A blind deconvolution algorithm based on backward automatic differentiation and its application to rolling bearing fault diagnosis

Abstract Blind deconvolution (BD) is an effective algorithm for enhancing the impulsive signature of rolling bearings. As a convex optimization problem, the existing BDs have poor optimization performance and cannot effectively enhance the impulsive signature excited by weak faults. Moreover, the existing BDs require manual derivation of the calculation process, which brings great inconvenience to the researcher’s personalized design of the maximization criterion. A new BD algorithm based on backward automatic differentiation is proposed, which is named backward automatic differentiation blind deconvolution (BADBD). The calculation process does not require manual derivation so a general solution of BDs based on different maximization criteria is realized. BADBD constructs multiple cascaded filters to filter the raw vibration signal, which makes up for the deficiency of single filter performance. The filter coefficients are determined by Adam algorithm, which improves the optimization performance of the proposed BADBD. BADBD is compared with classic BDs by synthesized and real vibration signals. The results reveal superior capability of BADBD to enhance the impulsive signature and the fault diagnosis performance is significantly better than the classic BDs.