基于静位移和多指标的贝叶斯模型修正方法

Bayesian model updating method based on static displacement and multiple indices

提出了一种新的基于静力数据的贝叶斯模型修正方法,用静力灵敏度方程和位移残差建立了多修正指标的待修正参数的后验概率密度函数,然后用马尔科夫链蒙特卡罗抽样方法获取修正参数样本,以实现对修正参数后验概率密度函数的估计,并得到结构修正参数的最可能值.另外,为了提高抽样过程中计算效率,引入随机响应面代理模型计算结构静力位移.数值算例表明:提出的方法能在结构静力位移测量数据具有不确定性的情况下,准确修正结构参数.修正结果的精度和稳定性优于传统的基于静力灵敏度方程的方法和基于位移残差的智能优化方法.铝合金简支梁的静力实验数据进一步验证了提出的方法对实际结构进行随机模型修正的有效性.

A new Bayesian model updating method based on static data was proposed.The posterior probability density function of the structural updating parameters was established using static sensitivity equation and displacement residuals,and then the Markov Chain Monte Carlo sampling method was used to obtain the sample of the updating parameters to realize the estimation of the posterior probability density function of the updating parameters and the most probable value of the structural updating parameters were obtained.In addition,in order to improve the efficiency of the sampling process,the random response surface proxy model was introduced to calculate the static displacement of the structure.Numerical examples show that the proposed method can accurately update the structural parameters under the uncertainty of the structural static displacement measurement data.The accuracy and stability of the updating results are better than those of the traditional methods based on static sensitivity equations and the intelligent optimization method based on displacement residuals.The static experimental data of an aluminum alloy simply supported beam further verify the effectiveness of the proposed method for randomly updating the actual structure.