Due to the complexity and diversity of aviation hydraulic pipeline systems, there has been a lack of qualitative formulas or characteristic indicators to describe clamp failures within these systems. In this paper, based on the data-driven idea, an improved KPCA-based feature extraction method is proposed and combined with the optimized KELM for fault diagnosis and condition monitoring of aviation hydraulic line clamps. Firstly, the kernel parameters of KPCA are combined using polynomial and Gaussian kernels based on their proportional weights. Secondly, a GA–PSO (Genetic Algorithm–Particle Swarm Optimization) hybrid algorithm is employed to optimize the kernel parameters, selecting 13 time-domain and 4 frequency-domain feature indicators to form the initial feature dataset, which is then subjected to dimensionality reduction using the improved KPCA. Finally, diagnosis is conducted using a KELM optimized by the whale optimization algorithm. The results indicate that, across multiple diagnostic trials, the average diagnostic accuracy can reach 99.99%, providing a feasible approach for the precise diagnosis of clamp faults in aviation hydraulic pipeline systems.