# A Response-Adaptive Method for Design of Validation Experiments in Computational Mechanics
## 5 Conclusions  
This paper presented a new method to design validation experiments called response-adaptive experiment design (RAED) for computational models in mechanics. The RAED method adaptively selects the next experimental condition from among candidates of various operating conditions (experimental settings). RAED consists of six key steps: (1) define experimental conditions, (2) obtain experimental data, (3) calculate u-values, (4) compute the area metric, (5) select the next experimental condition, and (6) obtain additional experimental datum. To demonstrate the effectiveness of the RAED method, a case study of a numerical example was shown. The case study accounted for real engineering applications in the field. It was shown that RAED can effectively reduce type II error (the possibility of accepting an invalid computational model) during model validation. RAED can also help to avoid unnecessary experiments for model validation by allocating validation resources effectively.  
The existing study based on HTVC only considered type I error (or significance level) to evaluate whether a computational model is valid. The HTVC-based approach does not provide any way to reduce type II error. Different from the HTVC-based approach, this study proposed a response-adaptive experiment design (RAED) approach for model validation with limited experimental samples. The RAED-based approach can reduce type II error while maintaining type I error at  
Figure 8: PDF of each area metric (\(U\)) for the three design conditions.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Experimental** & **Mean** & **Standard** & **Skewness** & **Kurtosis** & **Pearson Type** & **Type II** \\
**Design** & **Mean** & **Deviation** & **Skewness** & **Kurtosis** & **System Type** & **Error** \\ \hline Design A & 0.2190 & 0.0542 & \(-\)0.0566 & 2.8346 & Type I & 0.068 \\ Design B & 0.2390 & 0.0562 & \(-\)0.1761 & 2.8332 & Type I & 0.040 \\ Design C & 0.3206 & 0.0675 & \(-\)1.0643 & 4.6404 & Type I & 0.016 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical information of the \(f_{u,18}\) for the three experimental designs.  
Figure 9: Histogram of the number of sampled data at each operating condition. (**a**) \(\zeta=3\); (**b**) \(\zeta=5\); (**c**) \(\zeta=7\).  
an acceptable level, especially for the validation of computational models of safety-related and mission-critical systems.  
Future works are suggested in two folds. First, the adequacy of the proposed method will be evaluated after implementing to a real system. This paper employed a numerical example to demonstrate the effectiveness of the proposed method. Second, further improvement of RAED will be made to account for the effect of a modeling errors on RAED. Experimental data can be collected at the condition where the prediction capability of computational models is dependent on modeling errors. The modeling errors are another source for failing model validation, which was ignored in this study.  
Conceptualization, B.C.J.; formal analysis, Y.-H.S.; funding acquisition, B.C.J. and H.O.; investigation, S.H.L.; methodology, B.C.J.; project administration, B.C.J.; resources, Y.C.H.; writing--original draft, B.C.J.; writing--review and editing, H.O. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No.20171520000250, No.20162010104420), and partially supported by the main project of Korea Institute of Machinery and Materials (Project Code: NK213E).  
The authors declare no conflict of interest.