## 1 Introduction
[PERSON] used PCA to reduce the data dimension from six to three, reducing the complexity of the back-end algorithm [17]. Using digital signal processing, feature extraction transforms the original time domain into a frequency domain or time-frequency domain signals, while fast Fourier transform (FFT) and wavelet transform (WT) [18; 19; 20; 21; 22; 23; 24] have been verified as effective methods. However, FFT is only suitable for stationary signals, and cannot be effectively analyzed for non-stationary signals caused by different time domains. Continuous wavelet transform (CWT) improves the disadvantage of a set FFT sliding window regardless of frequency; it can simultaneously extract the features of time domain and frequency, and the result is output as image data, which is very suitable as the input feature of CNN. [PERSON] et al. used Morlet wavelet CWT to capture the spectrogram as the input of the CNN illustrating the effectiveness of the time-frequency map as a feature [25]. According to [PERSON] et al., the effective features of hydraulic axial piston pumps are extracted by CWT, and an improved CNN performs fault classification [26]. Traditional machine learning requires expertise, experience, and more manpower to extract features, while in recent years, deep learning has been proven to have feature learning capabilities. It can learn useful features from the hierarchical neural network architecture and achieve feature fusion to improve model accuracy. CNN is an effective method for deep learning image processing and classification and has been successfully used in mechanical fault diagnosis [27; 28] and the filter kernel of the CNN convolution layer, with effective information and patterns to extract input features. The pooling layer reduces the size of the feature map to reduce the training parameters and reduce the phenomenon of overfitting. Research by [PERSON] et al. has shown that utilizing a multi-head 1D CNN to diagnose motor faults is very accurate for multi-sensor detection of vibration time series [29]. Combining infrared thermal images and vibration signals, FDACNN is used to achieve gearbox fault diagnosis in various environments, and the features extracted by the model are mapped to two-dimensional space using PCA, proving that extracted features derived from visualization can be separated [30]. Mechanical equipment production is often very loud due to its harsh environment, varied working conditions, and multiple motors of varying sizes moving at different speeds. If these noises superimpose the original data of the sensor, the accuracy of the model will be reduced. Therefore, the de-noising process under various production conditions is crucial for feature extraction. The adaptive method [31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41] can strengthen the system's robustness in actual production, and improve the utilization rate and yield of the process equipment. Adaptive methods can be implemented differently depending on the nature of the target object being predicted. The adaptive moment estimation (Adam) improves the inefficiency of traditional fixed learning rate methods and the problem of finding the global minimum effectively. It enhances the performance of sparse gradients by dynamically adjusting the learning rate. Additionally, it uses exponential moving averages to maintain the average magnitude of weight gradients, thereby adaptively reducing the impact of noise in non-stationary signal classification models. The adaptive gradient optimizer is implemented by adjusting the learning rate. It allows for smaller updates with a lower learning rate for parameters associated with frequently occurring features, and larger updates with a higher learning rate for parameters associated with infrequently occurring features. This approach improves the self-extraction effectiveness of model features and reduces model errors caused by manual feature extraction. VMD (variational mode decomposition) is an adaptive, non-recursive method for mode decomposition and signal processing.