## 1 Introduction
Vibration signals are classified as contact measurements. This may present challenges if the bearing seat material is non-ferromagnetic and cannot be magnetically attached to the unit using a buckle. Moreover, excessive unit vibration may lead to sensor detachment, resulting in unnecessary complications during signal acquisition. Consequently, non-contact measurement methods are gradually being employed in bearing fault diagnosis, with increasing emphasis placed on experts and scholars within the field of fault diagnosis utilizing acoustic radiation signals as a non-contact measurement method [18; 19; 20]. For acoustic fault diagnosis, [PERSON] et al. [21] successfully achieved weak fault detection of rolling bearings by extracting comprehensive status information from acoustic signals, thereby providing a novel approach for bearing condition monitoring. [PERSON] et al. [22] proposed a frequency component shortening method to classify the feature components of acoustic power tool fault diagnosis. [PERSON] et al. [23] utilized microphone-collected acoustic signals and employed small beamforming enhancement technology for rolling bearing fault diagnosis, ultimately diagnosing train bearing faults. However, due to significant background noise interference in the acoustic radiation signal, effectively filtering the collected signal becomes crucial. In the case of complex mechanical equipment operation, the collected signal contains substantial interference information and exhibits strong non-stationarity. Directly inputting the original collected signal into a neural network would reduce classification accuracy; hence, it is imperative to filter and denoise the acquired sound signal. Mathematical morphology has been extensively applied in mechanical vibration signal processing, serving as an effective nonlinear and time-varying method for extracting fault characteristic information by directly operating on time domain signals. The mathematical morphology theory has been extensively investigated by scholars. [PERSON] et al. [24] employed grey correlation analysis (GCA) to determine the optimal scale of multi-scale mathematical morphology's structural element, successfully achieving fault feature extraction for rolling bearings. [PERSON] et al. [25] proposed a novel research approach for planetary gearbox fault diagnosis that combines adaptive multi-scale morphological filtering with improved hierarchical arrangement entropy. Numerical and experimental results demonstrate the capability of this method to identify various types of faults in planetary gearboxes. [PERSON] et al. [26] introduced a sparse envelope spectrum evaluation index factor called IESS to select the optimal scale for the AVG-Hat operator's structural element, aiming at identifying different bearing faults effectively. [PERSON] et al. [27] presented a fault diagnosis research methodology based on multi-scale morphology to accurately distinguish between various types of bearing faults. [PERSON] et al. [28] put forward an average combined differential morphological filtering operator named ACDIF and a new index evaluation factor TEK to determine the optimal scale for selecting structural elements, effectively suppressing noise, and extracting shock pulses from vibration signals according to experimental results. In summary, most scholars have concentrated on developing mathematical morphological operators and selecting appropriate structural elements for scaling purposes. Currently, there is a dearth of literature regarding the implementation of mathematical morphological filters in deep learning networks as well as fault diagnosis of acoustic signals. Therefore, this paper aims to address the challenge of constructing an end-to-end learning network that can effectively extract features from pulse signals. The above research serves as the foundation for proposing a novel mathematical morphological network aimed at extracting shock features from acoustic array signals.