28 Applying Uncertainty Quantification to Structural Systems: Parameter Reduction for Evaluating Model Complexity 253 Fig. 28.10 The R 2 results from(a–f) for cases 1–6, respectively, and the colors labeled 1–8 represent the outputs from Fig. 28.2 by ¯yp, while the mean response value for a given parameter level i is represented by ˆyp,i. The full-factorial level Lis used to evaluate the sensitivity of the response features to a given parameter. In this study, a two-level full-factorial designL=2was performed by sampling a single value at both the 2.5% lower and 97.5% upper limits from each variable’s 95% confidence bound. The confidence bounds for each regression coefficient were calculated using the standard deviation values provided in Tables 28.2, 28.3, 28.6, and 28.7. As a result, this design frame has L N numerical evaluations with a scaled output R 2 ∈ [0, 100] provided for each of the eight response features. The value of R 2 was then used to evaluate if a parameter could be kept constant using its mean value or if it needed to vary based onR 2. For example, R 2 =0 indicated that a variable had negligible or no influence on the value of a selected response feature; whereas, a value of R 2 = 100 indicated that a variable contributed all of the variability to the selected response feature. For consistency, the additional payload mn and drop height hf were held constant for all full-factorial evaluations. Figure 28.10 indicates the results for all the cases in Table 28.5. The columns presented in Fig. 28.10 indicate the R 2 sensitivity of all the response features to each set of parameters. As can be seen, each parameter for each case appears to have some influence on at least one of the subject outputs. To evaluate which parameters exhibited the least influence, a weighted total was calculated by taking the average R 2 for each parameter. If a parameter was found to have a weighted R 2 value of less than 2%, that parameter was considered to be non-influential and thrown out of the calibration space (i.e. held constant at its mean value). As can be seen in Table 28.8, each of the cases from Table 28.5 has at least one parameter that
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