Abstract
This paper proposes a new stochastic model updating method to update structural models based on the improved cross-model cross-mode (ICMCM) technique. This new method combines the stochastic hybrid perturbation-Galerkin method with the ICMCM method to solve the model updating problems with limited measurement data and uncertain measurement errors. First, using the ICMCM technique, a new stochastic model updating equation with an updated coefficient vector is established by considering the uncertain measured modal data. Then, the stochastic model updating equation is solved by the stochastic hybrid perturbation-Galerkin method so as to obtain the random updated coefficient vector. Following that, the statistical characteristics of the updated coefficients can be determined. Numerical results of a continuous beam show that the proposed method can effectively cope with relatively large uncertainty in measured data, and the computational efficiency of this new method is several orders of magnitude higher than that of the Monte Carlo simulation method. When considering the rank deficiency, the proposed stochastic ICMCM method can achieve more accurate updating results compared with the cross-model cross-mode (CMCM) method. An experimental example shows that the new method can effectively update the structural stiffness and mass, and the statistics of the frequencies of the updated model are consistent with the measured results, which ensures that the updated coefficients are of practical significance.
Highlights
As an important numerical method, the finite element (FE) modeling is widely used in engineering
It can be found that the probability density functions (PDF) curves of the hybrid perturbation-Galerkin model updating method (HPG)-improved cross-model cross-mode (ICMCM) method are in a very good agreement with those of the measured frequencies, the PDF curves of the updated frequencies calculated by the proposed HPGICMCM method are closer to the PDF curves of the measured frequencies than those by the HPG-cross-model cross-mode (CMCM) method
ICMCMmethod methodtotothe thestochastic stochasticdomain, domain, this mainly including the establishment and solution of the stochastic model updating equamainly including the establishment and solution of the stochastic model updating equations. This new method sufficiently uses the advantage of the ICMCM method, which can tions
Summary
As an important numerical method, the finite element (FE) modeling is widely used in engineering. Based on the existing CMCM method, Liu [22] proposed the ICMCM method, which makes full use of measurement data to further increase the number of updating equations. These CMCM methods are only involved in deterministic FE model updating. Different from the abovementioned stochastic model updating methods, Huang et al [12] recently proposed a hybrid perturbation-Galerkin model updating method (HPG), which is of high accuracy and efficiency for model updating. The updating results of an experimental beam show that the new method can effectively update the stiffness and mass of the beam, and the statistical results of the updated frequencies are consistent with the measured results
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