Stochastic Structure Nonlinear Model Updating Based On Modular Bayesian Inference

When engineering structures are subjected to extreme loads such as typhoons and earthquakes during service,they tend to show strong nonlinear behavior.At the same time,when performing structural nonlinear model updating,they are inevitably affected by various uncertainties such as measurement noise,model errors,and discretization,resulting in uncertainty in the results of nonlinear model updating.This thesis focuses on the actual engineering requirements of structural health monitoring,and considers the effects of various uncertainties to carry out the study of nonlinear model updating for stochastic structures under strong loads.This thesis utilizes Variational Mode Decomposition(VMD)to extract the principal components of structural dynamic response,and combines Hilbert transform to extract the instantaneous characteristic parameters of the principal components to construct nonlinear indicators.The constructed nonlinear indicators are further used for stochastic structural nonlinear model updating under the Bayesian inference framework.The Transitional Markov Chain Monte Carlo(TMCMC)algorithm is combined with a Gaussian process model for accelerating the parameter posterior distribution solution.In order to consider the effects of model error and measurement error on structural nonlinear model updating at the same time,the whole model updating process is divided into three modules based on Bayesian inference,and a modular Bayesian-based stochastic structural nonlinear model updating method is proposed.The feasibility and robustness of the proposed method are verified by numerical cases and experiments as well.The main research contents of the thesis are as follows.(1)The development and research status of deterministic structural model updating and stochastic structural model updating are described.The instantaneous characteristic parameters of time-varying nonlinear systems are identified based on the VMD algorithm,and the feasibility of the VMD algorithm is further verified with numerical examples.(2)From the source of structural uncertainty,the likelihood function required for structural model updating based on Bayesian inference is derived,and the posterior probability distribution of the updating parameters based on different measured data conditions is obtained by combining the prior information with the likelihood function.(3)A stochastic structural nonlinear model updating method based on modular Bayesian inference is proposed by combining the TMCMC algorithm and Gaussian process model.The design variables are introduce to create the model error function,and the likelihood function that considers model and measurement errors is further constructed based on the Bayesian inference.(4)The feasibility of the proposed method is verified by numerical simulations of a three-story nonlinear frame structure,and a three-span continuous girder bridge.The proposed method has good robustness by considering different noise levels,number of response points,and range of design variable changes.(5)The shake table test of a five-story frame structure is conducted to verify the proposed method,and the stochastic nonlinear model is updated by using the shaking table test data.The calculated response of the updated model agrees well with the measured response,which demonstrates that the proposed method can effectively achieve stochastic nonlinear structural model updating.