Abstract
The posterior density of structural parameters conditioned by the measurement is obtained by a differential evolution adaptive Metropolis algorithm (DREAM). The surface of the formal log-likelihood measure is studied considering the uncertainty of measurement error to illustrate the problem of equifinality. To overcome the problem of equifinality, the first two derivatives of the log-likelihood measure are proposed to formulate a new informal likelihood measure for the sake of improving the accuracy of the estimator. Moreover, the proposed measure also reduces the standard deviation (uncertain range) of the posterior samples. The benefit of the proposed approach is demonstrated by simulations on identifying the structural parameters with limit output data and noise polluted measurements.
Highlights
Recent years witness the increasing desire of Bayesian estimation for structural parametric system when quantifying the inevitable uncertainties, such as measurement error or structural model error and so forth, as is reviewed by Simoen et al [1]
Gibbs sampling and transitional Markov chain Monte Carlo (TMCMC) were used by Ching and Chen [4] to obtain the posterior PDF of parameters
If the measurement error is considered as obeying the Gaussian distribution with a constant variance, σj2, the posterior PDF in (2) is as follows:
Summary
Recent years witness the increasing desire of Bayesian estimation for structural parametric system when quantifying the inevitable uncertainties, such as measurement error or structural model error and so forth, as is reviewed by Simoen et al [1]. To solve higher dimensional problems, Muto and Beck [3] developed an adaptive Markov chain Monte Carlo (MCMC) simulation for the Bayesian model updating. Cheung and Beck [5] used a hybrid Monte Carlo method, known as the Hamiltonian Markov chain, to solve higher dimensional model updating problems. Because of the noise corrupted measurement, the surface of the prediction error lies in a hypersurface of a multidimensional parametric space It will cause the surface of the probability density for the posterior sequences to have multiple regions of attraction and numerous local optima. It inevitably yields a biased estimator (no matter what is called maximum likelihood estimator, ML, or maximum a posteriori estimator, MAP). Numerical examples of a linear structural system are presented, with which the effectiveness and efficiency of the proposed method are investigated
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