Fault Detectability Conditions for Linear Deterministic Heat Equations

With the rise of distributed and connected modern engineering systems, the need for safe and reliable distributed parameter systems is becoming increasingly prominent. However, fault detection of partial differential equation systems remains relatively unexplored compared to its ordinary differential equation counterpart. In this letter, we attempt to advance such research by addressing the fault detectability problem for linear deterministic heat equations with additive faults. Fault detectability examines whether a fault is detectable given a system model and measured outputs. Essentially, similar to controllability and observability, fault detectability is an intrinsic property of the system and has to be verified before designing diagnostic algorithms. In this context, we derive fault detectability conditions for heat equations by utilizing the singular values of fault-to-output transfer function. We illustrate the proposed detectability conditions on battery thermal fault diagnosis case study.