## 1 Introduction  
Bearings are important components of many mechanical systems, including aircraft, vehicles, and CNC machines [1]. Due to the crucial role of these components, detecting and diagnosing any defects is an ongoing challenge [2] which has prompted researchers to look for solutions. The innovation of neural networks (NNs) has provided researchers with new solutions that primarily rely on deep learning [3, 4, 5]. In this case, fault diagnosis can be viewed as a pattern recognition problem where the pattern is related to the conditions of the bearings. The traditional method for defect classification can be divided into two main stages: a signal processing stage for identifying appropriate features, and a feature classification stage. The first stage, which involves feature extraction, depends on processing vibration-based signals either in the time domain, frequency domain, or sometimes in the time-frequency domain. To understand the spectral formation of a signal, frequency-domain techniques are typically used. One of the most commonly used tools in this domain is the Fast Fourier Transform (FFT) [6]. Processing a signal in the time domain provides statistical features of the signal, such as zero crossing rate and signal frame power [7]. In most cases, operating conditions change over time, and the signal becomes non-stationary. Commonly used techniques in the time-frequency domain include the wavelet transform [8] and the Short-Time Fourier Transform (STFT) [9]. Recently, the Empirical Mode Decomposition (EMD) time-frequency signal analysis method has become widely used [10]. EMD can adaptively decompose a complex signal into several intrinsic mode function components, but it has the disadvantage of mode mixing when dealing with noisy non-stationary signals, which affects the efficiency of time-frequency analysis. To address this issue, the Ensemble EMD method was proposed [11], but it requires large computational resources [12]. Another method, Variational Mode Decomposition (VMD), uses adaptive Wiener filters, but the decomposition parameters of VMD significantly influence the decomposition results [13]. At the classification stage, machine learning algorithms are employed to use the resultant features from the processed signals as input and group them into clusters. In machine learning, there is a wide range of classifiers such as Support Vector Machines, Re-current Neural Networks (RNNs), and Convolution Neural Networks (CNNs) [14; 15; 16]. [PERSON] [17] employed a deep normalized CNN for the imbalanced fault classification of machinery and analyzed its mechanism. [PERSON] [18] introduced VMD and deep CNN to classify the faults of rolling bearings in wind turbines. [PERSON] [19] proposed a fault diagnosis framework for rolling bearings using an RNN and Auto-Encoder. The performance of these algorithms often has some limitations and high computational costs [20]. Deep learning-based methods have disadvantages mainly related to the need for a large number of labeled samples [21]. The performance of such methods is sensitive to an unbalanced dataset, where there is a larger amount of data collected related to healthy conditions. In addition, deep learning models are typically slow and require a significant amount of processing power and memory, making them very time- and re-source-intensive. In general, the trend in bearing failure diagnostics is towards more complex, deeper machine learning models. In actual working conditions, however, the amount of labeled fault data available is relatively small, so a deep learning model with good generalization and high accuracy is difficult to train. Some researchers are considering the need for alternative, simpler, and more application-oriented methods [22; 23; 24]. Linear predictive coding (LPC) is a speech coding algorithm [25] and is widely used in speech processing [26].