# Fault Diagnosis of Rolling Bearings Based on Acoustic Signals in Strong Noise Environments
## 1 Introduction
This method employs the kurtosis value as a metric, selecting the intrinsic mode function (IMF) with the highest kurtosis for analysis. [PERSON] [17] also introduced a rolling bearing acoustic signal fault diagnosis method based on adaptive variational mode decomposition (AVMD) to enhance accuracy in noisy environments. Furthermore, [PERSON] [18] proposed a novel method based on frequency band entropy (FBE) for selecting sensitive intrinsic mode functions (IMFs) that contain variational mode decompositions (VMDs) rich in fault information. Subsequently, envelope power spectrum analysis is conducted on the selected IMFs to extract the fault characteristic frequencies of rolling bearings. [PERSON] [19] proposed Feature Mode Decomposition (FMD), a novel adaptive decomposition method specifically designed for mechanical fault feature extraction. FMD updates the adaptive finite impulse response (FIR) filter bank using correlation kurtosis (CK), thereby overcoming the limitations of the variational mode decomposition (VMD) and Empirical Wavelet Transform (EWT) algorithms regarding filter shape and bandwidth. This enhancement allows for the extraction of more fault information, making FMD more advantageous than VMD in mechanical signal decomposition analysis, particularly in scenarios where prior knowledge of the failure cycle is lacking. [PERSON] [20] introduced a fault feature extraction method that integrates an improved whale optimization algorithm (WOA) to optimize FMD. This approach refines the FMD parameter settings, employs information entropy as the fitness function, and selects the optimal intrinsic mode function (IMF) through kurtosis for fault feature extraction. [PERSON] [21] developed a bearing fault detection method based on adaptive feature mode decomposition (Adaptive FMD) and the health index (HI). [PERSON] [22] proposed a fault diagnosis method based on adaptive multivariate eigenmode decomposition (AMFMD). The method addresses the challenge of fault information in mechanical equipment being easily obscured by significant noise, and it overcomes the limitation of potentially missing valuable features when relying solely on data from a single sensor. [PERSON] [23] designed the signal period kurtosis-to-noise ratio (SCKNR) as the objective function for the adaptive parameter search of FMD. He selected the primary mode component based on the characteristic energy rate and computed its square envelope spectrum for fault identification. However, he did not consider the influence of the frequency band cutting number \(K\) on the decomposition results. [PERSON] [24] proposed an adaptive feature mode decomposition (AFMD) method for analyzing noisy bearing vibration signals. The method optimizes parameters using a cuckoo search algorithm and employs the feature frequency ratio (FFR) to improve fault diagnosis accuracy and efficiency, particularly in the presence of strong noise levels (\(-15\) dB). Meanwhile, [PERSON] [25] introduced a novel method known as Graph Modeling Singular Values (GMSV), which successfully balances sensitivity to early faults with robustness against noise. This method employs a Gaussian distribution for fault detection. Nevertheless, in practical engineering scenarios, the dynamic characteristics of bearings may exhibit greater complexity, necessitating verification of the feasibility of this assumption. The effectiveness of FMD is highly sensitive to key parameters: mode number \(n\), filter length \(L\), frequency band division \(K\), and cycle period \(m\)[19]. A mode number \(n\) that is too small may miss critical fault information, while an overly large \(n\) can introduce noise and redundancy. Similarly, a short filter length \(L\) may cause inaccurate separation, whereas an excessively long \(L\) increases computational demands. A higher \(K\) enhances frequency resolution but also raises computational complexity. An insufficient iteration period \(m\) may hinder algorithm convergence, while an excessive period can lengthen calculation time.