# A Brunnstrom Stage Evaluation System with Fuzzy-Accelerometer
## 2 System Development
### Accelerometer Data Processing  
Table 1 shows the features s and descriptions of the three actions in the experiment. When the Flexion action is performed, the \(y\)-axis values will clearly rise and fall, producing a waveform-like motion as shown in Figure 2. The maximum value (peak) is scaled and averaged to produce the first features value FAA (Flexion Average Angle), and Flexion Angle Standard Deviation (FASD) is the standard deviation of the obtained peak value. Finally, Flexion Lateral Stability (FLS) calculates the standard deviation based on the \(x\)-axis data for the Flexion. If the Flexion is performed with high stability, the \(x\)-axis data will show little variability. However, high variability in the \(x\)-axis will also result in parameter value variability in the \(z\)-axis during action performance. However, given that the Flexion action is mainly performed in the vertical and horizontal axes, it is not discussed in this experiment. Pronation is similar to Flexion in that it uses \(z\)-axis data to obtain the average angle, where the PAA (Pronation Average Angle) and the PASD (Pronation Angle Standard Deviation) are used to calculate the standard deviation of the peak angle, while standard deviation of the PVS (Pronation Vertical Stability) is calculated using \(y\)-axis data. Thus a stable pronation action will result in minimal \(y\)-axis variability, and vice versa. Pronation will also produce \(x\)-axis variability, but the action's before and after position are mostly level, and thus is not discussed here. Lap to Chin variability is based on inconsistency between the patient's affected and healthy sides, and neither accuracy nor stability are considered, thus the \(z\)-axis data can be taken as the action peak. We first tested the simulation data for different levels and conditions, confirming that the simulation algorithm can correctly classify the various data as belonging to ST2-ST6 (stage 2 to stage 6) and Healthy. ST1(stage 1) is omitted because it is defined by [PERSON] as \"Flacidity\" or lack of movement and thus cannot be detected by use of the accelerometer. The definition of ST2-ST6 are list in Table 2.  
Figure 1: Schematic diagram of measurement system. Figure 2 shows the raw acceleration data of ST2-ST6 along the \(y\)-axis for the Flexion action performed by the health limb. The horizontal access shows a data sequence with 20 data points per second, and the acceleration value of the vertical axis is (g, g = \(9.81\times s^{2}\)), thus the time required to perform the operation differs with stage, so Figure 2 extracts the acceleration signal for five movements. From Figure 2 we can see that some micro-vibrations produced a jagged signal during the action, causing system errors when identifying feature values. Therefore, this paper used low-pass \begin{table}
\begin{tabular}{c c c} \hline
**Motion Name** & **Features** & **Description** \\ \hline \multirow{3}{*}{Flexion} & FAA & Average angle of peak values for \(y\)-axis \\  & FASD & Standard deviation of peak values for \(y\)-axis \\  & FLS & Standard deviation of values for \(x\)-axis \\  & PAA & Average angle of peak values for \(z\)-axis \\ \multirow{3}{*}{Pronation} & PASD & Standard deviation of peak values for \(z\)-axis \\  & PVS & Standard deviation of values for \(y\)-axis \\ \multirow{2}{*}{Lap to Chin} & LTCMR & Times of the peak value for \(z\)-axis \\ \hline \end{tabular}
\end{table} 
Table 1: Define motions Features. \begin{table}
\begin{tabular}{c c c} \hline
**Flexion** & **Pronation** & **Simulate Level** \\ \hline
0-30 & 0–30 & ST2 \\
30–60 & 30–60 & ST3 \\
60–90 & 60–90 & ST4 \\
90–120 & 90–120 & ST5 \\
120–150 & 120–150 & ST6 \\
150–180 & 150–180 & Healthy \\ \hline \end{tabular}
\end{table} 
Table 2: Definition of Brunnstrom Stages. Figure 2: Flexion motion’s \(y\)-axis’s raw data from top to bottom ST2, ST3, ST4, ST5, ST6, and Healthy. filtering to filter out noise prior to identification. The characteristic values of each action are shown in Equation (1) [20].