Failure detection is essential to ensure that distributed parameter processes, such as thermodynamics and fluid dynamics, can operate safely and efficiently. Therefore, this study explores an iterative learning failure g observer for nonlinear polarised distribution parameter systems (DPSs) and proposes an output-based feedback-accelerated iteration learning error estimation strategy. In the end, using the λ norm, the L 2 norm method and the mathematical induction method, we have the convergence conditions. According to the simulation results, we can see that this method is feasible, because after about ten iterations, accurate error estimates can be obtained.