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首页> 外文期刊>Applied Mathematical Modelling >A Bayesian finite element model updating with combined normal and lognormal probability distributions using modal measurements
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A Bayesian finite element model updating with combined normal and lognormal probability distributions using modal measurements

机译：使用模态测量结合正态和对数正态概率分布的贝叶斯有限元模型更新

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摘要

The present work is associated with Bayesian finite element (FE) model updating using modal measurements based on maximizing the posterior probability instead of any sampling based approach. Such Bayesian updating framework usually employs normal distribution in updating of parameters, although normal distribution has usual statistical issues while using non-negative parameters. These issues are proposed to be dealt with incorporating lognormal distribution for non-negative parameters. Detailed formulations are carried out for model updating, uncertainty-estimation and probabilistic detection of changes/damages of structural parameters using combined normal-lognormal probability distribution in this Bayesian framework. Normal and lognormal distributions are considered for eigen-system equation and structural (mass and stiffness) parameters respectively, while these two distributions are jointly considered for likelihood function. Important advantages in FE model updating (e.g. utilization of incomplete measured modal data, non-requirement of mode-matching) are also retained in this combined normal-lognormal distribution based proposed FE model updating approach. For demonstrating the efficiency of this proposed approach, a two dimensional truss structure is considered with multiple damage cases. Satisfactory performances are observed in model updating and subsequent probabilistic estimations, however level of performances are found to be weakened with increasing levels in damage scenario (as usual). Moreover, performances of this proposed FE model updating approach are compared with the typical normal distribution based updating approach for those damage cases demonstrating quite similar level of performances. The proposed approach also demonstrates better computational efficiency (achieving higher accuracy in lesser computation time) in comparison with two prominent Markov Chain Monte Carlo (MCMC) techniques (viz. Metropolis-Hastings algorithm and Gibbs sampling).
机译：目前的工作与贝叶斯有限元（FE）模型更新相关联，该模型使用基于最大化后验概率的模态测量代替了任何基于采样的方法。这种贝叶斯更新框架通常在参数更新中采用正态分布，尽管在使用非负参数时正态分布通常存在统计问题。建议将这些问题纳入非负参数的对数正态分布。使用此贝叶斯框架中的组合正态-对数正态概率分布，为模型更新，不确定性估计和结构参数的变化/损坏的概率检测进行了详细的表述。本征系统方程和结构（质量和刚度）参数分别考虑正态分布和对数正态分布，而似然函数则共同考虑这两个分布。在这种基于正态-对数正态分布的组合提出的有限元模型更新方法中，有限元模型更新的重要优势（例如，利用不完整的测量模态数据，不需要模式匹配）也得以保留。为了证明该方法的有效性，考虑了具有多个损伤情况的二维桁架结构。在模型更新和随后的概率估计中观察到令人满意的性能，但是发现性能水平随损坏情况的增加而减弱（通常）。此外，针对那些表现出相当相似性能水平的损坏案例，将这种提出的有限元模型更新方法的性能与基于正态分布的典型更新方法进行了比较。与两种著名的马尔可夫链蒙特卡洛（MCMC）技术（即Metropolis-Hastings算法和Gibbs采样）相比，该方法还展示了更高的计算效率（在更短的计算时间内实现了更高的精度）。

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