# A New Data Processing Approach for the SHPB Test Based on PSO-TWER
## 3 Results
### Analysis of Results  
According to the mathematical model described above, two groups of signals of incident and transmitted waves with a total of 28,000 points were selected for the experimental results. In this operation, the initial population number was set to 500, the population dimension was 2, the maximum iteration time was 50, the limit of the time-window length was 2 to 10,000, and the speed limit was \(-200\) to 200; then, the mathematical model was solved by MATLAB. The complete stress wave signal taken in this study had 28,000 points. There were no explicit requirements regarding the time-window length in past research. Figure 7 shows the relationship between the time-window length and the detection results for the incident-wave, reflected-wave, and transmitted-wave arrival times. In Figure 7a,b, areas A and B provide a more suitable range for the incident-wave initial arrival time. During the test process, the incident wave and the reflected wave were recorded by the strain gauge of the incident bar. The incident and reflected waves had two apparent peaks in a complete time domain. In Figure 7a, the incident wave curve changes significantly when the time window is about 5000, which shows that the reflection wave affected the result of arrival picking. For the arrival picking of the reflection wave, the position of the arrival time shows a linear decreasing trend with the time-window length. This explains the fact that the time-window length significantly affected the arrival picking. In Figure 7b, the suitable time-window length is between 2000 and 6000, which explains the fact that the suitable time-window length was about 7% to 21.5% of the total number of signals. In the application of the particle swarm algorithm, the inertia weight mainly controls the global and local search ability of the PSO algorithm, and the appropriate inertia weight factor and learning factor should be selected according to the solution problem [25; 26; 27]. However, there is still no exact parameter calculation method. In this optimization, the learning factor was 0.5 and the inertia weight was 0.1-2.0 for 20 iteration sets of 50 iterations. The calculation results are shown in Table 1, and the convergence curves are shown in 6. The convergence of the fitness values for \(\omega\) = 0.1 to 1.0 is shown in Figure 8a. As shown in Table 2, in only 6 of the 10 sets of optimization results did the search reach the optimal fitness in 50 iterations. When \(\omega\) = 0.4, 0.6, the search results were better and the algorithm was able to complete convergence within 20 iterations, while in the interval of \(\omega\) = 0.7 to 1.0, the number of iterations required to reach convergence was greater than 20, and for \(\omega\) = 0.9, 1.0, nearly 50 iterations were required to complete convergence. It can thus be seen that although it has a significant effect on optimization results, there is no obvious functional relationship with the increase in \(\omega\). In addition, in the experimental results that did not reach the optimum in Figure 8a, the fitness curve converges to a horizontal straight line after 30 iterations, and the fitness at this stage basically ceases to change; the  
Figure 7: Relationship between peak stress and temperature and strain rate. (**a**) The relationship between time window and first arrival (**b**) The calculation result is in the original signal. particles are trapped in a local optimum. A similar situation exists in Figure 8b, where the particles show a relatively good result in finding the optimum, but the local optimum also exists in the same way, and the speed of the optimal convergence is relatively slow, close to 50 iterations. Five different methods for updating inertia weights were selected, as shown in Table 3. Methods (1), (2), and (5) are used to limit a range of inertia weight factors and calculate the inertia weight factor for each iteration according to the boundary size and the process of the iterations, and the positions of all particles in the population are updated based on \(\omega\).