parameter set that showed the lowest Mahalanobis distance in Fig.5 was used in all calculations. Figure 6 (a) is the RMSE plot of additional twenty numerical runs, indicated in green points, presented with that of previous 200 runs. It was clearly observed that comparably high accuracies were obtained in all runs. Calculated Mahalanobis distances from the twenty runs are also presented in Fig.6 (b). All of them are thus distributed in the same Mahalanobis distance order as that of the experimental distribution. These results indicate that the parameter set that shows a low Mahalanobis distance can constantly provide accurate numerical outputs and vice versa. It can then be concluded that the statistical validity of uncertain parameters can be evaluated by this Mahalanobis distance comparison method. Fig.5. Mahalanobis distance plot for validating damping parameters (a) RMSE plots using the accurate parameter set (b) Mahalanobis distance distributions Fig.6. Consistency check of the Mahalanobis distance comparison method 4.2.3. Discussion: difficulty in validating correlated uncertain parameters The success in the damping parameters validation presented in the previous section was realized by appropriate response feature selection. This need for appropriate response feature selection was further confirmed in the nonlinearity modeling parameters validation study. The uncertain parameters were Gap and '; however, it was difficult to find appropriate features that could assess the validity of each parameter independently. In the validation, the experimental baseline distribution was created from twenty experimental data acquired under the same random excitation as that in the linear system data acquisition. Notice that the clearance between the bumper and the suspended column (= Gap) was set to 0.1mm in all measurements. However, the clearance adjustment was carried out in each data acquisition using a feeler gauge. This measurement method led to variability in actual conditions related to Gap and '. Fourhundred numerical runs were then created using sampled parameter sets (Gap, '). The same 161
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