To update the structural finite element model through stochastic static displacement measurement data and maintain the computational efficiency

we proposed a stochastic model updating method based on homotopy meta-model and Bayesian sampling method. First

the objective function was constructed by using the static displacement of the structure

and the delayed rejection adaptive sampling algorithm was used to estimate the posterior probability density of the updated parameters. In the process of sampling

the homotopy meta-model was adopted instead of the finite element model to calculate the static displacement of the structure. Numerical examples and test results show that when updating the finite element model of variable cross-section beam

as opposed to the quadratic response surface model

by incorporating the homotopy meta-model into the static Bayesian model method

the posterior probability density of the updated parameters could reproduce the stochastic response of the structure more accurately

making the probability density function of the stochastic response of the updated structure more consistent with that of the measured results. Even when the coefficient of variation of the stochastic measurement error was large and the difference between the prior information and the real updated parameters was large

the proposed method could quickly obtain the posterior probability density of the updated parameters

so that the probability density function of the structural stochastic displacement response calculated by the updated parameters was consistent with that of the measured results. The homotopy meta-model combined with Bayesian sampling algorithm can update the stochastic model of the structure quickly and accurately within the probability framework.