Fault diagnosis of a class of distributed parameter systems modeled by parabolic partial differential equations

In this paper, a partial differential equation (PDE) representation of a system is directly utilized to construct a fault diagnosis observer for distributed parameter systems (DPS) in contrast with the traditional fault detection observers which are based on the approximated ordinary differential equation (ODE) representation of the system. A fault is detected by comparing the detection residual, which is the difference between measured and estimated outputs, with a predefined detection threshold. Once the fault is detected, an online approximator is activated to learn the fault function. The stability of the observer along with the online approximator is discussed analytically in the paper. Upon detecting a fault, the estimated fault parameters are compared with their failure thresholds to provide an estimate time to failure (TTF) of the system. The scheme is verified in simulations on a Lithium-ion battery which is described by parabolic PDEs.