<p>This paper investigates a fault diagnosis method for an interconnected flexible manipulator system with a random variation cycle. By analyzing the dynamic equations of the flexible manipulator and considering the nonlinear coupling characteristics of the system, this paper proposes a fault estimation method based on iterative learning control (ILC). The method introduces the mean value operator and the exponential variable gain acceleration control law, combines with the ILC algorithm, constrains the information change caused by the random variable cycle, solves the problem of missing information and information redundancy, and improves the robustness and rapidity of fault tracking. In order to reduce the false alarm rate, the method adopts a threshold-based fault detection mechanism, i.e., the distributed iterative learning observer is activated only when the system residual exceeds a set threshold. Through theoretical derivation and simulation validation, it is demonstrated that the proposed method is effective in estimating faults when there are periodic variations and perturbations during system operation. The method provides an effective fault diagnosis solution for complex manipulator systems.</p>