In response to the challenge posed by the difficulty in accurately extracting features from the multidimensional sound-vibration signals resulting from mechanical faults in Gas Insulated Switchgear (GIS) and the low accuracy of traditional fault diagnosis algorithms, this study proposes an innovative approach. It combines an improved Intrinsic Computing Expressive Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) algorithm and Hilbert-Huang envelope spectrum energy entropy for fault feature extraction, along with a CNN-LSTM diagnostic model for fault identification. Initially, the original audio-vibration signals are decomposed into intrinsic mode functions (IMFs). Then, the Hilbert-Huang envelope spectrum energy entropy is employed to calculate the feature vectors of each IMF, which are subsequently fed into the CNN-LSTM deep learning model for diagnostic identification. Experimental results demonstrate that the proposed method achieves an average fault identification accuracy of 97.78%, affirming its effectiveness in the field of GIS mechanical fault diagnosis.