The accuracy of all 200 numerical outputs against the experimental data #10 was plotted in Fig.3. The RMS error values were calculated using the 3rd floor acceleration outputs. The highest accuracy was shown in Run #114, and the lowest one was in Run #174 corresponding to damping values of ( ]2, ]4) = (0.046, 0.070) and ( ]2, ]4) = (0.0122, 0.0013), respectively. By examining these two responses when overlaid on the experimental data they were attempting to predict as shown in Fig.4, it can be seen that the different damping parameters mainly influence the amplitude of response as mentioned in the previous chapter. Fig.3. RMSE plots of all 200 numerical data (a) The highest RMSE numerical run #114 (b) The lowest RMSE numerical run #174 Fig.4. Overlays of numerical (Red) and experimental (Blue) time-histories from linear system 4.2.2. Response feature extraction and Mahalanobis distance comparison Response features selected for validating the damping parameters from random and linear responses here were then the peak amplitude and the standard deviation. The two values were extracted from outputs in the 2nd and 3rd floors producing a four-dimensional feature vector. Figure 5 is the corresponding Mahalanobis distance plot. Notice that the blue dots are the experimental baseline distribution, and the black dots are distances of the 200 numerical runs. Accurate and inaccurate numerical runs, which showed 10% lowest and highest RMSE values in Fig.3, are indicated by red and green circles, respectively. Seeing this figure, the accurate numerical runs have Mahalanobis distance values that predominantly fall within the experimental baseline distribution. In addition, the numerical runs that show the minimum/maximum Mahalanobis distance agree with Run #114 and #174, respectively as identified by an arrow. It can be said that the Mahalanobis distance derived by using the peak amplitude and standard deviation response features, has appropriate sensitivity to the timehistories; to be appropriated features for validation of the damping parameters. The consistency check was then also carried out to confirm the effectiveness of this method for the statistical model validation. Consistency here meant that the parameter set that showed the low Mahalanobis distance provided accurate responses to any input forces. Additional twenty numerical runs were created by using each of twenty input force data in Exp. data #1~#20. Notice that the damping 160
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