Research On The Modification Of Finite Element Model Based On Bayesian Method

Structural finite element model is the base of static and dynamic response analysis,structural health monitoring and optimization design. But because of the geometryerrors, material parameter error and grid discretion error, finite element model needs tobe amended in order to match with the actual structure. Due to the presence of structuralmaterial parameters randomness, uncertain spatial location, changeability constructionquality, as well as the measured data and the uncertainty in the finite element model, theresults of finite element model updating is full of uncertainty, however, the existingcorrection method based on deterministic models is unable to consider the impact ofthese uncertainties.Based on Bayesian statistical theory and Markov Monte Carlosimulation (MCMC), this paper establishes Bias finite element model updating on thebasis of design parameters and proposes regression analysis based on the relevant vectormachine to overcome inefficiencies, enabling large-scale civil engineering structuresrectification work finite element model.The main contents and main conclusions are as follows:①Aiming at the prior distribution selection of Bayesian statistical theorysusceptible to human factors issues, the paper deduces a prior distribution based on theprinciple of maximum entropy principle of selecting. When the design parameters to becorrected mean and standard deviation are known, the maximum information entropy ofthe prior distribution is Gaussian; When the change interval to be corrected of designparameters is known only, the maximum entropy and Bayesian distribution areassumed to be uniformly distributed. Then a discussion to the impact of using differentmodel selected is taken by numerical simulation. The results show that with the increaseof tests times, the uniform prior distribution is limit state of Gaussian prior distribution.②Based on Bayesian statistical theory, the paper derives posterior probabilitydensity function of design parameters to be corrected, and calculates the value of theposterior probability density function by using the Metropolis-Hastings algorithm, inorder to establish a Bayesian uncertainty FEM model correction method. By CharpyNumerical examples show that: the standard MH algorithm simulation test sample cansolve Bayesian model updating of corrected the design parameters,but there are easystagnation defects in the sample.③The DRAM Bayesian algorithm is introduced to the finite element model updating via an adaptive algorithm (AM) to achieve self-adjust the sampling step;refusal by delaying (DR) algorithm improves the probability of accepting a new sample,which effectively overcome the standard MH algorithm high-dimensional parameterconvergence to be slow or unable to fix the problem of convergence. Five-storyshear-type frame structure numerical example shows that: DRAM algorithm is able tocalculate successfully the posterior probability density function of more than amendedof design parameters. The modified cantilever model test results shows that: Bayesianmodel updating DRAM algorithm makes that modal frequency error is reduced from10%to less than1%, while the modal correlation coefficient increased from a minimumof0.9MAC to around1.0, reaching a better correction effect; and in the same condition,the modal frequency correction algorithm DRAM maximum error is0.8%compared tothe first-order optimization algorithm2.56%smaller, to achieve a more accuratecorrection effect.④The inverse problem of model modification for the prevalence low calculationefficiency problem, the response calculation of finite element model softwareimplementation by the finite element turn into mathematical regression by RVM, thepaper proposes Bayesian fast calculation method based on relevance vector machine(RVM), and factor of influence on RVM regression accuracy are analyzed, and thesimulation results show that modified speed raises around60times, which realizes fastBayesian model updating.⑤Excitation four two-span steel frame structure experiment by pulse load asingle point, using frequency domain decomposition method for identifying the framestructure frequencies and mode shapes, and then based on the measured modalinformation, the initial finite element model is carried on Bayesian correction. Thecorrection results show that: Bayesian model updating, so that the error term reducedfrom24%of the initial model to about2%, indicating that the Bayesian model can beapplied to the model updating of actual structure.