# A New Data Processing Approach for the SHPB Test Based on PSO-TWER
## 2 Related Work
### Denoising of Waveform Signals  
The complexity and fractal characteristics of a waveform signal are calculated by the box dimension method. The principle is that the signal curve is covered by a box with a side length r, and the number of nonempty boxes in the whole area is recorded as N(r). Then, as r is constantly changed, N(r) changes accordingly, and the fractal dimension (D) can be calculated by Equation (2) [23]. \[D=\lim_{\text{r}\to 0}\frac{\log N(\text{r})}{\log(1/\text{r})} \tag{2}\]  
Signals measured via the SHPB test in the Impact Dynamics Laboratory of the School of Mining Engineering at the University of Science and Technology Liaoning were selected for analysis. Six different filters were selected to denoise the stress wave signals, namely, moving average, lowess, loess, Savitzky-Golay, robust lowess, and robust loess filters. The raw signal and smoothing results are shown in Figure 2a. It can be seen that there is a large amount of noise in the original image. From a qualitative point of view, the scale of the noise signal of the stress wave data is small. Due to the existence of the rod end shaper, the incident-wave waveform is close to a sine wave; each of the six filters preserves the overall trend of the stress wave signal. The difference between the results is reflected in the degree to which the signal details are retained. Since the dynamic response characteristics of rock loading depend on the values monitored by the strain gauges, the accuracy of subsequent data processing will be affected if the peak value of the smoothed curve is too large. If the moving average result leads to a decrease in the peak value of the curve, the transmitted-wave smoothing result of robust lowess is too different from the original waveform, and the result of the robust lowess filter not only retains the trend of the curve better but also has a small numerical error. The fractal dimension calculation curve for each group of results is calculated using Equation (2), as shown in Figure 2b-e. The fractal dimension of the original image and the smoothed result are significantly different, and the fractal dimensions of the incident wave and the transmitted wave are 1.3014 and 1.5471, respectively, which are the highest values in the results. After denoising, the fractal dimensions of the first group were between 1.0178 and 1.0282, and those of the second group were between 1.0178 and 1.0432. The reduction in fractal dimensions indicates a reduction in curve complexity, which further verifies the validity of the filtering results. Since the difference in the fractal dimension for each component after filtering was small, combined with the analysis of Figure 2a, it was decided to use the robust loess filter for subsequent smooth denoising. When using a robust loess filter for denoising, a span with a range of (0,1) needs to be used; the sets value represents the number of data points used for smoothing as a percentage of the total number of curve points. In order to further discuss the influence of span on the smoothing effect of curves, spans of 0.01, 0.05, 0.1, 0.2, 0.25, and 0.5 were used for calculations. The results obtained are shown in Figure 3. Analyzing the overall trend, the size of the span significantly affects the overall trend of the results. When the span values are 0.2, 0.25, and 0.5, the filtering results are quite different from the overall trend of the original curve. The trend of transmitted waves at a span of 0.5 is even close to the level, indicating that there are too many data points for smoothing; the noise of the original signal is removed, while the signal details are lost to too great an extent. When the span is 0.1, the transmitted-wave denoising effect is basically the same as the original signal, and the incident wave is significantly different from the original signal at 420 us; the filtering results for the spans of 0.01 and 0.05 are not much different, which ensures the details of the signal while removing noise.