窗口伸缩优化的同步压缩算法及其在变转速工况瞬时频率估计上的应用  

Synchrosqueezing Algorithm for Window Extension and Compression Optimization and Its Applications in Instantaneous Frequency Estimation under Variable Speed Conditions

作　　者：吴红安 吕勇[1,2] 易灿灿 袁锐 WU Hongan;LYU Yong;YI Cancan;YUAN Rui(Key Laboratory of Metallurgical Equipment and Control of Education Ministry,Wuhan University of Science and Technology,Wuhan,430081;Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering,Wuhan University of Science and Technology,Wuhan,430081)

机构地区：[1]武汉科技大学冶金装备及其控制教育部重点实验室,武汉430081 [2]武汉科技大学机械传动与制造工程湖北省重点实验室,武汉430081

出　　处：《中国机械工程》2022年第1期34-44,共11页China Mechanical Engineering

基　　金：国家自然科学基金(51875416,51805382);湖北省自然科学基金创新群体项目(2020CFA033)。

摘　　要：针对传统时频分析方法的固定窗在分析非线性调频信号时存在时频聚集性不高等问题,在短时傅里叶变换基础上引入同步压缩理论,利用信号的局部信息特征,提出一种窗口伸缩优化的时频同步压缩变换算法,并在此基础上推导出二阶及高阶的窗口伸缩优化的同步压缩变换算法。该方法能够兼顾同步压缩变换和重排的优势,进一步锐化时频脊线,从而增强时频表示的能量聚集水平,提高信号时频分辨率。鉴于信号的先验知识未知,以最小信息熵准则为依据对截取信号窗口进行伸缩优化,利用熵值对时变窗口参数进行估计从而确定各时刻的最优窗宽。仿真信号和实际信号分析结果验证了该方法的有效性。The fixed window of traditional time-frequency analysis method had the problems of low time-frequency aggregation when analyzing nonlinear frequency modulation signals.The synchrosqueezing theory was introduced on the basis of short-time Fourier transform,and a time-frequency synchrosqueezing transform algorithm for window scaling optimization was proposed by using the local information characteristics of the signals,and the second-order and high-order synchrosqueezing transform algorithms for window scaling optimization were deduced.This method might take into account the advantages of synchrosqueezing transform and reassignment method,and further sharpen the time-frequency ridges,thereby enhancing the energy concentration level of the time-frequency representation and improving the signal time-frequency resolution.In view of the unknown prior knowledge of the signals,the minimum information entropy criterion was used to optimize the window width of the intercepted signals,and the entropy values were used to estimate the time-varying window parameters to determine the optimal window parameters at each moment.The effectiveness of the method was verified through the analysis of the simulated signals and the actual signals.

关 键 词：时频分析 多分量非平稳信号 短时傅里叶变换 同步压缩变换 窗口伸缩优化 

分 类 号：TH113[机械工程—机械设计及理论] TH133.33