An energy time-convexity second-order synchrosqueezing transform and application in weak fault diagnosis of rolling bearings in an aerospace engine

Although the original short-time Fourier-transform-based synchrosqueezing transform (FSST) and its second-order transform (FSST2) can effectively improve the readability of quasi-stationary signal and time-varying signal, respectively, the weak components of time-frequency representation are often submerged easily by noises and large-amplitude instantaneous frequencies (IFs). Moreover, aerospace engines always work in fierce vibration and non-steady states, and this easily causes the weak fault feature of rolling bearings obscured in the time-frequency domain. To solve this problem, we propose a time-frequency analysis algorithm called energy time-convexity second-order synchrosqueezing transform (ET-FSST2). This can sharpen the time-varying IFs like FSST2, and more importantly, it can extract the time-varying IFs with small amplitudes such as weak impulse-like components from multi-component vibration signals. The ET-FSST2 firstly calculates the energy convexity function in the time direction to extract the non-stationary IFs after employing FSST2. It then structures an optimization function by combining a hyperbolic tangent function with a chi-square distribution function as well as optimizing the targeted parameters, aiming to extract the weak components of the non-stationary IFs. Moreover, the effectiveness and robustness of the proposed method are validated by numerical simulation and rolling bearing fault tests. Finally, two case studies of weak fault diagnosis of Ni-Cu-Ag-based PVD-coated rolling bearings operating in cryogenic surroundings are given to illustrate the effectiveness of the proposed method for aerospace engine bearing fault diagnosis.