Studies On Finite Element Model Updating Method Considering Parameter Uncertainty

In recent decades, finite element model updating (FEMU) technology has generallybeen researched and applied. However, presently the vast majority of model updatingmethods belong to deterministic categories and will lose their feasibility whenconsidering the influence of uncertainty, which largely confines their applied scopes andeffects. Therefore, model updating methods considering parameter uncertainty havebeen valued in recent years. But there are few research results relating to this topic.Meanwhile, the construction and solution of updating problem involving theprobabilistic and the non-probabilistic analyses are relatively complicated, whichusually lead to large amount of calculation. Duo to it, this thesis aims to developstochastic repsonse surface models (SRSMs) and interval repsonse surface models(IRSMs) based model updating methods respectively from probabilistic andnon-probabilistic aspects for the purpose of simplifying the updating process, benefitingthe efficiency and accuracy of model updating. The former accomplishes uncertaintyanalysis based on the theories of probability and statistics, while the latter is viewed as asupplement and perfection of probabilistic method which is mainly based on the intervalanalysis method. First of all, the relationships between structural uncertain parametersand corresponding responses are correlated by explicit SRSMs. Then by establishing amodel updating process, parameter statistical characteristics are evaluated. A two-phaseupdating strategy is proposed in this thesis, namely updating the deterministic part ofparameters (mean) firstly, and then updating the uncertain part (standard deviation), bywhich the subjective selection of weights is avoided and the number of unkownvariables is decreased which benefits the convergence speed of the inverse optimizationprocess. Meanwhile, SRSMs are reconstructed during the optimization iteration processto avoid the construction and analysis of sensitivity matrices, which considerablyimproves the computational efficiency in the precondition of maintaining the predictionaccuracy of parameter uncertainty. Secondly, this thesis firstly proposes a concept ofIRSMs. By expanding and transforming the traditional response model and substitutingthe deterministic variables with interval number, the finial IRSMs are obtained, bywhich the interval operation is directly carried out. IRSMs largely avoid thephenomenon of interval expansion, and at the same time interval parameter sensitivitycalculation is directly accomplished through the interval response surface expression, which could simplify the interval optimization problem, and complete the intervalmodel updating within of the framework of interval analysis. In addition, this thesis alsoproposes sensitivity analysis methods respectively based on stochastic response surfaceand interval analysis theory from probabilistic and non-probabilistic aspects. The formerbased on stochastic response surface expression and differential derivative method,proves that the coefficients of the first order items represent the main effects ofparameters. The latter uses the subinterval analysis method for estimating parametersensitivity, which is suitable for unknowing probability distribution of parameters andstill valid for the condition of extreme of response existing in the parameter ranges.Therefore, it extends the application range of existing methods. Finally, the feasibilityand reliability of the proposed methods have been verified by some different numericalexamples and experiment data.