Bearing Fault Diagnosis Under Small Data Set Condition: A Bayesian Network Method With Transfer Learning for Parameter Estimation

Bearings are broadly applied in various types of industrial systems. Fault diagnosis, as a promising way for reliability of modern industrial internet of thing applications, has attracted increasing attention from both academia and industry fields. Being ideal modeling and inference tool in uncertainty situations, Bayesian network (BN) is becoming increasingly popular in many systems. However, in practical uncertain and complicated engineering surroundings, it's difficult or expensive to collect massive labeled fault data for the sake of fault diagnosis model learning. To address the issue of BN parameter learning under small data set conditions, this paper proposes a Varying Coefficient Transfer Learning (VCTL) algorithm based on aggregation and transfer learning, that considers both knowledge from the resource domain and the resource relevance contributions. The balancing weight function is designed to determine whether the learning task in the resource domain is activated. Relevance weight factors are proposed to measure the relevance of resource and target parameters quantitatively, by combing parameter information from resource domains with those obtained from the target domain, using maximum a posterior (MAP) or maximum likelihood estimation (MLE). Finally, the target parameters are aggregated with both the target initial parameters and the parameter knowledge from the resource domain. Based on VCTL, a bearing fault diagnosis approach is proposed and verified. The experimental results show that, under the condition of the small data set, learning accuracy of VCTL algorithm with varying coefficient aggregation is better than MLE algorithm, MAP algorithm or state-of-the-art parameter transfer method, local linear pooling transfer learning (LoLP) algorithm. Under the condition of sufficient data set, learning accuracy of VCTL algorithm approaches the classical MLE or MAP, and the correctness of the proposed algorithm is verified. Moreover, we illustrate the successful application to real-world bearing fault diagnosis case with VCTL, where we had access to expert-provided resource knowledge and real fault diagnosis data.