## 5 Conclusions
The specified normality model allows us to get various pairs of thresholds that can be used to detect transient faults in the residual evaluation. We find out one optimal pair achieving the best performance required by CPS as the adaptability and sensitivity are considered to minimize uncertainties of modeling and environment. To do this, after the performance measures that can represent two comparable variables are defined, the optimization problem is formulated by using the nonlinear programming method in order to maximize the interests of two measures. These experimental results show that there is an obvious difference among the performance results of three thresholds. In terms of accuracy, recall, and precision, performance evaluation of our AT is performed based on various scenarios, compared with the performance of other dynamic threshold techniques. When the performance is analyzed by varying the duration and intensity for three kinds of faults, AT generated by the proposed method is not influenced by the change of the intensity and duration at each velocity. KT could not detect faults properly if the intensity is low or/and the duration is short. Since RT is sensitive to small changes of measurements, its performance is significantly changed according to duration and intensity and showed similar performance regardless of velocity. The AT method helps prevent misleading interpretations that the cyber system concludes some intermittent anomalous data and noises as fatal faults even though they occur naturally, disappear soon, and do not affect adversely the control of the system. AT is not only competent to diagnosis the faults with high levels of sensitivity and adaptability, but also it achieves good performance with only a small amount of data with a certain uncertainty limited by time intervals. In particular, it is noteworthy that the thresholds are optimally determined in response to the obtained measurements that change significantly as the velocity is varied because it proves that the intensity and duration have nothing with the performance of AT. Therefore, the adaptive threshold generated from the combination of our threshold generation method and the normality model can be a good criterion for distinguishing between normal and anomalous states as well as detecting faults. The AT determined from the equilibrium can be said to have high degrees of adaptability and sensitivity. In future work, at lower velocities, the performance of AT needs to be improved by varying the time window size. Conceptualization, Y.B. ; Methodology, Y.B. ; Resources, M.J.; Supervision, Y.B. ; Writing--original draft, Y.B. ; Writing--review and editing, Y.B. This research was supported in part by Global Research Laboratory Program (Grant No. : 2013K1A1A2A02078326) through the NRF of Korea. I would like to thank researchers (in Convergence Research Center for Future Automotive Technology, DGIST), [PERSON] and [PERSON], for providing technical support for the modeling of dynamics of mechanical systems. The authors declare no conflict of interest. For the residual generation, dynamics of mechanical systems is modeled as follows. Let the dynamics be given by the following standard state equation in a vector form:  
\[\mathbf{x}(\dot{t}+1)=A\mathbf{x}(t)+B\mathbf{u}(t), \tag{1}\] \[A=\left[ \begin{array}{cc}-\frac{R_{A}}{L_{a}}&-\frac{K_{EMF}N}{ L_{a}}\\ \frac{K_{m}N}{J_{v}}&-\frac{(B_{j}+B_{v})}{J_{v}}\end{array} \right],\ B=\left[ \begin{array}{cc}\frac{1}{L_{a}}&0\end{array} \right]^{T},\]  
where \(A\) is a \(2\times 2\) square matrix of the constant coefficients, and \(B\) is a \(2\times 1\) matrix of the coefficients to weight inputs because both matrices \(A\) and \(B\) are determined by the structure and elements of Jackal. The coefficients for both matrices \(A\) and \(B\) is described in motor modeling as mentioned below. The set of two state variables is represented as a state vector \(\mathbf{x}(t)\) of which each state variable is a time-varying component, an input vector \(\mathbf{u}(t)\) consists of inputs at time \(t\).