Matching demodulation transform and its application in machine fault diagnosis

In this chapter, matching demodulation transform (MDT), an iterative algorithm, is introduced to generate a time-frequency (TF) representation with satisfactory energy concentration, and thus to extract the highly oscillatory frequency-modulation (FM) feature of rotating machine fault. As opposed to conventional time-frequency analysis (TFA) methods, this algorithm does not have to devise ad hoc parametric TF dictionary. Assuming the FM law of a signal can be well characterized by a determined mathematical model with reasonable accuracy, the MDT algorithm can adopt a partial demodulation and stepwise refinement strategy for investigating TF properties of the signal. The practical implementation of the MDT involves an iterative procedure that gradually matches the true instantaneous frequency (IF) of the signal. Moreover, because the MDT is a linear TFA method, it can reconstruct individual components from a multicomponent signal’s TF representation. Theoretical analysis of the MDT’s performance is provided, including quantitative analysis of the IF estimation error and the convergence condition. The validity and practical utility of the MDT is then demonstrated on simulation study, an experiment rotor system and a practical heavy oil catalytic cracking machine set with rotor rub-impact fault. The analysis results show that the MDT method is powerful in the analysis of FM signals and is an effective tool for the feature extraction of machine faults.