Distance-Aware Risk Minimization for Domain Generalization in Machine Fault Diagnosis

Industrial Internet of Things (IIoT) connects machines, and it is important to build intelligent models to prevent machine failures by identifying incipient faults. To develop intelligent fault diagnosis models, empirical risk minimization (ERM)-based modeling paradigm has been prevalently applied. However, during model training, ERM primarily focuses on instance-to-prototype (ItP) distances from a prototypical perspective, which may limit its effectiveness in analyzing data of diverse distributions. To improve the ERM model, we propose considering additional instance-to-instance distances (ItI) and prototype-to-prototype (PtP) distances, leading to a new modeling framework—distance-aware risk minimization (DARM). To gain awareness of extra types of distances, two novel losses are proposed based on reformulations of soft-max cross entropy. Theoretical explorations are conducted to justify the significance of collectively considering ItP, ItI, and PtP distances. Methodologically, DARM can jointly minimize three types of distance-aware losses to train neural networks for fault diagnosis in the same fashion as ERM. In a comprehensive computational study, DARM consistently outperformed ERM in domain generalization (DG) tasks based on various machine fault diagnosis data sets. In addition, DARM has superior performance over several recent DG methods. The code is available at
https://github.com/mozhenling/doge-darm
.