Dynamic Penalty Adaptive Matrix Machine for the Intelligent Detection of Unbalanced Faults in Roller Bearing

The correlation between the rows and columns of the matrix can reasonably express the feature information extracted from the vibration signals, and support matrix machine (SMM) can effectively learn those feature information and perform well in machinery fault diagnosis. Nonetheless, SMM has limited performance in imbalanced cases, and its nuclear norm minimization framework will lead to some weak correlation information in the extracted low-rank result. Given those problems, a novel classification method is proposed, called dynamic penalty adaptive matrix machine (DPAMM). Firstly, DPAMM is established based on the adaptive low-rank approximation minimization framework, in which an adaptive low-rank operator is introduced to capture the low-rank information. Specifically, the adaptive low-rank operator can adaptively select the larger singular values related to the strong correlation low-rank information. Furthermore, a dynamic penalty factor is designed into the loss penalty part, and can dynamically adjust the punishment degree to between-class samples according to the unbalance rate. Finally, the resulting objective function is solved by introducing an alternating direction multiplier method (ADMM). Experimental results on three datasets show that DPAMM has excellent fault diagnosis performance, especially in the case of imbalanced samples.