Quasi-online failure times identification of mobile heat sources in 2D geometry

Identifying the failure instants in thermal systems subject to 2D parabolic partial differential equations presents a significant challenge, especially when the systems involve mobile heat sources. In the context of this study, mobile heat sources are examined, along with a set of stationary sensors, while assuming known and constant-velocity trajectories for the heat sources. This research introduces a quasi-online methodology that incorporates Exponentially Weighted Moving Average (EWMA) charts for immediate failure detection. When a failure is detected via the EWMA charts, the Conjugate Gradient Method, traditionally developed for offline applications, is activated. This method is adapted to a quasi-online framework, facilitating a more rapid and precise identification of malfunctioning heat sources, the exact time of their failures, and the possibility of restoring normal operations. To assess the performance and reliability of this approach, it is compared with a Bayesian filter-based method, particularly using the Kalman filter for this purpose. Monte Carlo simulations are employed to evaluate the resilience and effectiveness of the quasi-online method, focusing on the system’s sensitivity to the accuracy of sensor measurements.