A Lightweight Cognitive Digital Twin for Fault-Aware Control of Cyber–Physical Systems: Stochastic Modeling, Anomaly Detection, and Experimental Validation

Abstract

This paper presents a lightweight Cognitive Digital Twin (CDT) framework for fault-aware monitoring and control of industrial Cyber-Physical Systems (CPS). The framework integrates: (i) a stochastic fault progression model using coupled differential equations with physically interpretable parameters, (ii) a computationally efficient anomaly detection method based on information-geometric divergence measures with provable false alarm bounds, and (iii) a fault-aware optimal control strategy with input-to-state practical stability guarantees. Complete proofs are provided for all theoretical results. Validation is conducted through two complementary approaches: Monte Carlo simulation using a turbine-inspired CPS simulator (20 trials per scenario across four fault types), and a synthetic vibration benchmark modelled on the Case Western Reserve University bearing fault paradigm. Comparisons against Extended Kalman Filter-based fault detection, robust Model Predictive Control, Proportional-Integral, and reactive baseline controllers demonstrate that the CDT achieves 85–98% true positive detection rate with detection lead times of 46–542 steps (0.5–5.4 s). Under bearing fault conditions, the CDT maintains a stability index of 0.902 compared to 0.516 for the reactive baseline, a 75% improvement. The framework maintains robustness under Student-$t$ and Gaussian mixture noise distributions, detects faults across a fourfold range of progression severities with 100% success rate, and degrades gracefully under progressive sensor loss. Computational cost remains below 0.1 ms per control cycle on standard hardware.