Application Of GM(J,M) Optimization Model Based On Interval Grey Number In Smog

Smog is one of the greatest challenges facing China's sustainable development,which seriously affects China's economy,ecology and human health.Smog pollution in China has characteristics of time-varying and time-lag,and the relevant index data of smog have grey characteristics such as uncertainty,short time series and limited amount of data.The traditional GM?1,N?model has limitations in dealing with such problems,so the linear time-varying GM?1,N?model and time-lag GM?1,N?model will respectively established,which are extended from real number sequence to interval grey number sequence,and then GM?1,N?optimization models based on interval grey number are built,and those optimization models are applied to predict smog in key cities of China.The specific research contents are as follows:?1?When the probability function of interval grey number is unknown,considering the influence of the dynamic time variation of the related factors on the system characteristic data,the linear time polynomial is introduced into the traditional GM?1,N?model to construct the linear time-varying GM?1,N?model,and extend this model from real number sequence to interval grey sequence.Therefore,this paper establish the linear time-varying GM?1,N?model based on kernel and degree of greyness,and the parameters of this model are solved by the least square method.Finally,the linear time-varying GM?1,N?model based on kernel and degree of greyness is to predict the annual PM₁₀ average concentration in Beijing for 2019 to 2021.The results show that the annual PM₁₀ average concentration in Beijing has a downward trend for2019 to 2021,but still exceeds the national standard,which shows that this model has the practical value of providing scientific basis for the government to formulate smog control policies.?2?When the probability function of interval grey number is unknown,considering the time-lag effect between the related factors and the system characteristic data,the time-lag parameter is introduced into the traditional GM?1,N?model to build a novel time-lag GM?1,N?model,and extend this model from real number sequence to interval grey sequence.Therefore,the time-lag GM?1,N?model based on kernel and degree of greyness is established.The time-lag parameter is solved with the minimum average relative error of the model as the optimal objective function.Finally,this paper establishes the time-lag GM?1,N?model based on kernel and degree of greyness to predict the PM_2.5 monthly average concentration in Beijing for October to December 2018,and compares the PM_2.5 concentration in Beijing for 2014 to 2018.The results show that the PM_2.5 monthly average concentration in Beijing has a downward trend for October to December 2018,and the PM_2.5 concentration in Beijing has a fluctuating downward trend for 2014 to 2018,especially the PM_2.5 concentration of Beijing decreased sharply in autumn and winter,which indicates that this model can provide smog control and decision-making for support to the government.?3?When the probability function of interval grey number is known,the kernel and degree of greyness of interval grey number are reconstructed.Considering the time-lag effect of the previous related factors on the current system characteristic data,the GM?1,N?model based on novel kernel and degree of greyness is built,and determine the time-lag parameter estimation method.Finally,the GM?1,N?model based on novel kernel and degree of greyness is established to predict PM₁₀ daily average concentration for November 21 to 23,2019 in Nanjing.The results show that the PM₁₀ daily average concentration in Nanjing have a fluctuating growth trend for November 21 to 23 in 2019,which shows that this model can provide a reference for the government to carry out smog early warning and control.