Sparsity-Constrained Invariant Risk Minimization for Domain Generalization With Application to Machinery Fault Diagnosis Modeling

Machine learning has been widely applied to study AI-informed machinery fault diagnosis. This work proposes a sparsity-constrained invariant risk minimization (SCIRM) framework, which develops machine-learning models with better generalization capacities for environmental disturbances in machinery fault diagnosis. The SCIRM is built by innovating the optimization formulation of the recently proposed invariant risk minimization (IRM) and its variants through the integration of sparsity constraints. We prove that if a sparsity measure is differentiable, scale invariant, and semistrictly quasi-convex, the SCIRM can be guaranteed to solve the domain generalization problem based on a few predefined problem settings. We mathematically derive a family of such sparsity measures. A practical process of implementing the SCIRM for machinery fault diagnosis tasks is offered. We first verify our theoretical exploration of the SCIRM by using simulation data. We further compare SCIRM with a set of state-of-the-art methods by using real machinery fault data collected under a variety of working conditions. The computational results confirm that the machinery fault diagnosis model developed by the SCIRM offers a higher generalization capacity and performs better than the other benchmarks across the different testing datasets.