Domain Adaptation Based Fault Detection in Label Imbalanced Cyberphysical Systems

In this paper we propose a data-driven fault detection framework for semi-supervised scenarios where labeled training data from the system under consideration (the “target”) is imbalanced (e.g. only relatively few labels are available from one of the classes), but data from a related system (the “source”) is readily available. An example of this situation is when a generic simulator is available, but needs to be tuned on a case-by-case basis to match the parameters of the actual system. The goal of this paper is to work with the statistical distribution of the data without necessitating system identification. Our main result shows that if the source and target domain are related by a linear transformation (a common assumption in domain adaptation), the problem of designing a classifier that minimizes a miss-classification loss over the joint source and target domains reduces to a convex optimization subject to a single (non-convex) equality constraint. This second-order equality constraint can be recast as a rank-1 optimization problem, where the rank constraint can be efficiently handled through a reweighted nuclear norm surrogate. These results are illustrated with a practical application: fault detection in additive manufacturing (industrial 3D printing). The proposed method is able to exploit simulation data (source domain) to substantially outperform classifiers tuned using only data from a single domain.