Modeling Error Estimation and Response Prediction of a 10-Story Building Model Through a Hierarchical Bayesian Model Updating Framework

Song, Mingming; Behmanesh, Iman; Moaveni, Babak; Papadimitriou, Costas

doi:10.3389/fbuil.2019.00007

Cited by 28 publications

(19 citation statements)

References 47 publications

(42 reference statements)

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“…where c is a constant value. Considering the covariance matrix θθ Σ to be symmetric, the optimization will involve (24) Note that the MAP estimation of θ μ can be calculated directly from Eq. (23) giving:…”

Section: Uncertainty Quantificationmentioning

confidence: 99%

“…In structural dynamics, Behmanesh et al [14] have developed a hierarchical framework to model and consider the variability of modal parameters over dissimilar experiments. This framework has found extensive applications in uncertainty quantification and propagation of dynamical models based on experimental modal data when they are updated and calibrated under modeling errors [23][24][25]. Nagel and Sudret [26,27] have proposed a unified multilevel Bayesian framework for calibrating dynamical models for the special case of having noise-free vibration measurements.…”

Section: Introductionmentioning

confidence: 99%

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Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework

Sedehi¹,

Papadimitriou²,

Katafygiotis³

2020

Probabilistic Engineering Mechanics

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In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconceptions in the Bayesian framework since it is absolutely robust with respect to the modeling assumptions and the observed data. Rather, this issue has deep roots in users' inability to develop an appropriate class of probabilistic models. This paper bridges this significant gap, introducing a novel Bayesian hierarchical setting, which breaks time-history vibrational responses into several segments so as to capture and identify the variability of inferred parameters over multiple segments. Since computation of the posterior distributions in hierarchical models is expensive and cumbersome, novel marginalization strategies, asymptotic approximations, and maximum a posteriori estimations are proposed and outlined under a computational algorithm aiming to handle both uncertainty quantification and propagation tasks. For the first time, the connection between the ensemble covariance matrix and hyper distribution parameters is characterized through approximate estimations. Experimental and numerical examples are employed to illustrate the efficacy and efficiency of the proposed method. It is observed that, when the segments correspond to various system conditions and input characteristics, the proposed method delivers robust parametric uncertainties with respect to unknown phenomena such as ambient conditions, input characteristics, and environmental factors.

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Section: Uncertainty Quantificationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework

Sedehi¹,

Papadimitriou²,

Katafygiotis³

2020

Probabilistic Engineering Mechanics

Self Cite

View full text Add to dashboard Cite

show abstract

“…This assumption ignores the stiffness correlations of different structural components. Alternatively, a full covariance matrix

can be estimated to characterize the stiffness correlations in off-diagonal terms, as it is done in some recent studies [ 53 , 57 , 58 ]. The error function distribution is often assumed to be zero-mean, i.e.,

, which neglects error bias and causes an inflated estimation of error covariance

in applications with error bias.…”

Section: Uncertainty Quantification and Propagation Through Hierarmentioning

confidence: 99%

“…An important feature of hierarchical Bayesian model updating is the capability to provide accurate and realistic confidence bounds on response predictions, by propagating the estimated structural parameters variability and error function uncertainty, as shown in Figure 2 . When response predictions of unobserved quantities (where error function estimate is not available) are required, two strategies can be adopted: (1) only consider and propagate the structural parameters variability into response predictions when error function is relatively small and negligible [ 44 , 53 ]; (2) extend the error function to unobserved degrees of freedom (DOFs) as proposed by Song et al [ 58 ] and validated through a numerical study. As mentioned previously, in most civil structure applications, error function uncertainty must be included in model-predictions to fully capture the measurement variability.…”

Section: Uncertainty Quantification and Propagation Through Hierarmentioning

confidence: 99%

“…The appropriate selection and tuning of the proposal distribution might improve the acceptance rate in some cases, but it becomes more challenging for sampling very peaked posterior PDFs [ 23 , 30 ]. Gibbs sampling is shown to be computationally efficient for this task, as it transforms the joint posterior PDF into individual conditional PDFs where the samples are taken from, as shown in [ 40 , 57 , 58 , 62 ]. Since conditional PDFs have smaller dimensions, the sampling acceptance rate can be adjusted to the desired range.…”

Section: Uncertainty Quantification and Propagation Through Hierarmentioning

confidence: 99%

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Accounting for Modeling Errors and Inherent Structural Variability through a Hierarchical Bayesian Model Updating Approach: An Overview

Song

Behmanesh

Moaveni

et al. 2020

Sensors

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Mechanics-based dynamic models are commonly used in the design and performance assessment of structural systems, and their accuracy can be improved by integrating models with measured data. This paper provides an overview of hierarchical Bayesian model updating which has been recently developed for probabilistic integration of models with measured data, while accounting for different sources of uncertainties and modeling errors. The proposed hierarchical Bayesian framework allows one to explicitly account for pertinent sources of variability such as ambient temperatures and/or excitation amplitudes, as well as modeling errors, and therefore yields more realistic predictions. The paper reports observations from applications of hierarchical approach to three full-scale civil structural systems, namely (1) a footbridge, (2) a 10-story reinforced concrete (RC) building, and (3) a damaged 2-story RC building. The first application highlights the capability of accounting for temperature effects within the hierarchical framework, while the second application underlines the effects of considering bias for prediction error. Finally, the third application considers the effects of excitation amplitude on structural response. The findings underline the importance and capabilities of the hierarchical Bayesian framework for structural identification. Discussions of its advantages and performance over classical deterministic and Bayesian model updating methods are provided.

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Fisher information‐based optimal sensor locations for output‐only structural identification under base excitation

Ghosh

Mukhopadhyay

2022

Structural Contr & Hlth

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A method is developed to determine optimal sensor locations for output-only identification of modal and stiffness parameters under a class of non-stationary base excitation. These optimal locations are obtained by maximizing the determinant of the associated Fisher information matrix (FIM), such that the optimally located sensors would contain the maximum information about the parameters of interest. To obtain the FIM, the input-output relation is formulated in a random vibration framework. The input base excitation, modeled as a uniformly modulated random process, is characterized through an evolutionary power spectrum. Under such motions, the sum of eigenvalues of the output power spectrum, considered as measurement parameter, is shown to follow an exponential distribution. The FIM is then shown to comprise of the sum of these eigenvalues along with the sensitivities of the output power spectrum to the parameters of interest.Analytical expressions are derived for the different response sensitivities. The approach is illustrated through numerical simulations using a laterallytorsionally coupled building, and experimental data from shake table tests. The effect of unobserved modes is discussed. It is seen that, while stiffness depending on unobservable modes are not identified or have high estimation uncertainty, the optimal sensor set-ups for identifying a stiffness and for identifying the modes most sensitive to that stiffness are not necessarily the same. The importance of optimal sensor locations in damage detection is also highlighted through the shake table tests. It is shown that the estimation uncertainties in structural parameters and damage severities are least for optimally located sensors.

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Modeling Error Estimation and Response Prediction of a 10-Story Building Model Through a Hierarchical Bayesian Model Updating Framework

Cited by 28 publications

References 47 publications

Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework

Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework

Accounting for Modeling Errors and Inherent Structural Variability through a Hierarchical Bayesian Model Updating Approach: An Overview

Fisher information‐based optimal sensor locations for output‐only structural identification under base excitation

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