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    基于主成分分析的结构参数自适应降维贝叶斯更新方法

    Bayesian Updating Method with Adaptive Dimensionality Reduction for Structural Parameters Based on Principal Component Analysis

    • 摘要: 贝叶斯方法可充分利用监测数据更新结构参数及其概率分布.基于结构可靠度的贝叶斯更新(BUS)方法可将复杂的结构参数反分析问题转化为等效的结构可靠度问题,并借助子集模拟求解参数的后验分布.然而,在融合大量监测数据进行贝叶斯更新时,BUS方法所构建的失效区域非常小且形态复杂,严重影响子集模拟中条件样本的生成,导致后验分布推断中出现严重的样本贫乏问题.为此,提出了基于主成分分析(PCA)的自适应降维贝叶斯更新方法.该方法在子集模拟的每一层中,提前对种子样本进行PCA降维处理,从而减少后验分布推断过程中的重复样本,提高候选样本的接受率,克服样本贫乏问题.最后,通过结构梁的腐蚀劣化案例验证了提出方法的有效性.结果表明:该方法不仅能较好地求解融合大量监测数据的结构参数贝叶斯更新问题,还可有效缓解高维贝叶斯更新中出现的样本贫乏现象,为利用海量监测数据更新工程结构参数及其概率分布提供了有效途径.

       

      Abstract: Bayesian methods can fully utilize the monitoring data to update structural parameters and their probability distributions.The Bayesian Updating with Structural reliability (BUS) method transforms the complex inverse analysis of structural parameters into an equivalent structural reliability problem,which can then be solved using subset simulation to infer the posterior distribution of the structural parameters.However,when integrating a large amount of monitoring data to update the posterior statistics of structural parameters,the failure region formulated via the BUS method grows exceedingly narrow and intricate.This affects the generation of conditional samples in the subset simulation and further results in a significant sample impoverishment issue during the posterior distribution inference.To address this issue,a Bayesian updating method with adaptive dimensionality reduction based on Principal Component Analysis (PCA) is proposed.By applying PCA to reduce the dimensionality of seed samples at each subset simulation level,the proposed method reduces the generation of duplicate samples during the posterior distribution inference,increases candidate sample acceptance rates,and alleviates the sample impoverishment.Finally,the effectiveness of the proposed method is validated through the case study of a structural beam considering corrosion deterioration.The results indicate that the proposed method not only can effectively solve the Bayesian updating problem of structural parameters with the massive monitoring data,but also can overcome the sample impoverishment issue commonly encountered in the high-dimensional Bayesian updating,which offers an effective way to update the engineering structural parameters and their distributions with the integration of extensive monitoring data.

       

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