# Fault Feature Extraction Using L-Kurtosis and Minimum Entropy-Based Signal Demodulation
## 1 Introduction
The study demonstrated that cepstrum pre-whitening, with its low computational requirements and simplicity, offers a promising alternative to traditional pre-whitening techniques like linear prediction filters and spectral kurtosis. [PERSON] et al. [21] presented a comprehensive comparative study of signal analysis techniques for rolling element-bearing diagnostics, focusing on fault detection, diagnosis, and prognosis. The study revealed that statistical parameters like RMS, kurtosis, and detectivity are effective in detecting the onset of faults in bearings. [PERSON] and [PERSON] proposed the first systematic approach of band selection using kurtogram. The optimal central frequency \(\hat{t}_{\text{c}}\) and bandwidth of the band pass filter can be determined by maximizing the kurtogram [22]. [PERSON] et al. [23] proposed a Single Ensemble Empirical Mode Decomposition (SEEMD) method, which demonstrates a significant advancement in fault detection for rolling element bearings, particularly within the challenging context of mining industry signals. [PERSON] et al. [24] proposed a novel and effective method for enhancing early weak fault features in rolling element bearings by combining resonance sparse decomposition with multi-objective information frequency band selection (MIFBS). This approach effectively addresses the challenge of interference components obscuring early fault signatures in vibration signals. [PERSON] et al. [25] provided a comprehensive comparative analysis of various signal-processing techniques designed to extract the signal of interest (SOI) from non-Gaussian noise in vibration signals acquired from machinery. [PERSON] et al. [26] addressed the critical challenge of identifying informative frequency bands for extracting weak damage components in vibration signals acquired from rotating machines operating under time-varying conditions. A novel framework is proposed that leverages angle-frequency instantaneous power spectrum and order-frequency cyclic modulation spectrum to construct consistent feature planes. [PERSON] et al. [27] proposed a novel and effective method for early fault detection in rolling element bearings, addressing the challenge of weak fault features being masked by environmental noise. The proposed method integrates the negative entropy of the square envelope spectrum approach with optimized stochastic resonance (SR) signal enhancement. [PERSON] et al. [28] presented a novel approach to constructing envelope spectra for the surveillance and diagnostics of rotating machinery, addressing limitations of existing methods like narrowband demodulation and cyclo-stationary analysis. The proposed Combined Weighted Envelope Spectrum (CWES) framework is designed to extract specific characteristic frequencies, effectively mitigating challenges posed by low SNR conditions, non-Gaussian noise, and cyclo-stationary noise. However, the current methods often struggle with non-stationary noise, common in real-world scenarios. This limits their accuracy and reliability, particularly for early fault detection. Many techniques rely on predefined or manually selected frequency bands, which may not be optimal for all fault types or operating conditions. Developing adaptive methods that automatically identify the most informative frequency bands is crucial. The existing techniques often assume stationary operating conditions, which are not representative of real-world machinery, especially in industries like wind turbines. Further research is needed to develop methods that can reliably function under time-varying conditions. Thus, an attempt is made in this work to address these issues. In this current work, cluster-based segmentation is used to divide signals into different segments. The frequency band and their central frequencies are automatically estimated using fuzzy C-mean clustering. The informative frequency band among the different segments was selected based on a combination of maximum L-kurtosis and minimum entropy in the segments [29].