## 4 Equilibrium Score (EQs) Estimation  
A high correlation between the COP in the Y-axis and the first principal component of acceleration signals has been validated in the previous section, and thus it is feasible to use the acceleration measurements representing the COP-based evaluation for human balancing ability. Furthermore, in the field of clinical medicine, the balancing ability of patients is generally assessed through the commercial computer-aid balance testing apparatus in SOT and is broadly quantified in terms of the equilibrium score (EQs). The EQs of patients' balancing ability is mainly computed through the measurement of COP. The EQs is defined from zero to one hundred. The EQs value of one hundred means an ideal stability while the EQs value of zero represents a tumble. In order to verify the accuracy of analogy between the acceleration measurements and the COP-based EQs evaluation at the balance testing apparatus, the datasets that include the synchronous measurements of body swaying acceleration and COP as well as the EQs evaluation were collected from the Department of Physical Therapy and Assistive Technology in National Yang-Ming University, in which the commercial computer-aid balance testing apparatus was utilized to assess the balancing ability of patients in the five visual conditions. The collected data consisted of 85 sets of acceleration signals and COP measurements that were recorded in the SOT of different examinees. The examinees that had normal balancing abilities in a majority were evaluated through some of C1 to C5 of SOT. All the data were available as the format of digits in text which can be processed and analyzed in MATLAB software. Before the EQs estimation was investigated, all the collected data was first processed through the correlation analysis to obtain the statistical result of correlation coefficients between the COP measurements and the acceleration signals. Figure 10 shows the results of correlation coefficients between the COP measurements in the AP direction and the three data sets that are the PC-1 of acceleration measurements through the sPCA (with segment length of 1.0 second), the PC-1 of acceleration measurements by using the PCA for the whole signal length, and the original acceleration measurements in the Y-direction, respectively. As shown in the figure, the COP signals in the AP direction have higher overall correlation with the PC-1 of the acceleration measurements with the sPCA process (mean correlation coefficient around 0.78) than the PC-1 through the pure PCA for the whole signal length (mean correlation coefficient around 0.41), as well as the original acceleration measurements in the Y-direction (mean correlation coefficient around 0.40). The correlation analysis apparently shows that the acceleration measurements can be utilized to accurately predict the COP  
Figure 9: (**a**) Comparison between COP in the Y-axis and first principal component of acceleration signals, (**b**) Comparison between COP in the Y-axis, second and third principal components of acceleration signals. signal in the AP direction through the sPCA, and hence, it is feasible to use the cheap bind-in accelerometer for estimating the human being's balancing ability instead of the expensive bulky COP measurement system. Since the transformation from the COP measurement to the EQs is unavailable in this study, the statistical computation can be used to simply derive the relationship between the COP signals and the EQs. Define the swaying level to be (100 EQs). The root-mean-square (RMS) values of COP measurement resultants and the corresponding (100 EQs) values are shown in Figure 11. It is apparent that the transformation between the RMS values of COP measurement resultants and corresponding (100 EQs) values can be derived through the regression analysis.