Matching synchrosqueezing transform: A useful tool for characterizing signals with fast varying instantaneous frequency and application to machine fault diagnosis

In this paper, we first introduce the motivation of MSST with three heuristic examples. Then we introduce a precise mathematical definition of a class of chirp-like intrinsic-mode-type functions that locally can be viewed as a sum of a reasonably small number of approximate chirp signals, and we prove that MSST does indeed succeed in estimating chirp-rate and IF of arbitrary functions in this class and succeed in decomposing these functions. Furthermore, we describe an efficient numerical algorithm for the practical implementation of the MSST, and we provide an adaptive IF extraction method for MSST reconstruction. Finally, we verify the effectiveness of the MSST in practical applications for machine fault diagnosis, including gearbox fault diagnosis for a wind turbine in variable speed conditions and rotor rub-impact fault diagnosis for a dual-rotor turbofan engine.