## 2 Related Work  
### Vibration Defects in Rotating Machinery  
In mechanical installations, vibration defects typically refer to vibrations that occur when abnormal motion occurs in a machine part or structure. These vibration faults can reveal the reliability, performance, and lifespan of a machine. Therefore, it is important to detect and respond to them early. Vibration faults can be caused by a variety of reasons, including imbalanced parts, misalignment, wear, breakage, interference between machine parts, pressure changes in fluids, poor assembly, and damaged bearings [3; 17]. For example, bearing defects cause vibrations with high-frequency components, while gear defects can produce low-frequency vibrations [18]. Identifying these vibration faults typically involves measuring and analyzing the vibration of the machine using sensors such as accelerometers, velocimeters, and displacement meters [2]. This process enables the identification of abnormal vibrations compared to the normal operating state of the machine and determines the causes of the defects. Recent advances in sensor technology and data acquisition devices have created an environment where large-scale vibration data can be analyzed in real time, and if machine learning or deep learning anomaly detection algorithms are utilized, it is possible to monitor facilities in real time and identify defects at an early stage to recognize problems quickly and respond effectively [11]. The analysis of vibration signals plays a key role in fault diagnosis. Signal processing techniques are used to analyze vibration data in the time and frequency domains to extract the characteristics of a fault. The main signal processing techniques include the fast Fourier transform (FFT), short-time Fourier transform (STFT), and wavelet transform (WT) [19; 20]. The number of shots determines the signal processing methodology. The Fourier transform is utilized as a frequency analysis tool in engineering and science [21]. In particular, the FFT is a discrete-time, algorithmic computer implementation of the Fourier transform that is used effectively in a variety of fields. Because the FFT is useful for identifying vibrations, it can be used in statistical anomaly detection to understand the behavior of a machine and find anomalies. To utilize the FFT for anomaly detection, you must first convert the data to the frequency domain using the FFT. The converted frequency spectrum is then analyzed using statistical methods such as mean and standard deviation to identify abnormal frequency components. The anomalous component frequencies are then identified to detect anomalies in the existing data. However, it is difficult to see frequency spectra that change over time because the FFT only analyzes a specific time period and shows the frequency components within a specific bin at once, rather than sequentially. This limits the use of the FFT in mechanical equipment, where it is necessary to see how frequency components change over time. In other words, unlike the Fourier transform, which can only provide information about the frequency components of the entire signal, the STFT can display the differences between the frequency components of the signal at different times [22]. Therefore, the STFT is more effective than the FFT for fault detection in mechanical equipment. In analyzing the time-varying spectrum, it can identify changes in the frequency content of the signal and effectively detect abnormalities that occur in a short period of time. The wavelet transform is a technique that can provide time and frequency information simultaneously, making them well suited for analyzing unstructured and nonlinear vibration signals. There are many variants of wavelet transforms, such as the discrete wavelet transform (DWT), continuous wavelet transform (CWT), and stationary wavelet transform (SWT) [19]. The DWT can decompose a signal hierarchically to separate high- and low-frequency components, while the CWT is suitable for analyzing changes in a signal over a continuous frequency band.