## 1 Introduction
### Related Literature  
AE refers to the release of elastic energy from materials undergoing deformation or fracture, detected by AE sensors as acoustic emission hits (AEHs). The presence of faults in a milling machine changes the distribution of the AE signals. Researchers are concentrating on extracting fault-related information from AE signals across the temporal domain (TD), spectral frequency domain (SD), and multiresolution time-frequency domain (TFD) [11]. Once fault indicators have been extracted, AI approaches are used to identify faults within milling machines. [PERSON] et al. [12] developed a framework for tool condition monitoring utilizing a temporal domain indicator, i.e., RMS, extracted from a fault-specific frequency band, and classified using a decision tree. [PERSON] et al. [13] employed AE Poincare plots with a random forest classifier to detect broken teeth, pitting, scuffing, and crack defects in gears. [PERSON] et al. [14] implemented long short-term Memory (LSTM) and support vector data description (SVDD) to detect wear states on one-dimensional TD signals. The frequency spectrum of the AE signal is changed by the faults in the mechanical components of milling machines, which makes spectral domain analysis a viable approach for identifying health conditions. [PERSON]. [15] introduced a lightweight deep-learning model for diagnosing faults in CNC electromechanical systems, which outperformed conventional neural network classification algorithms in terms of model classification accuracy when trained on TD and SD statistical indicators such as mean, mean frequency, variance, RMS, and RMS frequency, since the AE signals from milling machines are non-stationary [16]. To overcome these limitations, it is necessary to use modern TFD techniques to extract significant fault-related information. These techniques include wavelet transform (WT) [17], variational mode decomposition (VMD) [18], and empirical mode decomposition (EMD) [19]. [PERSON] et al. [20] used statistical indicators from signals decomposed by optimal WT including mean, max, min, standard deviation, kurtosis, skewness, and Shannon entropy to diagnose faults in the machining center. Their study identified coif8 and db14 fifty mother wavelets at decomposition level 3 as the most effective for the ongoing health conditions of the machining center. [PERSON] et al. [21] proposeda lightweight model for identifying faults in the tools and spindles using discrete WT and lightweight CNN. [PERSON] et al. [22] introduced a tool fault diagnosis framework using marine predator-optimized random forest trained on features extracted from machining center signals decomposed by EMD. Despite the high performance demonstrated for the diagnosis of faults in essential milling machine components such as bearings, gears, and tools, the literature has several limitations and challenges. The sensitivity of TD statistical indicators is compromised by interference noise in AE signals, making them less effective for diagnosing the health of machining centers. While SD analysis is suitable for stationary signals, the complexity and non-stationary nature of AE signals from milling machines limit the effectiveness of SD indicators for fault detection and identification. TFD techniques, though powerful, are computationally intensive when processing AE signals [23]; this means that EMD, though self-adaptive, suffers from issues like extreme interpolation and mode mixing. Faults in the mechanical components of milling machines result in changes in stiffness, which release elastic energy that is detected by AE sensors as acoustic emission hits (AEHs) [19; 20]. AEH features, such as hit peak, hit counts, rise time, decay time, and hit average frequency, are independent of the overall AE signal distribution. These features provide direct and valuable information about AE events caused by defects. They outperform traditional TD, SD, and TFD indicators in various applications, including railways [24], structural damage monitoring [25], pipelines [26], and rotating machinery [27].