Manifold assistant multi-modal multi-objective differential evolution algorithm and its application in actual rolling bearing fault diagnosis

The fault diagnosis of rotating mechanical systems is crucial for ensuring the reliability of industrial equipment. In actual industrial scenarios, different combinations of fault features may yield the same diagnostic accuracy, but the difficulty and cost of obtaining different features generally vary. Therefore, in the feature extraction process, if multiple optimal feature combinations can be provided to decision-makers, it would be beneficial to select the feature subsets with lower computational cost or measurement difficulty that achieve the same fault diagnosis performance. Therefore, we model the fault feature selection task as a multi-modal multi-objective optimization problem (MMOP). To better solve MMOPs, a manifold assistant multi-modal multi-objective differential evolution (MA-MMODE) algorithm is proposed. It can establish a regularity model based on the distribution of the population to generate offspring and approximate the true Pareto set. Subsequently, this paper presents a preselection strategy that considers the distributions of both the decision space and objective space. The proposed preselection strategy can ensure that individuals with more promising solutions enter the mating pool to generate new offspring, thus exploring the search space more comprehensively. Using the CEC 2019 test set, the proposed MA-MMODE is compared with state-of-the-art algorithms, and the experimental results illustrate the effectiveness of the proposed algorithm. Moreover, based on two real rolling bearing testbeds, the proposed MA-MMODE is applied for feature selection in actual fault diagnosis. The experimental results show that the proposed MA-MMODE can provide multiple equivalent feature subsets to decision-makers while effectively improving the fault diagnosis accuracy for rolling bearings.