# Weak Signal Processing Methods Based on Improved HHT and Filtering Techniques for Steel Wire Rope
## 4 Comparison and Results
### The New Proposed Method
#### 4.3.3 Influence of the Span in the Moving Average Method  
As mentioned above, when the moving average method was applied, the parameter of signal span should also be investigated. The influences of different moving average spans on the smooth filtering signals are presented in Figure 10. When the moving spans were set as 10, 50, 100, 200, 500, 1000, the averaging results for the lowpass filtered signal of S2 illustrated in Figure 8b manifested that as the moving average parameter of span increases, the processing signals became smoother, and the micro interferences also became weaker and smaller. Nevertheless, when the signal averaging span was less than 100, the smoothing results shown in the second to the fourth line box indicated that the processed signals were  
Figure 9: Signals processed by different averaging methods. nearly the same with the original signal, namely, little changes could be observed for these signals both in waveform shape and amplitude. When the averaging span was bigger than 500, some of the signal defect characterizations were also eliminated and reduced, especially for the signal amplitudes, and only little signal fluctuations were observed. Finally, the time-frequency joint analysis by short-time Fourier transform is presented in Figure 11. Specifically, the original signals of S1, S2, and S3 after the processing of HHT and differentiating are shown in Figure 11a-c, while the signals after the final step of smooth filtering are presented in Figure 11d-f, respectively. Figure 11: STFT analysis of the different processed signals. (**a**) STFT of HHT processed signal S1; (**b**) STFT of HHT processed signal S2; (**c**) STFT of HHT processed signal S3; (**d**) STFT of smoothing processed signal S1; (**e**) STFT of smoothing processed signal S2; (**f**) STFT of smoothing processed signal S3. Figure 10: Signals processed by different moving average spans. Comparing the STFT results of signal S1 expressed in Figure 11a,d, although the defect characterizations are still mixed with signal noises judged by the spectrum illustrated in Figure 11a, the spectrum of the signal defect could be apparently observed in Figure 11d when processed by the proposed methods after the smooth filtering by moving average technique. In other words, there are four signal strength enhancement regions in Figure 11d, which is exactly corresponding to the original defect features and numbers of signal S1 aforementioned in Figure 5a. Similarly, despite the mixed components of defect and interference signals expressed in Figure 11b after the signal processing by HHT and differentiating, the final smooth filtering processed signal S2 expressed in Figure 11e are distinguished with five signal enhancement regions, which is the reflection of the wire rope defects. As for the processing results of the original weak signal S3, both the HHT processed and the final smooth filtered signal spectrum presented in Figure 11c,f are featured with five obvious signal enhancement regions, which not only verified the accuracy of the STFT analysis technique, but also demonstrated the validity and feasibility of the proposed weak defect signal processing method. The final signal-to-noise ratio of these signals were calculated according to the formula as follows,  
\[\text{SNR}=10\text{log}_{10}(\text{P}_{\text{s}}/\text{P}_{\text{n}}) \tag{8}\]  
where \(\text{P}_{\text{s}}\) and \(\text{P}_{\text{n}}\) are the power of the defect signal and noise signal, respectively.