## 3 Results
### The Results of Joint Angle Prediction
#### 3.3.1 The Impact of the SMA on the Prediction Results  
In this research, a total of three upper limb movements were taken as research objects, including arm front raise, arm side raise, and elbow curl. In the arm front raise and arm side raise, the shoulder joint angle is the object to be predicted, and in the arm curl, the elbow joint angle is the object to be predicted. Table 1 reveals the refined parameters of the BLS and the parameters of the SMA. L2 regularization parameters and enhanced node reduction ratio, the number of windows in feature layer, number of feature nodes per window in feature layer, and number of nodes in the enhancement layer were hyperparameters of the BLS which were optimized by the SMA. The model was trained using data from subjects with no load on their hands, and the time in the future was 10 ms.  
Table 2 shows the results of model training. Table 2 confirms the SMA-BLS's exceptional predictive precision. Notably, for collective datasets, the peak metrics were MSE = 0.0019, RMSE = 0.0366, MAE = 0.0098, and R\({}^{2}\) = 0.970. Table 2 further highlights the SMA's proficiency in fine-tuning BLS hyperparameters, markedly elevating prediction reliability. To evaluate whether there is a statistically significant difference in the R\({}^{2}\) between the SMA-BLS and BLS, two-sample T-test was employed. According to Table 2, the \(p\)-value were significantly lower than the commonly accepted level (\(\alpha\) = 0.02). This indicated that there was strong evidence to suggest that there was a statistically significant difference in the mean accuracy rates between the SMA-BLS and BLS. Figure 14: (**a**) The results of Butterworth Bandpass Filtering of the MMG signal. (**b**) Marginal Hilbert Spectrum results of Butterworth Bandpass Filtering of the MMG signal. Figure 15: Raw MMG signal and prepared MMG signal. \begin{table}
\begin{tabular}{c c} \hline \hline  & (**a**) \\ \hline \hline
**Parameters** & **Value** \\ \hline L2 regularization parameters and enhanced node reduction ratio & 0.959 \\ Number of windows in feature layer & 52 \\ Number of feature nodes per window in feature layer & 51 \\ Number of nodes in the enhancement layer & 199 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: (**a**) Best parameters of shoulder joint angle prediction results during arm side raises. (**b**) Best parameters of shoulder joint angle prediction results during arm front raises. (**c**) Best parameters of shoulder joint angle prediction results during elbow curls. (**d**) Parameters of SMA. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{(**a**)} \\ \hline
**Method** & **MSE** & **RMSE** & **MAE** & **R\({}^{2}\)** & _p-Value_ \\ \hline SMA-BLS & 0.0019 \(\pm\) 0.0001 & 0.0366 \(\pm\) 0.0012 & 0.0098 \(\pm\) 0.0006 & 0.970 \(\pm\) 0.002 & / \\ BLS & 0.0046 \(\pm\) 0.0002 & 0.0658 \(\pm\) 0.0021 & 0.0564 \(\pm\) 0.0025 & 0.937 \(\pm\) 0.004 & 0.0077 \\ \hline \multicolumn{2}{c}{(**b**)} \\ \hline
**Method** & **MSE** & **RMSE** & **MAE** & **R\({}^{2}\)** & _p-Value_ \\ \hline SMA-BLS & 0.0020 \(\pm\) 0.0001 & 0.0387 \(\pm\) 0.0009 & 0.0108 \(\pm\) 0.0007 & 0.963 \(\pm\) 0.001 & / \\ BLS & 0.0051 \(\pm\) 0.0004 & 0.0677 \(\pm\) 0.0033 & 0.0587 \(\pm\) 0.0027 & 0.931 \(\pm\) 0.004 & 0.0086 \\ \hline \multicolumn{2}{c}{(**c**)} \\ \hline
**Method** & **MSE** & **RMSE** & **MAE** & **R\({}^{2}\)** & _p-Value_ \\ \hline SMA-BLS & 0.0021 \(\pm\) 0.0001 & 0.0402 \(\pm\) 0.0010 & 0.0119 \(\pm\) 0.0006 & 0.959 \(\pm\) 0.002 & / \\ BLS & 0.0062 \(\pm\) 0.0004 & 0.0734 \(\pm\) 0.0032 & 0.0631 \(\pm\) 0.0021 & 0.929 \(\pm\) 0.003 & 0.0084 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: (**a**) Prediction results of BLS and SMA-BLS during arm side raise. (**b**) Prediction results of BLS and SMA-BLS during arm front raise. (**c**) Prediction results of BLS and SMA-BLS during elbow curl.