### Related Work  
Denoising Autoencoders (DAEs) have been widely utilized for removing noise from various types of data, such as images and time series. However, most existing studies adopt the approach of training DAE models using added Gaussian noise, which poses a limitation in sufficiently capturing the complex noise patterns that arise in real-world industrial environments. For example, [PERSON] et al. employed an autoencoder to remove noise from induction motor sounds by adding Gaussian noise during training. However, their model was limited in its ability to fully reflect the complex noise characteristics present in industrial settings [1]. [PERSON] et al. applied a vanilla autoencoder to eliminate Gaussian noise from RGB and grayscale images, using added Gaussian noise for training. However, their study focused solely on image data, and thus was limited in addressing the characteristics of time series data [2]. [PERSON] et al. proposed a co-taught Denoising Autoencoder for time series denoising, which was trained only on noisy data. This approach, however, also failed to capture real-world noise patterns comprehensively [3]. [PERSON] et al. introduced Denoising-Aware Contrastive Learning for noisy time series data, but the method requires prior knowledge of specific noise types and has limitations in generalizing to a variety of noise patterns [4]. [PERSON] et al. suggested a method using autoencoders to remove Gaussian and salt-and-pepper noise from images. However, their work was restricted to image data and cannot be directly applied to time series analysis [5]. [PERSON] and [PERSON] proposed an adaptive Denoising Autoencoder scheme for indoor localization based on RSSI analysis in BLE environments. Although effective in its domain, the method is limited in its applicability to general time series noise removal [6]. [PERSON] et al. trained a Denoising Autoencoder on simulation-derived structures to reduce noise in chromatin scanning transmission electron microscopy images. This approach, however, is domain-specific and not suitable for time series data [7]. [PERSON] et al. proposed a denoising method for machine tool vibration signals based on Variational Mode Decomposition and the Whale-Tabu optimization algorithm. However, the method relies on traditional signal processing and lacks integration with deep learning approaches [8]. [PERSON] et al. also trained a Denoising Autoencoder on simulation-derived data to reduce noise in electron microscopy images. Similarly to previous studies, their method is limited to a specific application domain and is not readily extendable to time series denoising [7]. [PERSON] et al. proposed a deep recurrent Denoising Autoencoder to remove noise in gravitational wave signals. However, the method is specialized for gravitational wave data and is not broadly applicable to general time series noise removal [9]. [PERSON] et al. applied a denoising autoencoder (DAE) to suppress environmental noise in acoustic signals collected from induction motors [10]. In addition to conventional Gaussian noise, the model was trained using actual environmental noise sources, such as running tap water sounds. The results demonstrated effective noise reduction across both types of noise. Similarly, [PERSON] et al. proposed an adaptive DAE model that accounts for distance-dependent noise characteristics in Bluetooth Low-Energy (BLE) Received Signal Strength Indicator (RSSI) data [11]. Instead of relying on Gaussian noise, the model incorporated realistic variations in the signal-to-noise ratio (SNR) as a function of distance. This approach yielded an approximately 10.2% improvement in classification accuracy compared to models trained with Gaussian noise. These previous studies commonly rely on the use of Gaussian noise for DAE training. However, noise in vibration time series data collected from actual industrial environments includes not only Gaussian components but also complex, multi-frequency patterns.