针对变分模态分解(Variational mode decomposition, VMD)中难以确定分解分量个数k和惩罚参数α的问题。提出一种改进的变分模态分解方法—基于萤火虫算法及主模态分析法的变分模态分解（Variational mode decomposition based on firefly algorithm and Principle Mode Analysis，简称FA-PMA- VMD）方法。该方法首先用主模态分析（Principle Mode Analysis,简称 PMA）对VMD分解的带限内禀模态函数(Band-Limited Intrinsic Mode Function, 简称BIMF)分量进行排序；然后用萤火虫算法对变分模态分解的最佳影响参数[k,α]组合进行搜索，以新提出的正交低峰值作为萤火虫算法的优化目标，得到的最佳的惩罚参数α和分量个数k组合；最后根据预先设定的故障特征参数自适应地将信号分解为k个 BIMF分量。通过对仿真信号和齿轮齿根裂纹实际故障信号进行分析，分析结果表明FA-PMA- VMD具有良好的分解效果。
Abstract
Aiming at the decomposed components’ number k and the penalty parameter α in the method of variational mode decomposition (VMD) being difficult to determine, an improved VMD method, based on the firefly algorithm (FA) and the principle mode analysis (PMD), named the method of FA-PMA-VMD was proposed. Firstly, the new method used PMA to sort band- limited intrinsic mode function (BIMF) components obtained with VMD. Then, FA was used to search the optimal influence parameter combination k and α in VMD with a new proposed orthogonal low peak value taken as the objective of FA, the optimal combination of k and α was gained. Finally, a signal was decomposed into k BIMF components adaptively with FA-PMA-VMD according to the preset fault characteristic parameters. The analysis results of simulated signals and actual fault signals of gear tooth root cracks showed that the proposed method of FA-PMA-VMD has a good decomposition effect.
关键词
变分模态分解 /
主模态分析 /
萤火虫算法 /
齿根裂纹 /
故障诊断
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Key words
variational mode decomposition (VMD) /
principle mode analysis (PMA) /
firefly algorithm (FA) /
gear tooth root crack /
fault diagnosis
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