42 Robust Expansion of Experimental Mode Shapes Under Epistemic Uncertainties 425 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 sc αˆ Fig. 42.6 Robustness curve: nominal design 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 E2/E2 0 E4/E4 0 Fig. 42.7 Design space and the 24 tested design points modeled with an info-gap model of uncertainty. Hence, the fixed robust design should be as close as possible to this curve in order to protect the model against uncertainty effects. Figure 42.9 proposes the robustness of the most robust fixed designs. For instance, if the experience feedback or the expert judgment pinpoints that the error in the uncertain parameters corresponds with an horizon of uncertainty closed to 0.5, it would be preferable to use the design 24 in order to minimize the effect of lack of knowledge on the system model predictions. To conclude, the Fig. 42.10 shows the variations of the most robust parameters when the horizon of uncertainty increases. This curve can indicate which calibrated parameters are preferable to use in order to have a model less sensitive to lack of knowledge for each horizon of uncertainty. Once again, if the model is known within the horizon of uncertainty of O˛ D0:2, one should prefer to use the model with the parameter p DŒ0:75I 1 p0 with the aim to protect the model against uncertainties (cf. Fig. 42.10). 42.4 Conclusions The objective of this work is to develop and assess a robust mode shape ECRE-based expansion based on a nominal model in presence of large epistemic uncertainty. This proposed approach relies on a robust model calibration to minimize the impact of lack of knowledge in the model on expansion errors. After a state of the art concerning both expansion methods and model calibration techniques, the formulation is presented. An academical application is then shown to illustrate the potential gains
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