## 4 Experimental Study and Discussion
### Experimental Results
The reason that led to the fluctuations may be the nonstationarity of the EMG signal when it was one of the inputs to the model, and different from the proposed SSM, the BPNN was not able to make the EMG signal sufficiently smoothed. Such fluctuations might be fatal to the potential applications in the prediction control of exoskeleton systems when the position prediction error would give rise to huge interactive forces between human and exoskeleton. These extra loads would not only bring about extra burdens to the users, but may also lead to secondary damage when used in rehabilitation applications. The fluctuations in the BPNN prediction results also demonstrated the superiority of the proposed SSM over traditional BPNN when no visible fluctuation could be found in the SSM prediction results. The joint prediction performance comparison between SSM and BPNN of S2 is illustrated in Figure 11b. Although the SSM performance of S2 was worse than that of S1 when bigger derivations could be observed, the results were still acceptable when the FIT was 0.9309, the CC was 0.9759, and the RMSE was 0.0941 (\(p<1\times 10^{-5}\)). In addition, it could be found that performance of S2 using SSM was also better than that using BPNN. Compared to SSM, the corresponding values of BPNN were as follows: the FIT was 0. 8229 (decreased by 11.61%), the CC was 0.9372 (decreased by 3.97%), and the  
Figure 11: Joint prediction performance comparisons between the BPNN and SSM. (**a**) S1, (**b**) S2. RMSE increased to 0.1525 from 0.0941 (\(p<1\times 10^{-5}\)). Same as the results of S1 displayed in Figure 11a, there were visible fluctuations which seemed to be even more intense. That would be unacceptable when applied in human-exoskeleton systems. Although not illustrated in the figure, the angular velocity prediction performances of S2 using the proposed SSM were also satisfactory when the corresponding CC was 0.9879, the FIT was 0.9687 and the RMSE was 0.0252 (\(p<1\times 10^{-5}\)). Compared to SSM, the performances of BPNN were worse when the CC was 0.8751 (decreased by 11.42%), the FIT was 0.7415 (decreased by 23.46%) and the RMSE increased to 0.0738 from 0.0252 (\(p<1\times 10^{-5}\)). These results also demonstrated the advantage of the proposed SSM over traditional BPNN in the angular velocity prediction. Given that our emphasis was put on the joint angle prediction, the angle velocity comparison was not further discussed. In addition to the comparisons in Figure 11, the prediction performance comparisons of all the participated subjects including S3 to S6 were also conducted. The results of RMSE, CC and FIT were calculated using (27)-(29) and are displayed in Table 1. It could be clearly observed that obvious improvements were achieved through the application of the proposed SSM instead of BPNN when all the values of CC and FIT were increased and values of RMSE were decreased for the 6 participated subjects. Individual differences could also be observed. In addition to the nonstationarity of EMG signals as the input, the differences were probably caused by the fact that the acquired signal qualities from different subjects differed greatly. Especially for S3, the performances using BPNN were poor. Various attempts, including increasing the numbers of hidden layers and neurons in each layer, have been made to improve the performance and acquire the best-fit network. However, the prediction results using BPNN were still unacceptable. The reasons behind still needed further investigations. In contrary, the corresponding SSM performances were much more acceptable, which demonstrated the robustness of the proposed SSM. Except for S3, the BPNN performances of other participated subjects were all acceptable. When we ignore the results of S3, the improvements when applying the proposed SSM instead of BPNN were achieved regardless of individual differences. The results demonstrated the advantages of the proposed SSM over traditional BPNN when applied in joint angle prediction, and the effectiveness of the SSM was also proven.