## 4 Equilibrium Score (EQs) Estimation
Similar results were also obtained by linear regression to derive the relationship between the RMS values of COP measurements in the AP direction and the corresponding swaying levels, as shown in Figure 12. As shown in these two figures, it is noted that the EQs values can be accurately derived through the linear regression process only using COP measurements in the AP direction. Figure 11: Regression analysis for root-mean-square values of COP measurement resultants and the swaying level (100 equilibrium score (EQs)). Figure 10: Correlation coefficient: COP-AP signal versus acceleration signal in the Y-axis (black \(\diamond\)); COP-AP signal versus PC-1 of acceleration signals with principal component analysis (PCA) for the whole data length (blue \(\times\)); COP-AP signal versus PC-1 of acceleration signals via segmental PCA (sPCA) (red *); mean value of \(\diamond\) (black —); mean value of \(\times\) (blue...); mean value of * (red -..-). As mentioned previously, the analysis shows that the COP measurements in the AP direction have high correlation with the first principal component of the acceleration measurements. Therefore, it is feasible to estimate the EQs values through the analysis of the swaying acceleration signals that are measured by the tri-axis capacitive accelerometer. Figure 13 shows the flow chart of signal processing in estimating the EQs values in terms of the acceleration measurements. The human body swaying accelerations were measured by the bind-in tri-axis capacitive accelerometer that is capable of effectively capturing the signals at very low frequencies of human body swaying. The acceleration signals were then processed by using the proposed sPCA to extract the first principal component (PC-1). The signal of PC-1 was separated by the EMD method and the IMFs within the frequency range of 0-5 Hz were synthesized for the further procedure. The RMS value of the synthesized filtered PC-1 signal was calculated and then transformed to estimate the RMS value of COP signal in AP-direction by means of the a priori correlation analysis. Through the a priori linear regression analysis between (100 EQs) and the COP-AP RMS, the EQs values can be estimated. It is noted that the correlation analysis and the linear regression method were utilized as the decision support tools for data transformations among the acceleration signals, COP measurements and (100 EQs) values. The EQs values that were obtained by the commercial computer-aid balance testing apparatus were also utilized to compare with the ones that were estimated from the acceleration measurements. Figures 14-18 show the EQs values which were estimated through the acceleration measurements and the EQs values which were obtained by the commercial computer-aid balance testing apparatus in C1 to C5 of SOT. These figures demonstrate that most of the estimated EQs values are close to the EQs values that were obtained by the balance testing apparatus. Table 2 shows the mean absolute percentage error (MAPE) of the estimated EQs values in each visual condition of SOT compared with the EQs values that were displayed in the balance testing apparatus, which is defined as:  
\[MAPE=\frac{\left|EQs_{est}-EQs_{app}\right|}{EQs_{app}}\times 100\% \tag{6}\]  
where, \(EQs_{est}\) represents the estimated EQs value and \(EQs_{app}\) represents the EQs value displayed in the balance testing apparatus. As shown in Table 2, high accurate EQs estimation can be obtained through the swaying acceleration measurement of the human body as well as the proposed signal processing steps in most of the SOT cases except for some of the cases in C5. The overall accuracy of the estimated EQs values was 95.11%. Figure 12: Regression analysis for RMS values of COP measurement in the AP direction and the swaying level (100 EQs). Figure 16: Estimated EQs values compared with EQs values of commercial computer-aid balance testing apparatus in C3. Figure 17: Estimated EQs values compared with EQs values of commercial computer-aid balance testing apparatus in C4.