The continuous monitoring of the interactions between cyber-physical components of any industrial control system (ICS) is required to secure automation of the system controls, and to guarantee plant processes are fail-safe and remain in an acceptably safe state. Safety is achieved by managing actuation (where electric signals are used to trigger physical movement), dependent on corresponding sensor readings; used as ground truth in decision making. Timely detection of anomalies (attacks, faults and unascertained states) in ICSs is crucial for the safe running of a plant, the safety of its personnel, and for the safe provision of any services provided. We propose an anomaly detection method that involves accurate linearization of the non-linear forms arising from sensor-actuator(s) relationships, primarily because solving linear models is easier and well understood. We accomplish this by using a well-known water treatment testbed as a use case. Our experiments show millisecond time response to detect anomalies, all of which are explainable and traceable; this simultaneous coupling of detection speed and explainability has not been achieved by other state of the art Artificial Intelligence (AI)/ Machine Learning (ML) models with eXplainable AI (XAI) used for the same purpose. Our methods explainability enables us to pin-point the sensor(s) and the actuation state(s) for which the anomaly was detected. The proposed algorithm showed an accuracy of 97.72% by flagging deviations within safe operation limits as non-anomalous; indicative that slower detectors with highest detection resolution is unnecessary, for systems whose safety boundaries provide leeway within safety limits.

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