Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery, where weak fault characteristic signals hinder accurate fault state representation, we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform (FAWT) with Nonlinear Quantum Permutation Entropy. FAWT, leveraging fractional orders and arbitrary scaling and translation factors, exhibits superior translational invariance and adjustable fundamental oscillatory characteristics. This flexibility enables FAWT to provide well-suited wavelet shapes, effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults. In our approach, gearbox vibration signals undergo FAWT to obtain sub-bands. Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy, a feature that more accurately characterizes the operational state of vibration simulation signals. The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery. A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method. Comparative assessments with parameters derived from traditional permutation entropy, sample entropy, wavelet transform (WT), and empirical mode decomposition (EMD) underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.