A computer-implemented method for enhancing reliability and trustworthiness in a cyber-physical system, the method comprising:
- collecting, using a plurality of sensors mounted on or proximate to equipment of the cyber-physical system, real-time data from an environment or system, the plurality of sensors including at least two sensor types selected from vibration sensors, thermal sensors, acoustic sensors, and environmental sensors;
- receiving, by a data processing unit comprising one or more processors and a memory, the collected real-time data from the plurality of sensors via a low-power wide-area network (LPWAN) using a binary message payload;
- analyzing, by the data processing unit, the collected real-time data using a probabilistic circuit model having input nodes, sum nodes, and product nodes to generate a generative model of the environment or system, the probabilistic circuit model outputting a probability value indicative of a joint probability distribution over the collected real-time data, wherein (i) input nodes implement node-specific functions of sensor data associated with respective sensor types, (ii) sum nodes compute weighted sums of functions of child nodes that correspond to same-type sensors, and (iii) product nodes compute products of functions of child nodes that correspond to different sensor types;
- sequentially inputting, by the data processing unit, the probability value, as a sole input feature or as part of a reduced set of probabilistic features derived from the generative model, into an adversarial random forest (ARF) model distinct from the probabilistic circuit model;
- determining, via the ARF model, an anomaly score for the probability value by evaluating the probability value against a plurality of decision trees trained using different subsets of the collected real-time data and computing an anomaly score based on a proportion of the decision trees that classify the probability value as an anomaly;
- cross-validating the detected anomalies by comparing the anomaly score from the ARF model with the probability value from the probabilistic circuit model to determine if the anomalies are confirmed by the generative model, where the cross-validating includes checking for agreement across the at least two sensor types using metrics including timestamp alignment within a predefined window, duration of the anomaly, and correlations between sensor data pairs;
- cross-validating the consistent anomaly by comparing, according to predefined rules, the consistent anomaly across different sensor types based on at least one of the timestamps, duration, and severity, to verify that the consistent anomaly reflects a genuine issue in physical operation of the cyber-physical system;
- generating, by the data processing unit and based on the cross-validated analysis, one or more recommendations for improving the system and a trust score indicating a level of reliability and trustworthiness of the cyber-physical system;
- transmitting, via a communication interface, the one or more recommendations and the trust score to a user interface;
- and
- displaying, on the user interface, the one or more recommendations and the trust score to an end-user.