Research On Grey Modeling Technology For Time-delay And Periodic Systems With Application To The Smog Weather

Smog weather,which happens frequently in a larger and larger region in China,produces serious impacts on the traffic,health,and emotion.It has attracted the attention of Chinese leaders because it plays an important role in the construction of green ecological civilization as well as in improving the quality of people lives.The grey system is utilized to analyze the factors of the smog weather because of the limit data and uncertain system.A series of improved grey models,including the grey incidence models and grey prediction models,are proposed for the periodic data and the time-delay relationship in the air pollution system.Four perspectives are summarized of this paper as given follows:(1)The grey dynamic trend incidence model for periodic data is proposed.The modeling principles of trend measurement,panel data,and periodic data are described.A judgment factor which is used to determine whether the trend of two sequences is the same or different and a measurement factor for calculating the absolute degree of grey trend incidence are put forward by using the trigonometric functions.Then,a new grey incidence model called the grey dynamic trend incidence model is designed according to the above two parts.A time lag t is used when obtaining the trend of a sequence during a specific time period in the grey dynamic trend incidence model for data with equal period.In order to analyze the relationship between two sequences having different periods,an addition function and a multiply function are given in the grey dynamic trend incidence model for multivariable systems with varied periods.(2)Design of the grey dynamic trend incidence model for time-delay systems is given.Two kinds of the time-delay problems,called instantaneous and continuous time delays,are put forward according to the different time-delay processes.A time lag ? between two sequences is assumed to calculate the relationship in a time-delay system.In the continuous time-delay problems,the delay impacts from a specific factor may last a few years.Four types of time-delay weights,called equal weights,increasing weights,decreasing weights and unimodal weights,are analyzed in this paper.The function of each kind of time-delay weights is derived according the practical problems as well as the relationship with the length of time lags.(3)An improved grey interpolation approach considering the periodic and time-delay characteristics is established for producing the missing data or correcting the abnormal values.The missing data and abnormal values are assumed as interval grey numbers.Hence,two programming problems are designed to obtain the upper and lower bounds of the unknown or abnormal values.After producing the normal and equidistant sequences,four improved time-delay grey discrete forecasting models for multivariable systems according to the four types of time-delay weights are proposed to forecast the trends.The solutions based on the particle swarm optimization for the parameters in the proposed time-delay grey discrete forecasting models are given.The relationships among the four grey prediction models are portrayed in this work.(4)The above proposed grey evaluation models and grey forecasting theory for time-delay and periodic systems are utilized to analyze the factors to the smog weather in the region of Beijing,Tianjin and Hebei province.In order to analyze the impact on the smog weather from the economic and social indicators,the annual amount and average concentration of air pollutant are used as intermediate variables.Firstly,the relationship between the annual average concentration of air pollutant and smog weather is analyzed by using the grey dynamic trend incidence model for periodic data.Secondly,the grey dynamic trend incidence model for time-delay systems is utilized to study the relationship between the annual amount and average concentration of air pollutant.Thirdly,the grey dynamic trend incidence model is applied to obtain the relationship between the annual amount of air pollutant and the economic development.Then,the economic factors to the smog weather can be obtained.The data are given from 2008 to 2016.Three indicators which are the consumption of coal,electricity,and every ten thousands gross regional product play an important role to the smog weather and keep in a high relevance.The mixed impacts of gross industrial output value,the area of houses and buildings,the number of motor vehicles,and the funds for environmental protection are given by using the an addition function in the grey dynamic trend incidence model for multivariable systems with varied periods.Finally,seven suggestions for preventing the smog weather in this region are put forward according the relevant factor analysis.