Study On Statistical Characteristics For The Modes Decomposed By ESMD Method

The Extreme-Point Symmetry Mode Decomposition(ESMD) method is the development of Hilbert-Huang transform, making up for the defect that the number of screening is difficult to determine and the trend function of decomposed is too rough.The ESMD method not only intuitively reflects the time-varying of modal amplitude and frequency, but also clearly reflects the change of the total energy. The given time- frequency distribution is more intuitive sense. What’s more, the method has a unique advantage in the analysis of frequency change. But there still exist many problems, such as the problems about mode changes, what features obtained about the modals which disposed by ESMD method, the rationality about using the reckoned average frequency and amplitude to estimate the change of the mode, etc., this topic will be used to solve these problems with a lot of actual data. The main results of the researched summary are as follows:(1)After a large number of statistic research, we found that models’ frequency and amplitude generated by ESMD method are in normal distribution when the amount of data is appropriate. From the statistical standpoint, the coefficient of skew of the statistical sample proved that the sample statistical distribution can be handled as a normal distribution curve;(2)From the variance analysis, with the change of the variance, the curve of the sample statistical distribution trends also accord with the characteristics of normal distribution;(3)By the calculation, the error of the value estimation of the frequency and amplitude is within the scope of permissible. So, we can estimate average modal frequency in using the number of extreme value point. We can also use the estimated mean frequency to estimate the average change of the modal in math.This is also visible, the modal of decomposed by ESMD method is objective, this method is feasible in terms of the analysis of the data. In addition, the amount of date changed, whether the conclusion is reasonable. What different effects will occur when the number of screening is changed? All of these will be worth further research.