基于谐波小波变换的共振解调法

在滚动轴承的振动故障诊断中，广泛使用解调方法分析诊断故障。利用软件方法实现共振解调时，必须首先构造窄带高频带通滤波器，提取高频共振信息，然后利用Hilbert变换进行解调分析。通过分析谐波小波变换的实现过程，发现信号经谐波小波变换的实质是将信号带通滤波后，进行Hilbert解调。另外，共振解调中要求带通滤波器是窄带高频带通滤波器，广义谐波小波突破了传统二进小波在低频分辨率高，而在高频分辨率低的限制，能够实现超窄带高分辨率检波，满足共振解调的要求。在此基础上，提出了基于谐波小波变换的共振解调算法，为软件实现共振解调提供了一种新的途径。

Algorithm of Demodulated Resonance Based on Harmonic Wavelet Transform

Resonance demodulation analysis is widely employed to diagnose faults of rolling bearings.In implementation procedure of resonance demodulation using softwave method,a narrowband bandpass filter should be constructed to extract information about resonances with high frequencies firstly,and then the Hilbert transform is applied to the output signal of the bandpass filter for demodulation analysis.In this paper,through analyzing the process of harmonic wavelet fransform,it is found that its essence means after the signal is filtered bandpassingly it would be demodulated by the Hilbert transform.In addition,the generalized harmonic wavelet can realize the super-narrow bandpass filtering with high resolution to meet the requirement of resonance demodulation and to break through the limitation of the dyadic wavelet whose resolution is high in lowerfrequency range but low in higher frequency range.Thus,based on harmonic wavelet transform,the resonance demodulation algorithm is proposed,this method provides a new way to realize the resonance demodulation by software.