Theoretical analysis of adaptive harmonic window and its application in frequency extraction of vibration signal

The goal of this paper is to find an excellent adaptive window function for extracting the weak vibration signal and high frequency vibration signal under strong noise. The relationship between windowing transform and filtering is analyzed first in the paper. The advantage of adjustable time-frequency window of wavelet transform is introduced. Secondly the relationship between harmonic wavelet and multiple analytic band-pass filter is analyzed. The coherence of the multiple analytic band-pass filter and harmonic wavelet base function is discussed, and the characteristic that multiple analytic band-pass filter included in the harmonic wavelet transform is founded. Thirdly, by extending the harmonic wavelet transform, the concept of the adaptive harmonic window and its theoretical equation without decomposition are put forward in this paper. Then comparing with the Hanning window, the good performance of restraining side-lobe leakage possessed by adaptive harmonic window is shown, and the adaptive characteristics of window width changing and analytical center moving of the adaptive harmonic window are presented. Finally, the proposed adaptive harmonic window is applied to weak signal extraction and high frequency orbit extraction of high speed rotor under strong noise, and the satisfactory results are achieved. The application results show that the adaptive harmonic window function can be successfully applied to the actual engineering signal processing.摘要本文研究的目标在于寻找一个自适应的优秀窗函数, 来提取强噪声下微弱振动信号和高频段的振动信号。 首先分析了加窗变换与滤波的关系, 介绍了小波变换具有可变时频窗的优势。 其次分析了谐波小波与复解析带通滤波器的关系, 指出了复解析带通滤波器与谐波小波基函数的一致性, 发现了谐波小波变换对复解析带通滤波器的包含性。 然后对谐波小波变换进行拓展, 提出了不需要进行分层分解的自适应谐波窗的概念与理论表达式。 通过与汉宁窗对比, 分析了自适应谐波窗极其优秀的抑制泄漏能力, 和时频窗分析中心自由移动和任意改变尺度的优秀特性。 最后将所提出的自适应谐波窗应用到高速转子的强噪声下微弱周期信号的频率提取, 和高频轴心轨迹的提取中, 取得了满意的效果。 该应用效果显示出自适应谐波窗函数能够成功应用于实际工程信号处理中。