The time-resolution was also recognized as an important factor for investigating the nonlinear phenomena. The parameters; Gap and ', greatly influenced the frequency and the amplitude of impact events. Therefore, the feature that is sensitive to the number of impact events (i.e., the skewness for random response), had great sensitivity to the accuracy of numerical output as shown in the table. However, this feature alone could not be used in the detail validation of Gap and ' because the dynamic amplitude behaviour during the impact events was not well captured by this feature. The response feature that provided a time-resolution measure was the Holder exponent [5]; however, there was tradeoff between the feature dimension and the time-resolution. Table 2. Examples of response features for validating nonlinearity modeling (Blue: experiment, Red (accurate): numerical with '=0.5mm, Green; numerical with '=0.1mm) Feature description and definition: output xi Response feature plot AR model parameter i p j j i j i x x H D ¦ 1 ˆ Skewness (Basic statistics) ¦ N i x i x x x N S 1 3 3 1 1 P V Holder exponent 4. Statistical model validation using Mahalanobis distance comparison method As mentioned in previous section, if multiple aspects of the system response are of interest, the model validation process may require comparing several features that have sensitivity to each uncertain parameter. A multivariate analysis technique was then expected to be useful in this process. Worden et al. had proposed a Mahalanobis distance outlier detection method for comparing multivariate feature vectors for the application of statistical structural damage detection in their previous study [6]. Applicability of the same approach for the statistical model validation was investigated in this study. 158
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