## 3 Discussion
### The Investigation of Peak-to-Peak Values  
The maximum peak-to-peak values (the difference between adjacent crests and troughs) in unit time are extracted, which characterizes the severe degree of tremor, and also can be used for the evaluation of tremor behavior. Here, the lower limiting outlier was assigned as 0.2 mm. In addition, the corresponding data sequence within 65 s was:  
\[Q^{(0)}=(2,5,6,7,8,11,12)\]  
When \(i=1\), a new data subsequence was: \(Q^{(0)}(1)=(3,4,5,6,9,10)\). Thus, three new data subsequences were constructed under the dimensions from 4 to 6. The estimated values and original values were shown in Figure 9a-c, respectively. In addition,  
Figure 8: Estimated values and original values of each subsequence: (**a**) 8-D; (**b**) 7-D; (**c**) 6-D; (**d**) 5-D; (**e**) 4-D. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**GCP**} & \multicolumn{3}{c}{**DAGCP**} \\ \hline \multirow{2}{*}{**Tremor Times**} & **Time Series** & **Actual Time** & **Estimated Value** \(\hat{q}(k)^{(0)}\) & **Relative Error (\%)** & **Estimated Value** \(\hat{q}(k)^{(0)}\) & **Relative Error (\%)** \\ \hline
2 & 14 & 65–70 & 15.39 & 9.93 & 15.49 & 3.50 \\
3 & 15 & 70–75 & 17.51 & 16.73 & 17.05 & 13.67 \\
2 & 17 & 80–85 & 19.91 & 17.12 & 18.93 & 11.35 \\ \hline \hline \end{tabular} Note: Relative error = \(\left|\frac{\frac{q(k)^{(0)}-q(k)^{(0)}}{q(k)^{(0)}}}{\frac{q(k)^{(0)}}{q(k)^{(0) }}}\right|\times 100\%\).  
\end{table} 
Table 3: Estimated values and relative errors of grey catastrophe prediction (GCP) and dynamic additional grey catastrophe prediction (DAGCP). the model response, model accuracy, grey correction degree and fitting degree were displayed in Table 4.  
From Table 4 and Figure 9, although the grey correlation degree had achieved the basic requirement, the prediction precision of 4-D and 5-D models limited their applications in the prediction. Among them, 6-D model had the highest model accuracy and grey correlation degree, which showed a more accurate fitting degree. Thus, the 6-D model about tremor peak-to-peak value in unit time was used for the prediction and \(q(1)\) was also set as 2. The estimated values and relative errors were shown in Table 5. The actual peak-to-peak value was less than 0.2 mm during 75-80 s, which was allowed to happen. Therefore, it was not necessary to predict ahead in this circumstance. In the above analysis, the peak-to-peak values in 65-70 s, 70-75 s and 80-85 s were 0.6 mm, 0.5 mm and 0.2 mm, respectively. As shown in Table 5, the relative error of DAGCP was obviously less than that of GCP. To validate the effectiveness and accuracy of the proposed method, the catastrophe prediction results of 10 groups of chitosan-based artificial muscles with different process parameters based on GCP and DAGCP were shown in Table 6. Here, the data in the first 70 s was selected as original sequence and the last 10 s was used to assess the prediction accuracy. The lower thresholds of occurrence times and peak-to-peak values were assigned as 2 and 0.2 mm, respectively. If either of the conditions was satisfied, the tremor is considered to happen. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{
\begin{tabular}{c} **Sequence** \\ **Dimension** \\ \end{tabular} }} & \multicolumn{2}{c}{**Model Response**} & \multicolumn{2}{c}{**Grey Correlation**} & \multirow{2}{*}{**Fitting Degree**} \\  & \(\hat{q}(k+1)^{(0)}\) & & & & **Degree** \\ \hline
6 & 14.906\({}^{\text{\textasciitif{}}}\)0.23688k \(-\) 11.906 & 95.8616 & 0.6252 & satisfaction \\
5 & 4.9444\({}^{\text{\textasciitif{}}}\)0.3848k \(-\) 3.9444 & 87.1655 & 0.6117 & satisfaction \\
4 & 5.125\({}^{\text{\textasciitif{}}}\)0.42105k \(-\) 4.125 & 81.2634 & 0.6081 & satisfaction \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Model test results of different subsequences about tremor peak-to-peak values.