Utilizing Bayesian generalization network for reliable fault diagnosis of machinery with limited data

To address the issues of overfitting, domain generalization challenges, and lack of credibility brought by limited data samples in mechanical fault diagnosis in practical engineering, this paper proposes a reliable Bayesian generalization network (BGNet). A Bayesian convolutional layer is constructed based on variational inference, treating all parameters in the convolutional layer as random variables. This approach makes a single model function similar to an ensemble of an infinite number of models, and thus enhancing the model's capability of overfitting resistance and domain generalization. The parameters of the variational distribution are updated to approximate the posterior distribution by local reparametrization and Monte Carlo sampling to optimize the evidence lower bound (ELBO) loss. Confidence information is extracted from the model results and, uncertainty estimation and decomposition schemes are designed to provide interpretability. The proposed method is applied to analyze the experimental data of bearing and gearbox faults. The results show that in a multi-source domain scenario with limited samples, the proposed method demonstrates high diagnostic accuracy, effectively describes the relationship between domain variability and uncertainty, and significantly outperforms several benchmark and state-of-the-art models.