Fault Detection for a One-Dimensional Wave PDE System

In this paper, we design a fault diagnosis scheme for class of variable coefficient wave equation (an overhead crane system), which is composed an observer and its output error treated as residual signal. When the system in healthy state, signal decays exponentially. Due to existence external disturbance, not zero state without fault. Therefore, further reasonable threshold based on upper bound dynamics disturbance reduce influence determine whether occurs. The convergence properties partial differential (PDE) are analyzed by Lyapunov stability theory. Finally, effectiveness illustrated simulation can judge fails scheme.