Sparse Bayesian Learning Approach for Compound Bearing Fault Diagnosis

Abstract

Compound bearing fault diagnosis is an essentially challenging task due to the mutual interference among multiple fault components. The state-of-the-art methods usually take the potential fault characteristic frequencies as the prior knowledge and then try to recover every fault component by exploiting the impulse signal sparsity. However, they inevitably suffer from algorithmic degradation caused by energy leakage, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> -norm approximation, and/or improper parameter selection. To handle these shortcomings, in this paper, we propose a novel sparse Bayesian learning (SBL)-based method for the compound bearing fault diagnosis. We first present a new categorical probabilistic model to efficiently capture the truly-occurred fault components with a truncated feasible domain, which can greatly reduce the energy leakage effect. Then, we devise a more general SBL framework to recover the compound sparse impulse signal under the new categorical probabilistic model. The newly proposed method successfully avoids the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> -norm approximation and manual parameter selection, thus it can yield much higher accuracy and robustness. Both simulations and experiments demonstrate the superiority of the developed method.