基于贝叶斯理论的结构动力可靠度更新方法与分析

摘要

通过一种基于结构动力测试数据和贝叶斯理论的方法来更新结构可靠度。该方法考虑了结构可能受到的激励和结构模型及其参数的不确定性，利用结构在服役期间的动力测试数据，通过贝叶斯概率方法对结构参数进行了识别。利用拉普拉斯渐近估计解法，对仅根据设计条件得到的结构可靠度进行了更新。对受随机动荷载作用的某桁架结构在三种情况下的可靠度进行了计算：一为仅考虑荷载的随机性，二为考虑荷载的随机性和结构模型参数的先验分布，三为考虑荷载的随机性和结构模型参数的更新分布。比较了实际结构和有限元模型更新后的自振频率和振型，并对更新的可靠度计算结果进行了分析。结果表明，与确定性名义模型的失效概率相比，测点处自由度的更新失效概率与真实值较为接近；未测试自由度的更新失效概率可能与真实值差别较大；增加测点数不一定改善失效概率的更新效果。%An approach based on Bayesian theorem and structural vibration test data was presented for reliability updating.The approach takes account of uncertainties of the excitation,structural model and its parameters.Structural model parameters were identified based on the vibration test data and Bayesian parameter identification.According to Laplace asymptotic approximation,the dynamic reliability estimated purely in the light of design conditions was updated. The reliabilities of a truss structure subjected to dynamic random loading were calculated for three cases.Only the uncertainty of the loading was considered for the first case.The uncertainties of the loading and the prior probability distribution of model parameters were considered for the second case.The uncertainties of the loading and the updated probability distribution of model parameters were considered for the third case.Natural frequencies and mode shapes of the actual structure and the updated model were compared.Discussions about the updated reliabilities were made.The results show that the updated failure probability of the tested DOF agrees better with the actual value compared with that by deterministic nominal models.The updated failure probability of untested DOFs may deviate from the actual values. Increasing tested DOFs may have no effect on the updated failure probability.