Time-reassigned synchrosqueezing transform: The algorithm and its applications in mechanical signal processing Dong He a , Hongrui Cao a,⇑ , Shibin Wang a , Xuefeng Chen b a Xi’anJiaotong University, School of Mechanical Engineering, Xi’an, Shaanxi 710049, PR China b Xi’anJiaotong University, State Key Laboratory for Manufacturing Systems Engineering, Xi’an, Shaanxi 710049, PR China article info Article history: Received 1 February 2018 Received in revised form 4 April 2018 Accepted 2 August 2018 Keywords: Time-reassigned synchrosqueezing transform Time-frequency analysis Reassignment Group delay Transient feature extraction Fault diagnosis abstract Synchrosqueezing transform (SST) is an effective post-processing time-frequency analysis (TFA) method in mechanical signal processing. It improves the concentration of the time-frequency (TF) representation of non-stationary signals composed of multiple compo- nents with slow varying instantaneous frequency (IF). However, for components whose TF ridge curves are fast varying, or even nearly parallel with frequency axis, the SST still suffers from TF blurs. In this paper, we introduce a TFA method called time-reassigned syn- chrosqueezing transform (TSST) that achieves highly concentrated TFR for impulsive-like signal whose TF ridge curves is nearly parallel with frequency axis. Moreover, the TSST enables signal reconstruction, compared with the standard TF reassignment methods, such as reassigned short-time Fourier transform and reassigned wavelet transform. In the algo- rithm of TSST, the group delay estimator is calculated rather than the IF estimator. Furthermore, the TF coefficients are reassigned in the time direction rather than in fre- quency direction as the SST did. Then we compare the concentration between SST and TSST at different length of Gaussian window and chirp-rate, which is followed by the respective application scope of SST and TSST. Furthermore, we describe an efficient numer- ical algorithm for practical implementation of TSST. It is found that the SST is suitable for characterizing signal with small chirp-rate while TSST performs better for a large chirp- rate condition. Thus, the TSST is more capable of extracting transient features of impulsive-like signal. Finally, the effectiveness of the TSST and its inverse transform is ver- ified by simulation and experimental studies. Ó 2018 Elsevier Ltd. All rights reserved. 1. Introduction Mechanical fault diagnosis methods under non-stationary operating conditions play a significant role in machinery safe maintenance. The non-stationary operating conditions are easily caused by time-varying load [1], operating speed [2] and transient phenomena [3], which makes it much more difficult to extract fault features from such complex vibration signals [4]. For instance, frequency-based methods like spectral analysis are not suitable for non-stationary conditions as speed fluc- tuations in rotatory machines will smear the spectrum, resulting in a challenge for interpretation from the spectrum for fault feature extraction and the modeling of the control strategy. Therefore, signal processing, feature extraction, and control meth- ods under non-stationary conditions of machines are crucial technologies for health monitoring and fault diagnosis [5,6]. This paper presents an algorithm and its applications for mechanical signal processing under non-stationary operating conditions. https://doi.org/10.1016/j.ymssp.2018.08.004 0888-3270/Ó 2018 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: chr@mail.xjtu.edu.cn (H. Cao). Mechanical Systems and Signal Processing 117 (2019) 255–279 Contents lists available at ScienceDirect Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp