A Bilateral Second-Order Synchrosqueezing Transform and Application to Vibration Monitoring of Aerospace Engine

The synchrosqueezing transform (SST) and its ameliorated methods can enhance the energy concentration of the vibration signals in time-frequency domain, but it does not show enough effect for the weak feature extraction. Besides, many large-scale rotating machines such as aerospace engines and gas engines often work under complex vibrations, and this increases the difficulty for health monitoring based on vibration signals. This article presents a time-frequency analysis (TFA) named bilateral second-order SST (BFSST2). It can sharpen the instantaneous frequencies (IFs) like second-order SST (FSST2), and more importantly, it can extract the weak features such as amplitude-modulation frequency-modulation IFs and small-amplitude time-varying IFs which are easily ignored on time-frequency plane. To achieve the aforementioned target, the IFs are first obtained by employing FSST2, and then a bilateral function representing a novel negative-positive TFA is structured by combining the hyperbolic tangent function, exponential function, and sign function together. After that the large-amplitude IFs are transformed into small-negative amplitude ones by the product with the bilateral function, and this can not only enhance the original weak feature but also avoid its confusion with the transformed small-negative amplitude ones. The proposed BFSST2 is validated by a numerical simulation. At last, two case studies are given to illustrate its effectiveness in aerospace engine vibration monitoring.