Approximate Bayesian Computation for structural identification of ancient tie-rods using noisy modal data

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Probabilistic Engineering Mechanics Pub Date : 2024-07-01 DOI:10.1016/j.probengmech.2024.103674
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引用次数: 0

Abstract

Masonry arches and vaults are common historic structural elements that frequently experience asymmetric loading due to seismic action or abutment settlements. Over the past few decades, numerous studies have sought to enhance our understanding of the structural behavior of these elements for the purpose of preventive conservation. The assessment of the structural performance of existing constructions typically relies on effective numerical models guided by a set of unknown input parameters, including geometry, mechanical characteristics, physical properties, and boundary conditions. These parameters can be estimated through deterministic optimization functions aimed at minimizing the discrepancy between the output of a numerical model and the measured dynamic and/or static structural response. However, deterministic approaches overlook uncertainties associated with both input parameters and measurements. In this context, the Bayesian approach proves valuable for estimating unknown numerical model parameters and their associated uncertainties (posterior distributions). This involves updating prior knowledge of model parameters (prior distributions) based on current measurements and explicitly considering all sources of uncertainties affecting observed quantities through likelihood functions. However, two significant challenges arise: the likelihood function may be unknown or too complex to evaluate, and the computational costs for approximating the posterior distribution can be prohibitive. This study addresses these challenges by employing Approximate Bayesian Computation (ABC) to handle the intractable likelihood function. Additionally, the computational burden is mitigated through the use of accurate surrogate models such as Polynomial Chaos Expansions (PCE) and Artificial Neural Networks (ANN). The research focuses on setting up numerical models for simple structural systems (tie-rods) and inferring unknown input parameters, such as mechanical properties and boundary conditions, through Bayesian updating based on observed structural responses (modal data, strains, displacements). The main novelties of this research regard, on the one hand, the proposal of a methodology for obtaining a reliable estimate of the axial force in ancient tie-rods accounting for different sources of uncertainty and, on the other hand, the application of ABC to obtain the structural identification inverse problem solution.

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利用噪声模态数据进行古代拉杆结构鉴定的近似贝叶斯计算
圬工拱门和拱顶是常见的历史性结构构件,经常会因地震作用或台基沉降而承受不对称荷载。在过去的几十年里,许多研究都试图加强我们对这些构件结构行为的了解,以达到预防性保护的目的。对现有建筑结构性能的评估通常依赖于由一组未知输入参数(包括几何形状、机械特征、物理特性和边界条件)指导的有效数值模型。这些参数可以通过确定性优化功能进行估算,目的是尽量减小数值模型输出与测量的动态和/或静态结构响应之间的差异。然而,确定性方法忽略了与输入参数和测量结果相关的不确定性。在这种情况下,贝叶斯方法被证明对估计未知数值模型参数及其相关不确定性(后验分布)很有价值。这涉及根据当前测量结果更新模型参数的先验知识(先验分布),并通过似然函数明确考虑影响观测量的所有不确定性来源。然而,这其中存在两个重大挑战:似然比函数可能是未知的,或者过于复杂,难以评估;近似后验分布的计算成本可能过高。本研究采用近似贝叶斯计算(ABC)来处理难以处理的似然函数,从而解决了这些难题。此外,通过使用多项式混沌展开(PCE)和人工神经网络(ANN)等精确的代用模型,也减轻了计算负担。研究重点是为简单结构系统(拉杆)建立数值模型,并根据观测到的结构响应(模态数据、应变、位移),通过贝叶斯更新推断未知输入参数,如机械性能和边界条件。这项研究的主要创新点在于:一方面,提出了一种方法,用于获得古代拉杆轴向力的可靠估计值,并考虑到不同的不确定性来源;另一方面,应用 ABC 法获得结构识别逆问题解决方案。
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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
期刊最新文献
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