Adaptive synchronous demodulation transform with application to analyzing multicomponent signals for machinery fault diagnostics

The combination of the complex structure and the nonstationary operating pattern makes the measured signal of the machinery a multi-component one with a complex time-varying spectral structure, challenging most time–frequency analysis methods in resolution, adaptability, and objectivity. As such, we propose a novel time–frequency analysis method, namely, the adaptive synchronous demodulation transform (ASDT), by adaptively designing a demodulation term according to the spectral structures of the target signals. The proposed demodulation term can make each component of the windowed signal stationary simultaneously without any prior knowledge, such as the number of components and the corresponding estimated instantaneous frequencies. ASDT possesses three main advantages: it can be used to analyze signals with nonlinear instantaneous frequencies; it can obtain the optimum frequency resolution when window width is set; and the demodulation term is flexible, implying that it can be specifically designed according to the frequency structures of different types of signals. Furthermore, ASDT allows for signal recovery. To testify the superiority of the proposed ASDT, two synthetic signals with parallel and proportional IFs structures were built, and several real-life signals, vibration signals collected from a planetary gearbox test rig and water turbine, and an echo signal collected from a brown bat were used. A comparison of the analysis results of ASDT with those of STFT, continuous wavelet transform, and Wigner–Ville distribution demonstrated the superiority of ASDT over conventional methods.