2 Bayesian Uncertainty Quantification in the Development of a New Vibration Absorber Technology 23 start stop calculate mean curves of test data calculate mean curves of model data quantify test data variability quantify model data variability select threshold calculate the variance and add data variability acceptable? collect and normalize data calculate difference curves of test data Bayesian interval hypothesis testing no yes Fig. 2.3 Procedure of Bayesian uncertainty quantification 0 10 20 30 0 0.5 1 1.5 0 10 20 30 0 0.5 1 1.5 0 10 20 30 0 0.5 1 1.5 FREQUENCY in Hz FREQUENCY in Hz FREQUENCY in Hz TRANSMISSIBILITY / PHASE / FORCE / experiment model A model B model C Fig. 2.4 Analytical, simulation and experimental results. Transmissibility (left), phase shift (middle) and force (right) normalized with occurring maximum of experimental test data Vmax, T, ψmax, T, Fmax, T For this purpose, the deviation of the repeated measurements from the mean value is calculated, the error matrix reshaped and the mean value for each output variable ∗v formed and listed in the diagonal matrix. The same applies to the diagonal matrix of the repetition error of the model results. The next step is to create the difference matrixD=T −Mbetween the mean matrix of the tests T and the model M. The covariance D = 1 n n i=1 (di −μD)(di −μD) T (2.9)
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