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

doi:10.3969/j.issn.1004-132X.2022.01.004

Abstract

Abstract: 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.

Key words: time-frequency analysis, multi-component non-stationary signal, short-time Fourier transform, synchrosqueezing transform, window extension and compression optimization

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。

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

CLC Number:

WU Hongan, , LYU Yong, , YI Cancan, YUAN Rui, . Synchrosqueezing Algorithm for Window Extension and Compression Optimization and Its Applications in Instantaneous Frequency Estimation under Variable Speed Conditions[J]. China Mechanical Engineering, 2022, 33(01): 34-44.

吴红安, 吕勇, 易灿灿, 袁锐, . 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[J]. 中国机械工程, 2022, 33(01): 34-44.

References

［1］李林,王林,韩红霞,等.自适应时频同步压缩算法研究［J］.电子与信息学报,2020,42(2):438-444.
LI Lin, WANG Lin, HAN Hongxia, et al. Research on the Adaptive Synchrosqueezing Algorith ［J］. Journal of Electronics & Information Technology, 2020,42(2):438-444.
［2］张贤达, 保铮. 非平稳信号分析与处理［M］. 北京: 国防工业出版社, 1998: 1-3.
ZHANG Xianda ,BAO Zheng. Non-stationary Nonlinear Signal Analysis and Processing［M］. Beijing: National Defense Industry Press, 1998: 1-3.
［3］褚福磊, 彭志科, 冯志鹏. 机械故障诊断中的现代信号处理方法［M］. 北京：科学出版社, 2009.
CHU Fulei,PENG Zhike, FENG Zhipeng. Modern Signal Processing Methods in Machinery Fault Diagnosis［M］. Beijing：Science Press, 2009.
［4］赵明,林京.变转速下机械动态信息的自适应提取与状态评估［J］.金属加工(冷加工),2015(13):89.
ZHAO Ming, LIN Jing. Dynamic Signal Analysis for Speed-varying Machinery: a Review ［J］. Metal Working(Metal Cutting), 2015(13):89.
［5］HUANG N E, SHEN Zheng, LONG S R, et al. The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis［J］. The Royal Society A: Mathematical, Physical and Engineering Sciences, 1998, 454(1971): 903-995.
［6］AUGER F, FLANDRIN P. Improving the Readability of Time-frequency and Time-scale Representations by the Reassignment Method［J］. IEEE Transactions on Signal Processing, 1995, 43(5): 1068-1089.
［7］DAUBECHIES I, LU Jianfeng, WU H T. Synchrosqueezed Wavelet Transforms: an Empirical Mode Decomposition-like Tool［J］. Applied and Computational Harmonic Analysis, 2011, 30(2): 243-261.
［8］OBERLIN T, MEIGNEN S, PERRIER V. The Fourier-based Synchrosqueezing Transform［C］∥2014 IEEE International Conference on Acoustics, Speech and Signal Processing. Florence, 2014: 315-319.
［9］YANG Y . Parameterised Time-frequency Analysis Methods and Their Engineering Applications: a Review of Recent Advances［J］. Mechanical Systems and Signal Processing, 2018, 119.
［10］赵晓平, 吴家新, 周子贤. 改进的Seam Carving瞬时频率估计算法研究［J］. 南京信息工程大学学报, 2017, 9(2): 214-219.
ZHAO Xiaoping, WU Jiaxin, ZHOU Zixian. Instantaneous Frequency Estimation Based on Improved Seam Carving Algorithm ［J］. Journal of Nanjing University of Information Science & Technology, 2017, 9(2): 214-219.
［11］韩红霞. 基于时频同步压缩变换的多分量信号分离研究［D］. 西安:西安电子科技大学,2018.
HAN Hongxia. Research on Multicomponent Signal Separation Based on Synchrosqueezing Transform ［D］. Xi’an:Xidian University, 2018.
［12］陈小旺, 冯志鹏, LIANG Ming. 基于迭代广义同步压缩变换的时变工况行星齿轮箱故障诊断［J］. 机械工程学报, 2015, 51(1): 131-137.
CHEN Xiaowang, FENG Zhipeng, LIANG Ming. Planetary Gearbox Fault Diagnosis under Time-variant Conditions Based on Iterative Generalized Synchro Squeezing Transform ［J］. Journal of Mechanical Engineering, 2015, 51(1):131-137.
［13］潘兵奇,吕勇,易灿灿,等.自适应窗口旋转同步压缩变换及其在电机转速估计上的应用［J］.机械强度,2020,42(5):1017-1023.
PAN Bingqi, LYU Yong, YI Cancan, et al. Adaptive Window Rotating Synchrosueezing Transform and Its Application in Motor Speed Estimation ［J］. Journal of Mechanical Engineering, 2020,42(5):1017-1023.
［14］陈向民, 张亢, 晋风华, 等. 基于自适应时频滤波的变转速齿轮故障特征提取［J］.振动与冲击, 2018, 37(10): 135-140.
CHEN Xiangming, ZHANG Kang, JIN Fenghua. Adaptive Time-frequency Filtering Based Fault Characteristics Extraction Method for Gears under Variable Rotational Speed ［J］. Journal of Vibration and Shock, 2018, 37(10): 135-140.
［15］YU G, YU M，XU C. Synchroextracting Transform［J］.IEEE Transactions on Industrial Electronics, 2017, 64(10):8042-8054.
［16］YU Gang, WANG Zhonghua, ZHAO Ping. Multisynchrosqueezing Transform ［J］.IEEE Transactions on Industrial Electronics, 2019, 66(7):5441-5455.
［17］YU G, LIN T, WANG Z,et al. Time-reassigned Multisynchrosqueezing Transform for Bearing Fault Diagnosis of Rotating Machinery［J］. IEEE Transactions on Industrial Electronics, 2021,68(2) :1486-1496.
［18］YU Gang, WANG Zhonghua, ZHAO Ping, et al. Local Maximum Synchrosqueezing Transform: an Energy-concentrated Time-frequency Analysis Tool［J］. Mechanical Systems and Signal Processing, 2019,117:537-552.
［19］OBERLIN T, MEIGNEN S. The Second-order Wavelet Synchrosqueezing Transform［C］∥2017 IEEE International Conference on Acoustics, Speech and Signal Processing. New Orleans, 2017: 3994-3998.
［20］PHAM D H, MEIGNEN S. High-order Synchrosqueezing Transform for Multicomponent Signals Analysis—With an Application to Gravitational-wave Signal［J］. IEEE Transactions on Signal Processing, 2017, 65(12): 3168-3178.
［21］冯志鹏, 褚福磊, 左明健. 行星齿轮箱振动故障诊断方法［M］. 北京：科学出版社, 2015.
FENG Zhipeng, CHU Fulei, ZUO Mingjian. Vibration Fault Diagnosis Method of Planetary Gerbox［M］. Beijing:Science Press, 2015.
［22］Bat Echolocation Chirp.Digitized 2.5 Microsecond Echolocation Pulse Emitted by the Large Brown Bat, Eptesicus Fuscus ［DS/OL］. ［2020-08-05］.https:∥www.ece.rice.edu/dsp/software/bat.shtml.

[1]	CHEN Jian, YANG Bin, HUANG Kaixuan, CAI Kunqi, LIU Yuanyuan, LIU Xingfu, . Applications of a Ridgeline Extraction Method in Bearing Fault Diagnosis [J]. China Mechanical Engineering, 2021, 32(10): 1157-1163.
[2]	HE Qiang, TANG Xianghong, LI Chuanjiang, LU Jianguang, CHEN Jiadui. Bearing Fault Diagnosis Method Based on Small Sample Data under Unbalanced Loads#br# [J]. China Mechanical Engineering, 2021, 32(10): 1164-1171,1180.
[3]	CAI Yanping;FAN Yu;CHEN Wan;ZHANG Jinming. Applications of Improved Time-frequency Analysis and Feature Fusion in Fault Diagnosis of IC Engines [J]. China Mechanical Engineering, 2020, 31(16): 1901-1911.
[4]	LIU Yang;LIU Xiaobo;LIANG Shan. Aeroengine Rotor Fault Diagnosis Based on Fourier Decomposition Method [J]. China Mechanical Engineering, 2019, 30(18): 2156-2163.
[5]	WANG Youren;WANG Jun;HUANG Haian. Fault Diagnosis of Planetary Gearboxes Based on NLSTFT Order Tracking under Variable Speed Conditions [J]. China Mechanical Engineering, 2018, 29(14): 1688-1695.
[6]	LIU Yiya1,2;LI Ke1,2;CHEN Peng3. Fault Diagnosis for Rolling Bearings Based on Synchrosqueezing Wavelet Transform [J]. China Mechanical Engineering, 2018, 29(05): 585-590.
[7]	Li Baoqing, Cheng Junsheng, Wu Zhantao, Peng Yanfeng. Adaptive and Sparsest Time-frequency Analysis Method Based on Genetic Algorithm and Its Applications [J]. China Mechanical Engineering, 2016, 27(01): 66-72.
[8]	Yang Yu, Li Zizhu, He Zhiyi, Cheng Junsheng. The Rolling Bearing Fault Diagnosis Method Based on ASTFA De-noising and AKVPMCD [J]. China Mechanical Engineering, 2015, 26(21): 2934-2940.
[9]	Meng Zong, Wang Xiaoyan, Ma Zhao. Single-channel Vibration Signal Separation by Combining Wavelet Decomposition with Time-frequency Analysis [J]. China Mechanical Engineering, 2015, 26(20): 2751-2756.
[10]	Li Baoqing, Cheng Junsheng, Peng Yanfeng, Yang Yu. Generalized Demodulation Method Based on ASTFA Method and Its Applications [J]. China Mechanical Engineering, 2015, 26(19): 2564-2570.
[11]	Li Zheng, Wu Weiliang, Qu Wenzhong, Xiao Li. Fatigue Crack Detection Using Nonlinear Ultrasonic Modulation Method [J]. China Mechanical Engineering, 2015, 26(17): 2384-2388.
[12]	Yang Yu, He Zhiyi, Li Zizhu, Cheng Junsheng. ASTFA-BSS Method and Its Applications in Composite Fault Diagnosis for Gearbox [J]. China Mechanical Engineering, 2015, 26(15): 2051-2055,2061.
[13]	Meng Haodong, Li Shunming, Bai Ying, Sun Jianzhong, Zhuang Hualiang. Identification and Analysis of Noise Source and Its Excitation Source Response of V-cylinder Diesel Engine [J]. China Mechanical Engineering, 2013, 24(23): 3181-3185.
[14]	Meng Haodong1;Li Shunming1;Lü Zhixiang2;Li Dianrong3;Xu Yi4;Miu Yuechuan4. Identification Analysis and Improvement on Abnormal Noise Source for Front Gear Chamber Assembly of Diesel Engine [J]. China Mechanical Engineering, 2013, 24(17): 2295-2300.
[15]	YANG Yu, CENG Ming, CHENG Jun-Ku. #br# Research on Local Characteristic-scale Decomposition and Its Stopping Criteria [J]. China Mechanical Engineering, 2013, 24(02): 195-201,208.