Nonnegative bounded convolutional sparsity learning algorithm for envelope blind deconvolution

This paper considers the problem of extracting the envelope waveforms from observation signals modulated by transmission paths for fault feature recognition. Unlike previous blind deconvolution works, which firstly recover the source components via designing an inverse filter and then implement envelope analysis, the main goal of this study is to directly model the transmission path and the feature’s envelope wave-forms. By incorporating a envelope regularization description into a sparse learning procedure, a convolutional sparse learning algorithm is proposed to fulfill envelope blind deconvolution for reliably identifying latent feature information. The highlight is that a nonnegative bounded regularizer is established to describe the intrinsic structure of envelope signals and a sparse regularizer is further enforced to strengthen the latent fault features. Meanwhile, a multi-block ADMM solver is developed to achieve a desired solution. Numerical analysis and experimental investigation are performed comprehensively, and their results demonstrate that the proposed algorithm could directly extract the envelope waveforms from noisy measurements, but also outperforms the state-of-the-art blind deconvolution methods for latent periodic feature recognition.