结合同伦代理模型的静力贝叶斯随机模型修正

为了使用随机静力位移测量数据对结构有限元模型进行修正，并保证计算效率，提出了一种同伦代理模型与贝叶斯抽样方法结合的随机模型修正方法。首先以结构静力位移构建目标函数，然后采用延缓拒绝自适应抽样算法对修正参数的后验概率密度进行估计。抽样过程中，采用同伦代理模型替代有限元模型对结构静力位移进行计算。数值算例和试验结果表明：进行变截面梁的有限元模型修正时，与二次响应面模型相比，在静力贝叶斯模型方法中利用同伦代理模型，修正参数的后验概率密度能更准确地复现结构随机响应，使修正后的结构随机响应与测量结果概率密度函数更加吻合。即使在随机测量误差的变异系数较大、先验信息与真实修正参数之间差异较大时，所提方法仍能够快速得到修正参数的后验概率密度，使修正参数计算的结构随机位移响应与测量结果的概率密度函数保持一致。同伦代理模型结合贝叶斯抽样算法能在概率框架内快速而准确地对结构进行随机模型修正。

Static Bayesian stochastic model updating combining homotopy meta-model

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.