论文部分内容阅读
Abstract Nowadays， the quality of the air environment is closely related to the health of the ecosystem and the safety of people living. With more and more attention attached to the quality of the air environment， it is imminent to analyze the future development trend of air quality. In this paper， the grey correlation analysis was used to determine the weights of 6 pollution indexes， namely PM10， PM2.5， SO2， NO2， CO and O3. The fuzzy comprehensive assessment method was applied to determine the air quality eigenvalues H （2.145， 1.926， and 1.805） of Baoding City in 2014-2016， suggesting that the air quality in Baoding is getting better and better. In addition， the grey forecasting model GM （1，1） was used to forecast and test the air quality of Baoding City. The results show that the prediction is good.
Key words Fuzzy comprehensive evaluation； Grey theory； GM（1，1）； Air quality in Baoding City
In this paper， grey correlation analysis[1-4]， fuzzy comprehensive evaluation[5] and grey prediction model[6] were used to evaluate and predict the air quality of Baoding City， and PM10， PM2.5， SO2， NO2， CO and O3 were selected as the main factors affecting air quality. The air quality data in 2014-2016 of Baoding City were processed as follows.
Determination and Normalization of Association Degree
Grey correlation analysis was used to calculate the association degrees between the pollutant levels and air environmental quality with the time series of air pollutant concentration monitoring values in Baoding City as the target sequence and the times series of the influencing factors as the comparison sequence. And then， the degrees of association were normalized. The correlation degrees of air pollution factors to air quality in Baoding City in 2014 were （0.840， 0.845， 0.717， 0.704， 0.618， 0.732）
The normalized association degrees of various pollutants to air environmental quality in Baoding City in 2015 and 2016 were obtained in the same way， as shown in Table 1.
Fuzzy Comprehensive Evaluation Model and Result Analysis
Evaluation standard
The evaluation criteria referred to the classification standards of Air Quality Index （AQI） and the corresponding concentration limits of the Individual Air Quality Index （IAQI） in the Ambient Air Quality Standards （GB3095-2012） of the Peoples Republic of China.
Evaluation steps for fuzzy comprehensive evaluation
Determining evaluation factor set
According to the observation data of air quality monitoring in Baoding City， the set of evaluation factors was： Determining comment set
The comment set is a set reflecting the quality level of the air environment. The number of evaluation levels can be determined according to the actual situation. According to the national air quality assessment standards， combined with the characteristics of air monitoring in Baoding City and the purpose of evaluation， and AQI of the Ambient Air Quality Standards （GB3095-2012） of the Peoples Republic of China， the comment set was V = {Level I， Level II， Level III， Level IV， Level V， Level VI}.
Single factor evaluation
The total number of monitoring sampling of factor i was n. After analysis， the number of times belonging to Level I， Level II， Level III， Level IV， Level V， Level VI were n1， n2， n3， n4， n5， n6， respectively， and since n=n1+n2+n3+n4+n5+n6， the results of single factor evaluation were：
The comprehensive evaluation results of single factor were calculated by the following formula：
Then， according to the principle of maximum degree of membership， the rating of single factors could be determined. Hi is the eigenvalue of the level variable of the ith single factor evaluation result， and the smaller the value is， the better the evaluation result is.
Comprehensive evaluation of air quality
Based on the single factor evaluation result vectors， it could form the fuzzy comprehensive evaluation matrix R：
Since the evaluation indicators had different effects on the results of the comprehensive evaluation of air quality， they should be given different weights. According to the normalized association degrees from grey correlation analysis， the weights of the pollutants of SO2， NO2， CO， PM10， PM2.5 and O3 could be determined as follows：
From above， the fuzzy comprehensive evaluation matrix of air environment quality was：
Where，"o" is the fuzzy operator. For weights A=（a1， a2， a3， a4， a5， a6）， the fuzzy matrix synthesis operation was taken. After testing models M∧∨， M·， ∨ and M·， ， M·， +， the model M·， was found to be the best， so the model M·， was selected for comprehensive evaluation. In order to overcome the limitations of the principle of maximum affiliation， the eigenvalues of the level variables could be calculated.
From H， it was possible to determine the overall evaluation results of the air environment quality， that is， the standard level of air environment quality. The calculated degree of membership of pollutants at each level in 2014 is shown in Table 2. As shown in Table 2， the comprehensive evaluation indicator of air environmental quality in 2014 was 2.145， and in a similar way， the comprehensive evaluation index of air environment quality calculated in 2015 was 1.926， and the comprehensive evaluation index of air environment quality in 2016 was 1.805. Obviously， the value of comprehensive evaluation index for air quality became smaller， so the air quality from 2014 to 2016 became better.
Prediction of Air Environment Quality Development Trend in Baoding City and Result Analysis
Based on the grey GM （1.1） prediction model[7]， MATLAB software was used to program the calling program to predict the air environment quality. The results are shown in Table 3.
Conclusion
This paper uses the grey correlation analysis， fuzzy comprehensive evaluation and grey prediction model GM （1，1） to evaluate and predict the air quality in Baoding. Comprehensive evaluation has been done to the air quality in Baoding City from 2014 to 2016， and the obtained eigenvalues H are 2.145， 1.926， 1.805， respectively. It can be seen that H is getting smaller and smaller， indicating that the air quality is getting better. The obtained values of H are used as initial data for the prediction using the grey GM（1，1） model， getting the predicted eigenvalues H from 2014 to 2018， which are 2.145， 1.925， 1.804， 1.691， 1.585， respectively. The comparison results show that the prediction error for 2014-2016 is not more than 0.03%， and thus the model has a significant effect on air quality prediction. The evaluation methods and prediction models used in this paper require less data， have more accurate calculations and simple methods， promising with strong practicality.
References
[1] Weather hindcasting. www.tianqihoubao.com.
[2] LI BJ， ZHU CY， ZHOU J. Effect of non-dimensional quantities of original data on grey incidence order[J]. Journal of Henan Agricultural University， 2002， 36（2）：199-202.
[3] PAN L. Analysis of air quality changes and influencing factors based on grey system[D]. Tianjin， Tianjin University， 2011.
[4] ZHAO XF. An overview of grey system theory[J]. Journal of Educational Institute of Jilin Province， 2011， 27（3）： 152-154.
[5] XIAO XP， LI DY. The latest development of the application of grey relational analysis[J]. Exploration of Nature， 1996， 15（4）： 50-56.
[6] CHEN SY. Theory and application of engineering fuzzy sets[M]. Beijing： National Defense Industry Press， 1998.
[7] DENG JL. Basic method of gray system[M]. Wuhan： Huazhong University of Science and Technology Press， 1992
[8] Ministry of Environmental Protection of the Peoples Republic of China. Ambient air quality standards[S]. 2018.
Key words Fuzzy comprehensive evaluation； Grey theory； GM（1，1）； Air quality in Baoding City
In this paper， grey correlation analysis[1-4]， fuzzy comprehensive evaluation[5] and grey prediction model[6] were used to evaluate and predict the air quality of Baoding City， and PM10， PM2.5， SO2， NO2， CO and O3 were selected as the main factors affecting air quality. The air quality data in 2014-2016 of Baoding City were processed as follows.
Determination and Normalization of Association Degree
Grey correlation analysis was used to calculate the association degrees between the pollutant levels and air environmental quality with the time series of air pollutant concentration monitoring values in Baoding City as the target sequence and the times series of the influencing factors as the comparison sequence. And then， the degrees of association were normalized. The correlation degrees of air pollution factors to air quality in Baoding City in 2014 were （0.840， 0.845， 0.717， 0.704， 0.618， 0.732）
The normalized association degrees of various pollutants to air environmental quality in Baoding City in 2015 and 2016 were obtained in the same way， as shown in Table 1.
Fuzzy Comprehensive Evaluation Model and Result Analysis
Evaluation standard
The evaluation criteria referred to the classification standards of Air Quality Index （AQI） and the corresponding concentration limits of the Individual Air Quality Index （IAQI） in the Ambient Air Quality Standards （GB3095-2012） of the Peoples Republic of China.
Evaluation steps for fuzzy comprehensive evaluation
Determining evaluation factor set
According to the observation data of air quality monitoring in Baoding City， the set of evaluation factors was： Determining comment set
The comment set is a set reflecting the quality level of the air environment. The number of evaluation levels can be determined according to the actual situation. According to the national air quality assessment standards， combined with the characteristics of air monitoring in Baoding City and the purpose of evaluation， and AQI of the Ambient Air Quality Standards （GB3095-2012） of the Peoples Republic of China， the comment set was V = {Level I， Level II， Level III， Level IV， Level V， Level VI}.
Single factor evaluation
The total number of monitoring sampling of factor i was n. After analysis， the number of times belonging to Level I， Level II， Level III， Level IV， Level V， Level VI were n1， n2， n3， n4， n5， n6， respectively， and since n=n1+n2+n3+n4+n5+n6， the results of single factor evaluation were：
The comprehensive evaluation results of single factor were calculated by the following formula：
Then， according to the principle of maximum degree of membership， the rating of single factors could be determined. Hi is the eigenvalue of the level variable of the ith single factor evaluation result， and the smaller the value is， the better the evaluation result is.
Comprehensive evaluation of air quality
Based on the single factor evaluation result vectors， it could form the fuzzy comprehensive evaluation matrix R：
Since the evaluation indicators had different effects on the results of the comprehensive evaluation of air quality， they should be given different weights. According to the normalized association degrees from grey correlation analysis， the weights of the pollutants of SO2， NO2， CO， PM10， PM2.5 and O3 could be determined as follows：
From above， the fuzzy comprehensive evaluation matrix of air environment quality was：
Where，"o" is the fuzzy operator. For weights A=（a1， a2， a3， a4， a5， a6）， the fuzzy matrix synthesis operation was taken. After testing models M∧∨， M·， ∨ and M·， ， M·， +， the model M·， was found to be the best， so the model M·， was selected for comprehensive evaluation. In order to overcome the limitations of the principle of maximum affiliation， the eigenvalues of the level variables could be calculated.
From H， it was possible to determine the overall evaluation results of the air environment quality， that is， the standard level of air environment quality. The calculated degree of membership of pollutants at each level in 2014 is shown in Table 2. As shown in Table 2， the comprehensive evaluation indicator of air environmental quality in 2014 was 2.145， and in a similar way， the comprehensive evaluation index of air environment quality calculated in 2015 was 1.926， and the comprehensive evaluation index of air environment quality in 2016 was 1.805. Obviously， the value of comprehensive evaluation index for air quality became smaller， so the air quality from 2014 to 2016 became better.
Prediction of Air Environment Quality Development Trend in Baoding City and Result Analysis
Based on the grey GM （1.1） prediction model[7]， MATLAB software was used to program the calling program to predict the air environment quality. The results are shown in Table 3.
Conclusion
This paper uses the grey correlation analysis， fuzzy comprehensive evaluation and grey prediction model GM （1，1） to evaluate and predict the air quality in Baoding. Comprehensive evaluation has been done to the air quality in Baoding City from 2014 to 2016， and the obtained eigenvalues H are 2.145， 1.926， 1.805， respectively. It can be seen that H is getting smaller and smaller， indicating that the air quality is getting better. The obtained values of H are used as initial data for the prediction using the grey GM（1，1） model， getting the predicted eigenvalues H from 2014 to 2018， which are 2.145， 1.925， 1.804， 1.691， 1.585， respectively. The comparison results show that the prediction error for 2014-2016 is not more than 0.03%， and thus the model has a significant effect on air quality prediction. The evaluation methods and prediction models used in this paper require less data， have more accurate calculations and simple methods， promising with strong practicality.
References
[1] Weather hindcasting. www.tianqihoubao.com.
[2] LI BJ， ZHU CY， ZHOU J. Effect of non-dimensional quantities of original data on grey incidence order[J]. Journal of Henan Agricultural University， 2002， 36（2）：199-202.
[3] PAN L. Analysis of air quality changes and influencing factors based on grey system[D]. Tianjin， Tianjin University， 2011.
[4] ZHAO XF. An overview of grey system theory[J]. Journal of Educational Institute of Jilin Province， 2011， 27（3）： 152-154.
[5] XIAO XP， LI DY. The latest development of the application of grey relational analysis[J]. Exploration of Nature， 1996， 15（4）： 50-56.
[6] CHEN SY. Theory and application of engineering fuzzy sets[M]. Beijing： National Defense Industry Press， 1998.
[7] DENG JL. Basic method of gray system[M]. Wuhan： Huazhong University of Science and Technology Press， 1992
[8] Ministry of Environmental Protection of the Peoples Republic of China. Ambient air quality standards[S]. 2018.