Bayesian calibration for dynamic parameters of dam

UQ with UQLab Community Q&A and How To
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Hello @felix,

I have some observations,

  1. The values for mean and standard deviation for 'E1', 'D1', 'E2'and 'D2' provided in the definition of the prior measure are almost the same as the values in the chart computed from the posterior density.
  2. Since your setings for the discrepancy are not copied to BayesOpts.Discrepancy, UQLab follows it default setings, see Section 2.2.5 of the UQLab Bayesian Inversion Manual. In your situations this yields that UQLab assume that the error is an unknown additive Gaussian discrepancy term, and the prior distribution for \sigma^2 is uniform on [0,137^2] in the error for the first frequency, and for the 2nd to 6th inteveral we have [0,157^2], [0,304^2], [0,380^2], [0,488^2] ,[0,620^2]. Considering the mean and the standard deviation resulting from these distributions one can deduce that they are quite similar to the corresponding values for sigma2 in the charts in your results one realizes that the values are quite similar,
  3. Combing point 1 and 2 it seems that the prior density and the posterior density are quite similar. So either the scheme has not converged yet as Paul-Remo Wagner has pointed as possibility (in view for your recent trace plots, I suggest to increase the number of steps ) or that the variation of the likelihood function is small, or that the likelihood shows large variations only in some region with quite small discrepancy values and the MCMC-scheme is not able to find this region since it is small compared to the domain considered in the computations.
  4. In view of the values for sigma2 discussed in point 2 it follows that noise added to the result of the model during the computation of the posterior density will quite large, leading to the large variation observed. (To be able to get plots to investigate the variations of the model output without noise, I suggest to update your UQLab version to 1.4.0 and to follow the instruction in my topic afterwards. )
  5. It seems that the model output at the mean of the posterior density (which is marked by mean in your plots) is a quite good approximation of the measurement. And since the mean of the posterior density is almost identical to the mean of your prior density this should also hold for this mean.
    Hence, I suggest to compare the Realfrequency vector with the output of the surrogate model (i.e. the output of uq_evalModel( myPCE,[1.5E9 2200 3e10 2400]); or uq_evalModel( myPCE,[1.5E9 ,2200, 3e10, 2400]);) and with the output of your finite element software at this point. And using this difference, one may get a better idea for the form of the discrepancy and the corresponding prior distribution, such that the likelihood function may show larger variations leading to posterior density being more different from the prior density.
    I thinks that it is problem if the discrepancies sizes for all components are independent and
    use therefore one discrepancy size for all components. But, I am not sure if this was really the best idea, since the size of different components differ such that maybe the size of the added noise should be proportional to the size of the measured value, but I am not sure. Maybe @paulremo has a some suggestion.
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