The bleed air system of aircraft engines is a critical system to ensure flight safety, and fault detection is essential for maintaining it. This study addressed the fault detection problem of the bleed air system by first using the modified density-adaptive synthetic oversampling algorithm (MDADASYN) to handle the imbalanced fault data. Then, a multi-strategy improved energy valley optimization algorithm (IEVO), enhanced with good point set population initialization, Gaussian-Cauchy mutation strategy, and dynamic parameter adjustment, was applied to optimize the general regression neural network (GRNN) for fault diagnosis. Results from CEC2014 test functions demonstrated that the proposed strategy effectively improved population diversity as well as global and local search capabilities. Simulation experiments based on real fault data from the bleed air system verified that the MDADASYN-IEVO-GRNN fault diagnosis model significantly enhanced diagnostic accuracy for bleed air system faults in aircraft engines, contributing to improved operational safety and maintenance efficiency.