Differential time-frequency mode decomposition and its application in rotating machinery fault diagnosis

Abstract

Mode decomposition methods, such as Empirical Mode Decomposition (EMD), Empirical Wavelet Transform (EWT), Variational Mode Decomposition (VMD), and Singular Value Decomposition (SVD), are widely used in signal denoising. However, these methods essentially act as band-pass filter banks, decomposing signals into different frequency bands. This leads to two key challenges: on the one hand, they cannot remove noise within the frequency band; on the other hand, extracting sensitive components requires precise quantitative criteria, and the design principles of these methods may not apply to all signals. In practical industrial applications, most of the signals collected are from normal operating conditions. To address the aforementioned issues, this paper proposes a novel adaptive mode decomposition method—Differential Time-Frequency Mode Decomposition (DTFMD). This method decomposes signals into sensitive components (SC), reference components (RC), and noise. First, normalized time–frequency amplitude spectra (NTFAS) from easily acquired normal signals in industrial settings are used as reference signals, while the NTFAS from fault signals serve as mixed signals. A large-margin convex optimization model is then applied to identify the optimized weights time–frequency spectrum (OWTFS). Next, an adaptive thresholding strategy is developed to locate the time–frequency positions of the SC, RC, and noise on the OWTFS. Time-frequency inverse transformation techniques are then used to reconstruct the components. Finally, simulations, bearing experiments, and industrial truck gearbox data are used to validate the effectiveness and advantages of the proposed method, with comparisons made against existing mode decomposition techniques.