## 3 Discussion
### The Investigation of Tremor Times  
During the response process of artificial muscle, tremor occurrence times in each time unit are extracted, which characterizes the occurrence frequency of the tremor, and can be used as an important index for the evaluation of tremor behavior.  
By referencing Table 1, the lower limiting outlier of occurrence times covered by tremor behavior was assigned as 1. Thus, the corresponding tremor data sequence within the first 65 s was:  
\[Q^{(0)}=(2,5,6,7,8,9,11,12,13)\]  
When \(i=1\), the distances between the first and subsequent other points were computed to obtain a new data subsequence:  
\[Q^{(0)}(1)=(3,4,5,6,7,9,10,11)\]And then \(i=2\), the next subsequence was given:  
\[Q^{(0)}(2)=(1,2,3,4,6,7,8)\]  
Analogously, based on the dimension of the original sequence, five new data subsequences were constructed under dimensions from 4 to 8 as the candidate models. The estimated values and original values of each subsequence with respect to ordinal \(k\) were shown in Figure 8a-e, respectively. Meanwhile, model response, model accuracy, grey correction degree and fitting degree were calculated to evaluate the availability of the candidates (Table 2).  
From Table 2 and Figure 8, the results showed that the 4-D model had the highest prediction accuracy; however, it was not available for prediction because its grey correlation degree was less than 0.6 and the number of data samples was too small. Additionally, the lower correlation degree and accuracy of 5-D and 6-D models limited their applications in the prediction. Although both of them had high accuracy at the initial stage, compared with the 7-D subsequence, the model accuracy and grey correlation degree of 8-D were better as a whole, which showed a better fitting degree between the subsequence and original sequence. Therefore, the 8-D subsequence model about tremor occurrence times in unit time was used for prediction and the starting time point \(g(1)\) was set as 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Sequence Dimension**} & \multicolumn{2}{c}{**Model Response**} & \multirow{2}{*}{**Model Accuracy (\%)**} & \multirow{2}{*}{**Grey Correlation Degree**} & \multirow{2}{*}{**Fitting Degree**} \\  & \(\hat{\eta}(k+1)^{(0)}\) & & & \\ \hline
8 & \(24.853\pm 0.18151\)\(-21.853\) & 96.1503 & 0.6547 & satisfaction \\
7 & \(9.2955\pm 0.24238\)\(-8.2955\) & 89.6019 & 0.6009 & satisfaction \\
6 & \(8.2308\pm 0.28638\)\(-7.2308\) & 87.5976 & 0.5812 & dissatisfaction \\
5 & \(7.9231\pm 0.2872\)\(-6.9231\) & 86.4147 & 0.5774 & dissatisfaction \\
4 & \(10.75\pm 0.2872\)\(-9.75\) & 98.6546 & 0.5583 & dissatisfaction \\ \hline \hline \end{tabular}
\end{table}
Table 2: Model test results of different subsequences about tremor occurrence times.  
Figure 7: The distributions of values with DAGCP, SARIMA, GM (1, 1) and actual value. DAGCP: dynamic additional grey catastrophe prediction; SARIMA: seasonal autoregressive integrated moving average.  
The estimated values and relative errors of conventional GCP and DAGCP were shown in Table 3. Specifically, the conventional GCP was constructed by the original time sequence. It is obvious that the actual number of tremors only occurred once during 75\(\sim\)80 s and was affected by process parameters, experimental conditions and human factors, as well as existing contingency. Hence, it was not necessary to predict ahead in this circumstance.  
It was obvious that the occurrence times in 65\(\sim\)70 s, 70\(\sim\)75 s and 80\(\sim\)85 s were 2, 3 and 2, respectively. As shown in Table 3, there was a little difference between GCP and DAGCP in the relative error during 65\(\sim\)70 s. However, the relative error of DAGCP was smaller than GCP after 70 s. Therefore, the prediction accuracy of DAGCP was superior to that of GCP as a whole.