## 2 Related Work  
In recent years, audio analysis based mechanical anomaly detection become a research hotspot in the field of mechanical health diagnosis, primarily due to its high detection accuracy, strong generalization capability, non-intrusive measurement, and low cost. Traditional methods mainly achieve the goal of detection by analyzing the statistical features of audio signals and identifying abnormal characteristics. These methods typically rely on signal processing techniques. For instance, time-frequency filters combined with inverse short-time Fourier transform (ISTFT) [12] can be used to detect bearing damages through dynamic resampling techniques and envelope spectrum analysis. Although these traditional methods perform well in many cases, they often require expert knowledge [3] and have weak robustness. In real-world working environments, various random factors such as noises can interfere with audio signals, leading to a lower accuracy in anomaly diagnosis. Supervised learning-based methods require labeled data with known fault categories to guide the training of detection models, primarily used to determine whether the overall state of mechanical equipment is healthy and to identify the fault status of specific components, modules, or parts. Depending on the results of model, supervised learning-based methods can be further divided into binary classification and multi-class classification. Binary classification models learn audio features of labeled signal samples from healthy or abnormal equipment and combines with machine learning classification algorithms to assess the status of equipment. Some of the studies [13; 14; 15] extracted statistical features from audio signals, including mean, variance, entropy, and peak factor, and used them as inputs for a support vector machine (SVM) [16] classifier to identify the state of industrial equipment; this approach can achieve high accuracy on specific data. Currently, deep learning methods have gained significant attention due to their unique advantages. For instance, the methods proposed in [17; 18] extract the mel frequency cepstrum coefficient (MFCC) from audio clips and train a deep convolution neural network (CNN) model, reaching an accuracy over 90% in on-site experiments. On the other hand, multi-class classification model is typically used to identify various abnormal categories and different degrees of faults in the overall equipment or its individual components. For example, a biological population anomaly recognition system [19] based on the Internet of Things (IoT) and MFCC was proposed, in which the K-nearest neighbor (KNN) algorithm is used to perform multi-classification of biological sounds. It can accurately identify whether the organisms are infected by viruses or contaminated by pesticides, with a classification accuracy of 98.8%. Deep learning methods have also excelled in multi-class anomaly detection, such as the end-to-end CNN model constructed by [PERSON] et al. [20; 21], which accepts SPWVD-MFCC [20] as inputs and significantly improves classification accuracy in low signal-to-noise ratio (SNR) environments. Unsupervised learning-based methods do not require labeled data for model training and typically quantify the distance between input signals and normal audio signals, using thresholds to determine the \"normal or abnormal\" state of targets, making them suitable for practical application scenarios because collecting data can be difficult sometimes. A common approach involves the use of autoencoders and their variants, such as variational autoencoders (VAE) and sparse autoencoders, which learn feature representations by reconstructing normal audio signals and identify anomalies during the testing phase by calculating reconstruction errors [22]. The underlying assumption is that normal samplescan be well-reconstructed by the model, while anomalous samples, due to their different distribution, result in significantly higher reconstruction errors.