplifies the indices into a single index. Moreover， compared with AQI， neural network recognition is more significant in effectiveness， and its convergence speed is extremely fast， which can obtain the air quality level corresponding to the air quality index of a certain group quickly.
References
[1] QIU XZ， ZHU Y， JANG C， et al. Development of an integrated policy making tool for assessing air quality and human health benefits of air pollution control[J]. Frontiers of Environmental Science & Engineering. 2015， 9（6） ：1056-1065.
[2] GUALTIERI G， TOSCANO P， CRISCI A， et al. Influence of road traffic， residential heating and meteorological conditions on PM10 concentrations during air pollution critical episodes[J]. Environmental Science and Pollution Research International， 2015， 22（23） ： 19027-19038.
[3] SI SK， SUN ZL. Mathematical modeling algorithm and application[M]. Beijing： National Defense Industry Press， 2015： 216-230.
[4] ZHOU P. MATLAB neural network design and application[M]. Beijing： Tsinghua University Press， 2013： 156-191.
[5] LI GC， SUN W， HUANG GH， et al. Planning of integrated energy??environment systems under dual interval uncertainties[J]. International Journal of Electrical Power & Energy Systems， 2018.9（100）：287-298
[6] CUI DW. Application of hidden multilayer BP neural network model in runoff prediction[J]. Journal of China Hydrology， 2013（1）： 69-71.
[7] CHEN M. MATLAB neural network principle and example solution[M]. Beijing： Tsinghua University Press， 2013： 154-184.
Key words FCM clustering??BP neural network??Air quality assessment system
At present， the air quality problem has attracted much attention from the public， and many people have complained that China??s air quality report value is significantly different from the actual perception[1]， which is mainly caused by the existing air quality evaluation system. Currently， China uses AQI as the index for evaluating air quality. It is determined by the maximum air quality sub??index of each pollutant， and its evaluation results are relatively simple and cannot fully reflect the air quality. Therefore， in this paper， based on the existing data of 6 air indices， the air quality data were reclassified using FCM， and BP neural network was used to reconstruct the correspondence between the 6 air indices and air quality levels， with the aim to construct a new air quality evaluation system[2].
Clustering Classification of 6 Air Quality Indices Based on FCM Algorithm
Fuzzy c??means （FCM） clustering algorithm[3] divides n vectors into c fuzzy groups and finds the clustering center of each group to minimize the value function of the non??similar index. The clustering process is as follows：
Step 1， standardize the data matrix；
Step 2， establish a fuzzy similar matrix and initialize the membership matrix；
Step 3， start the iteration of the algorithm until the objective function converges to a minimum value；
Step 4， determine the class of the data of the final membership matrix according to the iterative result， and show the final clustering result.
Based on the above processes， MATLAB was used to conduct the FCM clustering analysis of the air quality data of 13 regions in the past three years， and the 9 174 sample data were divided into 6 classes， which provided data basis for BP neural network classification. Then 6 levels were classified according to the values of the clustering centers， namely， excellent， good， lightly polluted， medium polluted， heavily polluted， severely polluted （Table 1）. As shown in Table 1， the values of O3 did not increase with the increase of air pollution level， while the values of other indices increased with the increase of air pollution level， so that the influence of O3 on air quality pollution was not significant.
Construction of BP Neural Network Meeting the Relationship Between 6 Air Quality Indices and Air Quality Levels
BP neural network[4] can build an extremely complex and more accurate relationship network， especially for nonlinear relations[5]. And the various indices of air quality and air quality levels are not in significant linear relationship[6]， so it is believed that the relationship constructed using BP neural network is more accurate than that constructed using AQI. According to the above clustering classification method， FCM algorithm classified the data of various air quality indices in 13 regions of Beijing， Tianjin and Hebei in the past 3 years. Then， the 6 classes of data were trained and simulated using BP neural network to achieve the purpose of identification， thereby forming a new air quality evaluation system.
Brief description of BP neural network
BP neural network is a one??way forward neural network. First， BP neural network can be divided into single hidden layer and multi hidden layer. In the construction process， the proper selection of the number of hidden layers is the key， which is closely related to the output and input of the whole network. Secondly， there are selections of transfer function， output function and training function. Finally， it is also important to select the parameters in training.
Selection of various functions and parameters of BP neural network
It is generally believed that the BP neural network of single hidden layer is simple in principle， slow in convergence， and easy to result in the dilemma that the results are optimal in parts but not optimal for the whole. However， the BP neural network structure of more than 3 layers is too complicated， and the input is only 6 （the number of indices is not enough）， so BP neural network with two hidden layers is selected to construct the relationship[6].
Based on the previous experience， there were about 20 nodes in the first hidden layer， and 3-5 in the second. Through multiple debugging attempts， the results showed that the fitting degree reached the optimal state when there were 23 nodes in the first hidden layer and 5 nodes in the second.
The training function of the network was the trainbgf function， and the transfer function between each layer was the tansig function， while the final output function was the purelin function. In training， the number of training was 1 000 times， the maximum number of verification failures was 5， the minimum gradient of performance function was 1e??6， and the number of tests defaulted to 6.
Training process and simulation results of BP neural network with two layers of hidden layers
After inputting the classified 9 174 sets of data， the data were randomly divided into 3 groups of samples， namely training samples， validation samples， and test samples[7].
As shown in Fig. 1， the variation curves of the 3 groups of samples were basically consistent， showing high approximate degree.
As shown in Fig. 2， the degree of error and the convergence speed were both at low levels， achieving the desired goal. The effect reached the optimal at the 77th iteration. Mu decreased with the decrease of the error， so it was easy to see that the error became smaller and smaller with the increase of the number of iterations. When val fail reached 6， the program terminated itself， so there was no training data change after that， and the training was ended.
The value of R of each group of samples was close to 1， and the fitting effect was significant， which was believed to be the optimal situation. As shown in Fig.3， the curves of the 3 groups of samples were basically in coincidence， and the changes were basically consistent.
Conclusion
The establishment of the neural network is based on the comprehensive consideration of the 6 indices， and the final air quality level corresponds to the comprehensive consideration of the 6 indices， which makes up for the shortcomings of AQI which simplifies the indices into a single index. Moreover， compared with AQI， neural network recognition is more significant in effectiveness， and its convergence speed is extremely fast， which can obtain the air quality level corresponding to the air quality index of a certain group quickly.
References
[1] QIU XZ， ZHU Y， JANG C， et al. Development of an integrated policy making tool for assessing air quality and human health benefits of air pollution control[J]. Frontiers of Environmental Science & Engineering. 2015， 9（6） ：1056-1065.
[2] GUALTIERI G， TOSCANO P， CRISCI A， et al. Influence of road traffic， residential heating and meteorological conditions on PM10 concentrations during air pollution critical episodes[J]. Environmental Science and Pollution Research International， 2015， 22（23） ： 19027-19038.
[3] SI SK， SUN ZL. Mathematical modeling algorithm and application[M]. Beijing： National Defense Industry Press， 2015： 216-230.
[4] ZHOU P. MATLAB neural network design and application[M]. Beijing： Tsinghua University Press， 2013： 156-191.
[5] LI GC， SUN W， HUANG GH， et al. Planning of integrated energy??environment systems under dual interval uncertainties[J]. International Journal of Electrical Power & Energy Systems， 2018.9（100）：287-298
[6] CUI DW. Application of hidden multilayer BP neural network model in runoff prediction[J]. Journal of China Hydrology， 2013（1）： 69-71.
[7] CHEN M. MATLAB neural network principle and example solution[M]. Beijing： Tsinghua University Press， 2013： 154-184.