Wavelet-Based Diffusion for Unsupervised Machine Anomaly Detection

Unsupervised anomaly detection (UAD) based on deep learning plays a vital role in predictive maintenance and health monitoring (PHM) of major equipment. However, the black-box nature of the models hinders the deployment in real-world. Wavelet packet transform (WPT) is a well-established and highly interpretable method for analyzing vibration signals in PHM. However, applying it directly to reconstruction-based UAD is challenging. Because of the perfect reconstruction property of the inverse wavelet transform, it almost flawlessly reconstructs both normal and abnormal signals, failing to generate the reconstruction residuals necessary to identify anomalies. To address this, we integrate WPT with diffusion models (DMs), which have demonstrated a promising ability to detect anomalies by learning the manifold of normal data. In this paper, we propose a wavelet diffusion-based method for detecting anomalies in vibration signals. It can be regarded as a data-driven wavelet packet transform, which tries to eliminate failure information in the monitoring signals and consequently detects abnormal health states. Specifically, a learnable wavelet packet transform (LWPT) is firstly utilized to project the raw vibration signals into sub-frequency bands. Then the DM is applied on the first two sub-bands to get the reconstruction sub-bands. The DM enables effective reconstruction of normal signals while exposing deviations indicative of anomalies. At last, the reconstructed signal is built via inverse LWPT using the reconstructed sub-bands and the remaining sub-bands. We evaluate the effectiveness of our approach on a helicopter main gearbox (MGB) dataset. Experimental results demonstrate that the proposed method not only achieves state-of-the-art performance but also provides interpretable insights for users.