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The feature extraction and state recognition of vibration signals of hydroelectric generating units are of great significance for effectively ensuring the safety and lifespan of unit operation. This paper introduces a novel fault diagnosis approach that leverages a wavelet threshold algorithm for initial signal preprocessing and enhances the Radial Basis Function (RBF) neural network with an optimized Gravitational Search Algorithm (GSA). Initially, the Wavelet Transform (WT) algorithm is employed to denoise the raw signal, which is subsequently decomposed using Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). Intrinsic Mode Function (IMF) components are then selected based on their correlation coefficients for sample entropy calculation. A GSA-optimized RBF neural network is constructed to diagnose faults in hydroelectric units. To further enhance the model’s convergence speed and accuracy, Lévy flight and chaotic sequence optimizations are integrated into the GSA, resulting in the development of the LCGSA-RBF diagnosis model. Experimental results demonstrate that this method achieves a 100% accuracy rate, outperforming other comparative models. Specifically, this approach enhances accuracy by 12.5% over the CEEMDAN-RBF method, showing the highest alignment with actual fault diagnosis results. This research significantly contributes to the advancement of safe and reliable operations in hydroelectric generating units.