# Fault Feature Extraction Using L-Kurtosis and Minimum Entropy-Based Signal Demodulation
## 1 Introduction  
The condition monitoring and fault diagnosis of rotary components remains a crucial area of research within the scientific community. The ability to accurately assess the health of these components is essential for ensuring operational reliability, preventing catastrophic failures, and minimizing downtime in industrial processes [1, 2, 3]. Vibration and acoustic signals emitted by mechanical components offer a rich source of information about their health status. These signals contain valuable clues about the internal condition of the component, including wear, damage, or impending failure. The presence of specific frequency components in these signals can be directly linked to specific faults within the component [4, 5, 6]. Vibration-based techniques have emerged as a powerful tool for fault diagnosis in rotating machinery [7, 8, 9]. These techniques leverage the relationship between the frequencies present in the vibration signal and the corresponding faults within the machine. Spectral analysis of the vibration signal is a fundamental approach for extracting this crucial information [10]. For instance, [PERSON] and [PERSON] [11] successfully demonstrated the viability of a two-step artificial neural network approach for condition monitoring and fault diagnosis in rotating machinery. This approach has the potential to significantly improve operational efficiency by enabling proactive maintenance and minimizing costly downtimecaused by unexpected breakdowns. [PERSON] et al. [12] presented a compelling approach to vibration-based fault detection in rotating machinery, demonstrating the effectiveness of integrating the poly-coherent composite spectrum (pCCS) with machine learning techniques. By effectively condensing multi-location vibration data into a single spectrum, pCCS significantly reduces the computational burden associated with large datasets, while preserving critical amplitude and phase information. [PERSON] [13] presented a novel and effective feature extraction method for enhancing the accuracy of rolling bearing fault diagnosis under time-varying operating conditions. By combining the complementary ensemble empirical mode decomposition (CEEMD), Teager-Kaiser energy operator (TKEO), and self-organizing map (SOM), the proposed approach effectively removes unwanted noise components and extracts relevant bearing characteristics from the vibration signal. [PERSON] et al. [14] demonstrated the successful diagnosis and root cause analysis of bearing failure in a 2300 kW motor, highlighting the importance of a comprehensive approach that considers both vibration and lubrication factors. However, the conventional approach provides a robust framework for fault diagnosis in rotating machines but limitations arise from the presence of noise and the complex nature of real-world signals. Recent research focuses on developing advanced signal-processing techniques and machine learning algorithms to enhance the accuracy and efficiency of fault diagnosis in rotating machinery. The accurate demodulation of vibration signals is crucial for extracting fault-related information. The selection of the appropriate frequency band for filtering plays a vital role in achieving this accuracy. Several techniques have been developed in recent years to effectively extract the informative frequency band. [PERSON]'s Spectral Kurtosis (SK) method has proven to be highly effective for detecting transient events and pinpointing their location within the frequency spectrum. Notably, SK exhibits robustness against additive stationary noise. This technique provides a valuable tool for isolating the relevant frequency band within the vibration signal, paving the way for more precise fault diagnosis in rotating machinery [15; 16; 17; 18; 19]. [PERSON] et al. [20] investigated the effectiveness of cepstrum pre-whitening as a technique for enhancing rolling element-bearing diagnostics, particularly in industrial settings where heterogeneous vibration sources introduce challenges for traditional signal processing methods.