一种解决经验模态分解端点效应的边界延拓法

用于电子设备或系统辐射发射趋势预测的数据大多呈现非线性、样本量小的特点,这大大增加了预测建模的难度,而经验模态分解(EMD)可以将非线性、非平稳的数据分解成若干个呈现一定周期性的本征模态函数(IMF),并且EMD具有完备性和正交性,可通过分别对分解得到的IMF分量建模,从而完成对原始数据的建模。但EMD被端点效应问题所困扰,为了提高EMD的分解精度,针对分解过程中的端点效应问题,以及辐射发射趋势预测的时间序列数据样本量小的特点,利用建立灰色均值GM(1,1)预测模型所需数据量小的优点,提出了一种基于灰色均值GM(1,1)预测模型的边界延拓方法,在原始数据两端各拓展一个极大值和一个极小值,对原始数据进行边界延拓,从而抑制EMD的端点效应。仿真对比结果表明:该方法在分解层数和平均相对误差方面均优于未经延拓处理的EMD,且对数据样本量要求不高。

A boundary extension method for empirical mode decomposition end effect

The data used for individual or systematic radiation emission prediction always has the features like non-linear regularity and small sample volume, which provide significant difficulties for accurate model establishment. However, by introducing the empirical mode decomposition(EMD) method, the non-linear and non-stationary data can be decomposed into several periodic intrinsic mode functions(IMF). The advantages of the EMD method including completeness and orthogonaity enable us to decompose the modeling of initial data into the modeling of IMFs components. However, due to the characteristics of the electromagnetic compatibility test data, EMD suffers from the end effect which limits its precision. In order to enhance the accuracy of EMD, this paper presents a novel approach which is based on the mean gray GM(1, 1) prediction model with end-point extension. Specifically, based on the fact that the data volume required by mean gray GM(1, 1) prediction model is relatively small, the maximum and minimum values are added at each end point of the initial data set respectively to suppress the end effect of EMD method. Simulation results indicate that decomposition layer number and the average relative error are optimized significantly. Furthermore, the required sample data volume can be reduced much significantly than the existing EMD methods.