Weighted Criteria For Moving-mean Method And Improved Algorithm For ESMD Method

The most important way to observe the characteristics of things is to obtain the trend of changes in the data,so as to achieve the characteristics analysis and subsequent prediction of the data.In order to obtain the change trend of the data,it is necessary to screen the analysis method according to the characteristics of the data itself.Based on the essential characteristics of the data analysis method,this paper explores the rule of weighted moving-mean method window length and weight coefficient.Based on the representative function of extreme data points,the ESMD method is improved from accuracy and decomposition efficiency.The moving-mean method is one of the conventional approaches for trend-extraction from a data set.It is usually applied in an empirical way.The smoothing degree of the trend depends on the selections of window length and weighted coefficients,which are associated with the change pattern of the data.Are there any uniform criteria for determining them? The present article is a reaction to this fundamental problem.By investigating many kinds of data,the results show that:(1)Within a certain range,the more points which participate in moving-mean,the better the trend function.However,in case the window length is too long,the trend function may tend to the ordinary global mean.(2)For a given window length,what matters is the choice of weighted coefficients.As the five-points case concerned,the local-midpoint,local-mean and global-mean criteria hold.Among these three criteria,the local-mean one has the strongest adaptability,which is suggested for your usage.The ESMD method is the abbreviation of “Extreme-point Symmetric Mode Decomposition method”,which has certain advantages in data adaptive analysis.But according to the principle of ESMD data analysis method,it is generally suitable for the more symmetrical data about the midpoint in every half period.For asymmetric(peak-valley asymmetry)data,the midpoint selected in this method is unrepresentative.In this paper,the ESMD method is improved for the analysis of this kind of data,and the local mean of each half period is used to replace the pole symmetric midpoint in the original algorithm,so that the asymmetric data can be better reflected.The numerical simulation proves the method's feasibility and effectiveness.The two-line interpolation in ESMD method is not only symmetrical but also efficient in decomposition.In this paper,by studying the representative role of extremepoints in data fitting,the modal decomposition of four extreme-point center(FEC)algorithm is proposed on the basis of ESMD two-line interpolation.Through a lot of experimental verification and numerical calculation,the similarities and differences between FEC and ESMD?II and ESMD?III mode decomposition were analyzed.FEC algorithm is not only superior to ESMD method in terms of screening times and variance ratio,but also superior or similar to ESMD method in terms of modal decomposition efficiency and AGM curve effect.