Convolutional Sparse Learning for Blind Deconvolution and Application on Impulsive Feature Detection

Abstract

The mechanical structure or transmission path between fault source and sensor location always distorts the impulsive signatures of machine faults. It is thus an important task to estimate the desired impulsive feature and the influence of transmission path simultaneously from the noisy observation signals. Therefore, a convolutional sparse learning model (ConvSLM) is proposed to perform impulsive feature detection. The ConvSLM directly models the modulation process of the transmission path and is completely different from the indirect inverse filter design scheme as popular deconvolution techniques adopted. Meanwhile, to overcome the inherent drawbacks of the popular Kurtosis maximization strategy, the sparse structure of the impulsive feature is integrated into the objective function of the ConvSLM. Different from the recently developed two-stage solver, a new iterative algorithm with only one stage is also developed under a multiple-block nonconvex alternating direction method of multiplier framework to cope with the nonconvexity and nonsmoothness of the sparsity-regularized objective function, which not only reduces the algorithmic complexity but also has a convergence guarantee. Numerical experiments on synthetic data and test results corroborate the efficacy of the advocated approach. Compared with the state-of-the-art blind deconvolution techniques, the ConvSLM’s superiority is sufficiently verified through its application on the impulsive detection of the wind turbine gearbox gear.