This paper comprises a description of a data-driven approach to the real-time monitoring of a physical system. Specifically, a hierarchical anomaly detection algorithm that can identify both instantaneous pointwise anomalies and gradual trajectory anomalies is proposed. To detect anomalies, we first construct a multi-output Gaussian process regression (MOGPR) model that can predict, probabilistically, the outputs of the target system. Using the constructed prediction model, we then propose statistical decisionmaking strategies to determine the abnormal operations of the target system by comparing its measured and the predicted responses. The proposed monitoring strategy does both point wise and trajectory anomaly detection in a single framework. The proposed strategy was applied to detecting abnormal operations of gas regulators. Validating with the actual gas-regulator data demonstrated that it could identify anomalies robustly and accurately.
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