Robust fault detection of a class of uncertain linear parabolic PDEs

Robustness to uncertainties is one of the main challenges in model-based fault diagnosis. Robust fault diagnosis is a mature research area for Ordinary Differential Equation (ODE) systems. However, robust diagnostics for systems modeledby Partial Differential Equations (PDEs) is significantly under-explored in existing literature. Spatio-temporal evolution of faults make PDE fault diagnosis more challenging, as compared to its ODE counterpart where the fault evolves only temporally. Furthermore, robustness to uncertainties, that is, distinguishing the effect of uncertainties from faults is another key design challenge in fault diagnosis. This paper presents a robust fault diagnosis scheme for a class of uncertain linear parabolic PDEs. The proposed scheme consists of two subsystems: (i) Residual Generator and, (ii) Adaptive Threshold Generator. The Residual Generatoris a PDE observer whose output error is treated as a residual signal. Ideally, the residual signal should be zero if there is no fault and non-zero otherwise. However, the residual signal is non-zero even under non-faulty conditions, due to the presence of uncertainties. To achieve robustness against such uncertainties, we design a novel Adaptive Threshold Generatorthat generates an adaptive threshold. Finally, we illustrate the proposed scheme via simulation case studies on battery thermal fault detection.