Mahalanobis distance comparison procedure was carried out as that used in the damping parameters validation study. Even though some response features that were expected to be sensitive to the impact event; such as skewness, kurtosis, and time-series model parameters, the Mahalanobis distances from the most accurate numerical runs (as assess by RMSE) never distributed in the same order of the experimental baseline distribution. One main reason for these results was that the two parameters; Gap and ', were strongly correlated and response features that could have sensitivity to each of two parameters independently had to be used. Figure 8 is the parameter set plot, which indicates all parameter sets sampled in the creation of numerical runs. In this figure, the red dots are accurate numerical runs, which show low RMSE values, and the green dots indicate inaccurate numerical runs. Although the gap was set to 0.1mm in the experiment, the runs calculated using smaller Gap but with large ' are also recognized as accurate outputs; i.e., two parameters are correlated. This observation indicates that the correlation of uncertain parameters in the numerical model also is a significant issue for the feature selection process. If such correlation cannot be prevented in the numerical model construction, it will require using response features that are independently sensitive to the validity of each uncertain parameter. Moreover, results here then confirmed that the Mahalanobis distance comparison method could be effectively applied to the statistical model validation only by using appropriate response features. (a) Accurate numerical run (b) Inaccurate numerical run Fig.7. Overlays of numerical (Red) and experimental (Blue) time-histories from nonlinear system Fig.8. Map of sampled parameter sets with indicating correlation between Gap and ' 5. Conclusions - When selecting features for the model validation, issues that must be considered are not only dimension of the feature vector and type of response, but also the difference in sources of variability between experimental and numerical outputs. When using some features that require a fitting procedure, this variability can influence the feature’s sensitivity to the parameters of interest. 162
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