基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析  

BAYESIAN-BASED NONLINEAR MODEL UPDATING AND DYNAMIC RELIABILITY ANALYSIS

作　　者：丁雅杰 王佐才[1,2,3] 辛宇 戈壁 袁子青 DING Ya-jie;WANG Zuo-cai;XIN Yu;GE Bi;YUAN Zi-qing(Department of Civil Engineering,Hefei University of Technology,Hefei,Anhui 230009,China;Anhui Engineering Technology Research Center for Civil Engineering Disaster Prevention and Mitigation,Hefei,Anhui 230009,China;Anhui Engineering Laboratory of Infrastructural Safety Inspection and Monitoring,Hefei University of Technology,Hefei,Anhui 230009,China)

机构地区：[1]合肥工业大学土木与水利工程学院,安徽合肥230009 [2]土木工程防灾减灾安徽省工程技术研究中心,安徽合肥230009 [3]安徽省基础设施安全检测与监测工程实验室,安徽合肥230009

出　　处：《工程力学》2022年第12期13-22,59,共11页Engineering Mechanics

基　　金：国家自然科学基金优秀青年科学基金项目(51922036);安徽省重点研发计划项目(1804a0802204);中央高校基本科研业务费专项资金项目(JZ2020HGPB0117)。

摘　　要：提出一种基于贝叶斯推理的非线性结构模型修正方法,同时考虑激励的随机性,建立了复合随机振动系统的动力可靠度分析方法。利用实测结构动力响应主分量的瞬时特征参数作为非线性指标构建似然函数,结合拒绝延缓自适应(Delayed Rejection and Adaptive Metropolis,DRAM)算法和高斯过程替代模型实现了非线性结构模型修正及其参数的不确定性量化。根据首次超越破坏准则,利用广义概率密度演化方法,分别对仅考虑激励随机性的确定性模型和同时考虑结构参数与激励不确定性的复合随机振动模型进行动力可靠度分析,并利用蒙特卡洛随机抽样方法验证了计算结果的准确性。研究结果表明:基于振动响应瞬时特征参数的贝叶斯推理方法能够快速、准确地实现结构的非线性模型修正及其参数的不确定性量化。与具有初始设计参数名义值的确定性模型相比,考虑参数不确定性的复合随机模型的动力可靠度总体偏低,因此,在结构安全评估中应考虑非线性模型参数不确定性的影响,使评估结果更加安全、可靠。A Bayesian-based method for nonlinear model updating is proposed.Considering the randomness of excitation,a dynamic reliability analysis method of compound random vibration systems is established.The instantaneous characteristic parameters of the principal components decomposed from the measured structural dynamic response are considered as the nonlinear index that is applied to construct the likelihood function.The DRAM-Gaussian process model combined method is further performed for the uncertainty quantification of the calibrated model parameters.According to the first transcendental failure criterion,the generalized probability density evolution method is used to calculate the structural dynamic reliability.Both the deterministic nominal model and the compound random vibration system are considered.The accuracy of the calculated reliability is subsequently verified by Monte Carlo simulation.The results show that the Bayesian-based measured instantaneous characteristics can be used to quantify the uncertainty of the nonlinear model parameters with the advantages of high accuracy and efficiency.In addition,the dynamic reliability of the compound random model that considers the uncertainty of structural parameters is generally lower than that of the deterministic nominal model.Thus,it will make the evaluation results safer and more reliable by considering the effects of model parameters uncertainties in structural safety state assessment.

关 键 词：贝叶斯理论 非线性模型修正 瞬时特征参数 动力可靠度 复合随机振动 

分 类 号：TU311[建筑科学—结构工程]