A Perturbation-Based Self-Training Method to Enhance Belief Rule Base Learning for Fault Diagnosis

The fault diagnosis of complex systems is essential for ensuring operational safety. The belief rule base (BRB), a rule-driven framework based on expert knowledge, is widely applied in fault diagnosis because of its ability to manage uncertainty. However, existing BRB models rely heavily on large amounts of high-quality labeled data, and their performance decreases when labels are scarce or noisy. To address this limitation, a perturbed self-training-based BRB method (PS-BRB) is proposed. In this approach, pseudo-labels for unlabeled samples are first inferred by an initial BRB, and Gaussian noise is introduced into the inputs to simulate perturbations. Samples that produce consistent predictions before and after perturbation are retained through class consistency checking. The Jensen–Shannon (JS) divergence then measures the difference between belief distributions, and high-quality pseudo-labels are selected according to the 90th percentile criterion. These pseudo-labels are incorporated into the training set to optimize BRB rules and parameters. The method is validated on two bearing datasets, and the results show improved diagnostic accuracy and applicability, which indicates potential for use in practical engineering scenarios.