# Fault Diagnosis of Rolling Bearings Based on Acoustic Signals in Strong Noise Environments
## 1 Introduction  
Mechanical failure poses a significant threat to the safe and reliable operation of large mechanical equipment, including wind power generation systems, aerospace engines, and high-end Computer Numerical Control (CNC) machine tools [1]. Rolling bearings are critical components for the effective functioning of rotating machinery [2], and their condition is crucial for the overall performance of the entire mechanical system. In the realm of fault diagnosis, signal decomposition technology is regarded as one of the most established and technically comprehensive methods. This technique can effectively suppress environmental noise and extraneous components in mechanical vibration signals, thereby facilitating the extraction of fault features [3, 4]. In contrast to vibration signals, sound signals offer advantages such as non-contact monitoring and convenient remote assessment, making them valuable in specialized environments [5]. By performing time-frequency domain analysis on bearing sound signals, various bearing fault types can be identified. The diagnostic features derived from acoustic signals demonstrate greater accuracy than those obtainedfrom vibration signals, allowing for a more effective differentiation between healthy and faulty conditions [6]. In practical measurements, the sound field is inherently complex and is frequently contaminated by noise signals produced by various sources, including reverberation, machinery, motors, rotating shafts, and human activity. This leads to a notably low signal-to-noise ratio for the acoustic fault signal [7; 8]. Consequently, traditional signal processing methods often struggle to effectively separate and extract acoustic fault signals. As a result, the acoustic signal diagnosis methodology has been progressing at a slower pace compared to the vibration signal analysis techniques [9]. In recent years, the empirical mode decomposition (EMD) method proposed by [PERSON] et al. [10] has emerged as an adaptive signal processing technique for decomposing non-stationary signals into multiple intrinsic mode functions (IMFs). This method has been successfully applied to fault feature extraction from bearing vibration signals. However, EMD is associated with several challenges, including modal aliasing, under-envelopment, over-envelopment, and boundary effects. To address these issues, ensemble empirical mode decomposition (EEMD) [11] has been proposed, which offers improved accuracy and efficiency compared to traditional EMD. Nonetheless, the integration process of EEMD can be time-consuming. To mitigate this limitation, the Complementary EEMD (CEEMD) [12] method has been introduced, which enhances decomposition efficiency by adding Gaussian white noise with opposite signs to the signal. CEEMD effectively alleviates modal aliasing and reconstruction errors. Nevertheless, not all IMFs contain useful information, making the selection of the most informative IMF a critical step. For instance, [PERSON] and [PERSON] employed CEEMD to decompose bearing vibration signals into multiple IMFs and determined the grouping and selection of valuable modes based on correlation coefficients [13; 14]. [PERSON] et al. [15] proposed variational mode decomposition (VMD) based on empirical mode decomposition (EMD), which is a signal processing method with variable scaling. Unlike traditional recursive algorithms, VMD exhibits strong robustness and is supported by rigorous mathematical theory. The mode number \(K\) and the penalty factor \(\alpha\) significantly influence the results. If \(K\) is set too high, it can result in over-decomposition (modal loss); conversely, if \(K\) is too low, it may lead to under-decomposition (modal aliasing). Additionally, improper configuration of the penalty factor can result in mode aliasing and loss, which adversely affects the extraction of important features. [PERSON] [16] proposed an adaptive VMD method utilizing a bat algorithm search (BAS) optimization technique for the early fault diagnosis of rolling bearings.