This paper proposes an approach to detect and diagnose mechanical failures in transformer windings and iron cores. It combines adaptive noise complete set empirical mode decomposition (CEEMDAN) with a deep belief network (DBN). The vibration signal on the transformer tank surface is decomposed using CEEMDAN, and fault features are extracted from the decomposed components. Energy entropy is calculated for each component, forming a specialized vector set. The DBN is then trained on this feature set to classify the transformer's operating state. Comparative experiments demonstrate that CEEMDAN outperforms EMD and EEMD in fault feature extraction, while DBN surpasses BP neural networks and support vector machines in classification. The proposed method accurately identifies normal transformer conditions, winding deformations, and core looseness, making it valuable for practical applications.