Bayesian updating and identifiability assessment of nonlinear finite element models
Bayesian updating and identifiability assessment of nonlinear finite element models
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DOI：
10.1016/j.ymssp.2021.108517
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发表时间：
2021-11-11
影响因子：
8.4
通讯作者：
Conte, Joel P.
中科院分区：
文献类型：
--
作者：
Ramancha, Mukesh K.;Astroza, Rodrigo;Conte, Joel P.
利用非线性有限元(FE)模型进行工程系统的结构健康监测和损伤预测(DP)是一种很有前途和吸引力的方法。通常，有限元模型包含未知或已知的参数，具有很大程度的不确定性。需要使用从物理系统测量的数据来估计/更新/校准这些参数。模型更新/校准的贝叶斯范式很有吸引力，因为它使用严格的概率框架，考虑了现实世界中存在的众多不确定性来源。然而，将贝叶斯方法应用于大型土木结构系统的非线性有限元模型在计算上是非常困难的。此外，有限元模型参数的不可辨识性给模型更新过程带来了挑战。本文以具体的土木工程试验台--松坪混凝土重力坝为例，对非线性有限元模型进行了贝叶斯模型修正和可识别性分析。在递归模式下使用无迹卡尔曼滤波(UKF)进行模型更新，在批处理模式下使用过渡马尔科夫链蒙特卡罗(TMCMC)方法进行模型更新。讨论了大型非线性有限元模型修正的各种方法在适用性和计算上的局限性。然后使用局部和全局方法对模型进行了可辨识性和灵敏度分析。利用局部灵敏度与Fisher信息矩阵相结合的局部实用可辨识性分析来评估参数空间中某一局部区域的参数可辨识性。由于目前尚无一种评估全局实用可辨识性的方法，本文采用了基于方差的全局灵敏度分析(Sobol方法)。可辨识性和灵敏度分析结果被用来选择要包括在模型更新阶段的参数。
A promising and attractive way of performing structural health monitoring (SHM) and damage prognosis (DP) of engineering systems is through utilizing a nonlinear finite element (FE) model. Often, FE models contain parameters that are unknown or known with significant level of uncertainty. Such parameters need to be estimated/updated/calibrated using data measured from the physical system. The Bayesian paradigm to model updating/calibration is attractive as it accounts, using a rigorous probabilistic framework, for numerous sources of uncertainties existing in the real-world. However, applying Bayesian methods to nonlinear FE models of large-scale civil structural systems is computationally very prohibitive. Additionally, non-identifiability of FE model parameters poses challenges in the model updating process. This paper presents Bayesian model updating and identifiability analysis of nonlinear FE models with a specific testbed civil structure, Pine Flat concrete gravity dam, as illustration example. Model updating is performed in the recursive mode using the unscented Kalman filter (UKF) and in the batch mode using the transitional Markov chain Monte Carlo (TMCMC) method. Limitations in terms of applicability and computational challenges of each method for model updating of large-scale nonlinear FE models are addressed and discussed. Identifiability and sensitivity analyses of the model are then performed using local and global methods. Local practical identifiability analysis using local sensitivity in conjunction with the Fisher information matrix is used to assess the parameter identifiability in a certain local region in the parameter space. Due to the nonexistence of a method to assess global practical identifiability, variance-based global sensitivity analysis (Sobol's method) is used herein. Identifiability and sensitivity analysis results are used to choose the parameters to be included in the model updating phase.