Periodicity-constrained reweighted generalized minimax-concave regularization and its application in gearbox fault diagnosis

Abstract

In vibration-based gearbox fault diagnosis, accurately extracting periodic transient signals caused by defects is crucial for achieving fault diagnosis. However, the vibration signals measured in practice are often dominated by interference such as random noise and harmonic signals, making the extraction of the transient component highly challenging. To address the issue, this paper proposes a periodicity-constrained reweighted generalized minimax-concave (PC-ReGMC) regularization, which can effectively filter out interference and accurately reconstruct the periodic transient signals. This method is based on a weighted generalized minimax concave regularization model. First, the weight coefficients are initialized to perform the initial transient signal extraction. Then, the square envelope harmonic product spectrum (SEHPS) is introduced to identify the period of the transient signal, and a periodic weighting strategy based on the sinusoidal function is designed to update the weight coefficients. Finally, by reweighting the generalized minimax concave regularization model, the periodicity constraint is embedded into the optimization process of sparse coefficients, thus imposing penalties on non-periodic components to enhance denoising performance. Through the analysis results of simulations and practical cases, it is demonstrated that the proposed method outperforms other sparse regularization methods and the spectral kurtosis in terms of the reconstruction accuracy of the periodic transient signals, and thus provides more precise gearbox fault diagnosis results.