# Fault Feature Extraction Using L-Kurtosis and Minimum Entropy-Based Signal Demodulation
## 4 Results and Discussion  
The proposed scheme was implemented in the simulated signal with a fault frequency of 16 Hz. A sampling rate of 20 kHz was considered and a white noise of signal-to-noise ratio (SNR) equal to -5 was added to the simulated signal as shown in Figure 2a. The envelope spectrum of the simulated signal is shown in Figure 2b, where the fault frequency of 16 Hz is not clearly visible. Figure 1: Proposed signal-processing scheme. The envelope spectrum of the signal was divided into six segments using FCM segmentation, as shown in Figure 2c. The frequency band and their central frequencies are automatically estimated using fuzzy C-mean clustering. Each segment was reconstructed as a time domain signal using inverse FFT and L-kurtosis, and the entropy of each reconstructed signal was extracted. The informative frequency band among the different segments was selected based on a combination of maximum L-kurtosis and minimum entropy of the segment. This informative frequency band was further utilized to design a bandpass filter. The original signal was reconstructed using this bandpass filter, as shown in Figure 2d. [PERSON]'s transform-based envelope spectrum is applied to demodulate the filtered signals for extraction of the fault frequency, as shown in Figure 2e, where a fault frequency of 16 Hz and its harmonics are clearly visible. The effectiveness of the proposed scheme is further validated through its application to an experimental dataset obtained from a worm and wheel gearbox test rig (as depicted in Figure 3). The experimental setup utilizes a single-stage worm and wheel gearbox with a 20:1 gear ratio. The wheel, featuring 20 teeth and a pitch circle diameter of 65 mm, is driven by a 50 Hz, 1 hp DC motor (WAFRO) operating at 2880 rpm. Flexible coupling ensures the smooth transmission of power between the motor shaft and the gearbox. More details of the worm gearbox are tabulated in Table 1.  
Figure 2: (**a**) Simulated signal (considered as raw signal). (**b**) Envelope spectrum of simulated signal. (**c**) Segmentation of the simulated signal. (**d**) Reconstructed signal using band-pass filter. (**e**) Envelope spectrum of the reconstructed signal. To capture vibration signals, a piezoelectric uniaxial PCB accelerometer with a sensitivity of 100 mV/g is strategically placed on the bearing seat of the wheel shaft. This accelerometer operates based on internal excitation, ensuring accurate measurement. A seeded pitting tooth fault, as illustrated in Figure 4, is deliberately introduced on a tooth of the wheel, simulating a common failure scenario. The experiment focuses on acquiring data under three distinct speeds: 1600 rpm, 1800 rpm, and 2000 rpm, all sampled at a rate of 20 kHz. The proposed scheme is then employed to process this acquired data. Figure 5a displays the raw signal obtained, while Figure 5b presents its corresponding envelope spectrum. \begin{table}
\begin{tabular}{l l l} \hline \hline
**S. No.** & **Components** & **Specifications** \\ \hline
1. & Motor & DCmotor; power: 1 hp.; maximum speed: 2880 rpm. \\
2. & Worm gearbox & Single stage; worm and wheel; gear ratio 20:1. \\ \hline \end{tabular}
\end{table} 
Table 1: Details of worm gear test rig. Figure 4: Gear wheel with pitting tooth seeded defect. Figure 3: A typical photograph of the worm gearbox test rig. An analysis of the envelope spectrum reveals prominent frequency components associated with the Gear Meshing Frequency (GMF) at 26 Hz and its harmonics. This observation highlights the presence of regular tooth engagement within the gearbox. However, a crucial finding emerges: no identifiable fault signature related to the seeded pitting tooth fault is present in the spectrum. This absence of a discernible fault signature underscores the inherent challenges of detecting such faults in the presence of significant noise and complex gear meshing dynamics.