Research On Improvement Of Two Kinds Of Grey Prediction Models Considering Nonlinear Characteristics Of Data

Time series forecasting is one of the most important research topics today.In reality,due to the high cost,difficulty,long cycle and complex environmental impact factors of data collection,the sample size is "small" and "uncertain".Grey system theory has been widely used in many fields due to its advantages of simple structure,few modeling samples and wide application range.The time series studied by grey forecasting model can be divided into four categories according to their characteristics: monotonic sequence,S-shaped sequence,fluctuation sequence and random oscillation sequence.As prediction problems and scenarios become more complex,data characteristics are increasingly variable.Among them,under the influence of random factors,the S-shaped sequence will have certain oscillation and non-saturation,showing nonlinear characteristics;under the direct or indirect influence of fixed factors,the fluctuation sequence will also show a complex trend,which is expressed as nonlinear trend feature.At this time,it is difficult for the traditional grey prediction model to obtain the ideal prediction accuracy,and the prediction model needs to be expanded according to the data characteristics to fit the corresponding application scenarios.Based on the existing research,this paper analyzes the limitations of the grey generalized Verhulst model and the grey wave model corresponding to different feature sequences,and improves the two types of grey prediction models according to the data characteristics.The main research contents are as follows:(1)Improvement of grey generalized Verhulst model for nonlinear sigmoid sequences.The grey generalized Verhulst model has natural advantages for sigmoid sequence prediction.However,the traditional Verhulst model relies too much on the sigmoid sequence and is actually a more complex nonlinear sigmoid sequence.Therefore,this paper introduces the initial value weighted control function and the background value weight coefficient,and constructs a nonlinear collaborative optimization model between different parameters.The weighted control function makes full use of the "information" contained in the small sample sequence on the basis of conforming to the changing law of old and new information and the principle of prioritizing new information;the background value weight coefficient can dynamically correct the inherent error caused by the fluctuation of the sequence.Finally,the new model is proved to have better flexibility and fitting prediction performance through instance prediction,which has significant advantages compared with other classical grey prediction models.(2)Improvement of the grey wave model for nonlinear trend fluctuation series.The grey wave model can make good use of time series fluctuation patterns for forecasting.However,the traditional grey wave model is less effective for predicting fluctuation series with nonlinear trends.Therefore,this paper introduces a unary quadratic contour line and uses MATLAB to dynamically fit the contour line coefficients to obtain the nonlinear trend of the data.Finally,the effectiveness and advantages of the improved model are verified by two real cases with different growth trends.(3)The new model is applied to the prediction of relevant elements of environmental problems in my country.Scientific prediction results can provide strong support for further decision-making on environmental issues,and are of great significance to winning the tough battle of pollution prevention and control.Due to the lack of relevant statistical data on environmental problems in our country,and the data that is too old loses its timeliness,the entire system presents a "small sample" feature.The improved model in this paper has a good adaptability to this feature.Therefore,these two models are used to predict the development trend of the concentration of hazardous solid waste and air pollutants in my country’s environmental problems,thereby providing new solutions for environmental problems and other field prediction problems that conform to the characteristics of the data.