A robust model selection framework for fault detection and system health monitoring with limited failure examples: Heterogeneous data fusion and formal sensitivity bounds

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Fault detection models play a fundamental role in monitoring the health state of engineering systems subject to degradation processes. Data-driven fault detection models, albeit very effective when trained on large databases of failures, fail to perform well under a lack of failure examples. Because reliable engineering systems seldom fail, data shortage is often inevitable. To overcomes failure data scarcity, this work proposes a new model selection framework for the robust selection of fault detection and system health monitoring models. We combine heterogeneous sources of information (time-to-failure and sensors data), a model of the system structure, and mathematical bounds on the sensitivity and specificity of components fault classifiers. We use Support Vector Machines (SVMs) to detect components faults and Scenario theory to derive formal sensitivity and specificity bounds. The component predictions are combined within a system structure-function for system health states estimation. A novel model selection strategy optimizes the hyper-parameters of the SVM ensemble by minimizing system-level prediction errors and generalization error bounds of the individual fault classifiers. One of the main advantages of the proposed framework is a set of formal epistemic bounds on fault detection and false alarm probabilities quantifying the lack of data uncertainty affecting the fault detection rate. We test the method on three representative case studies: (1) On randomized fault detection experiments with synthetic data, (2) on ten SVM models for predictive maintenance of industrial health care imaging systems, and (3) on a real-world PHM challenge problem. The results prove the efficacy of the proposed approach and its usefulness for solving fault detection.