Sampling methods for solving Bayesian model updating problems: A tutorial

Lye, Adolphus; Cicirello, Alice; Patelli, Edoardo

doi:10.1016/j.ymssp.2021.107760

Cited by 91 publications

(57 citation statements)

References 187 publications

(243 reference statements)

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“…Uniform priors were used for both the stiffness (100Nm/rad to 103 Nm/rad) of the rotational springs and location (0.17m to 0.19m) of the rotational spring. The joint posterior distribution of 2 k and 1 L is calculated using two Bayesian model updating techniques [16]: Sequential Monte Carlo (SMC) sampling and the Transitional Markov Chain Monte Carlo (TMCMC). In the SMC sampling approach [16] the samples obtained from the prior were reused in all possible sensor locations to reduce the amount of forward simulations needed and to investigate how the bias resulting from this approach could affect the calculation of the utility functions.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The joint posterior distribution of 2 k and 1 L is calculated using two Bayesian model updating techniques [16]: Sequential Monte Carlo (SMC) sampling and the Transitional Markov Chain Monte Carlo (TMCMC). In the SMC sampling approach [16] the samples obtained from the prior were reused in all possible sensor locations to reduce the amount of forward simulations needed and to investigate how the bias resulting from this approach could affect the calculation of the utility functions. The results obtained with this implementation of SMC were compared with the result obtained using the unbiased TMCMC [20] that required new simulations each time a possible sensor location was considered.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Probability density functions are used to model the uncertain model parameters in the Bayesian inference framework [5,16]. The prior knowledge on the uncertain parameters before any measurements or data is obtained, is described by the prior density function ( )…”

Section: Bayesian Frameworkmentioning

confidence: 99%

“…Hence, it is important to obtain accurate estimations of both location (median or mean) and scale (interquartile range or standard deviation) of the posterior [13]. Most frequently, it is not possible to express the posterior distributions with a closed form, so computational methodologies are used to obtain samples from the posterior or to approximate it [16][17][18][19][20][21]. In this work, the samplingbased model updating techniques are used.…”

Section: Bayesian Frameworkmentioning

confidence: 99%

“…In this work, the samplingbased model updating techniques are used. Specifically, the Sequential Monte Carlo (SMC) [16] sampling and the Transitional Markov Chain Monte Carlo (TMCMC) [20] are chosen to infer the two physical parameters of the case study investigated.…”

Section: Bayesian Frameworkmentioning

confidence: 99%

See 4 more Smart Citations

On the Investigation of the Effect of Population Uncertainty on Optimal Sensor Locations

Igea¹,

Chatzis²,

Cicirello³

2021

4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering

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Structural Health Monitoring uses data collected from sensors placed on structures to determine their operating condition and whether maintenance is required. Often, optimal sensor placement strategies are used to find the optimal locations for the identification of their modal properties, structural parameters and/or abnormal behaviours under the influence of model and measurement uncertainty. An approach that has been frequently used to solve the problem of sensor placement is the Bayesian experimental design. This approach chooses the locations using the data measured by the sensors to reduce the prior uncertainty of the parameters that are being inferred. The Bayesian experimental design minimizes the uncertainty of the parameters to be inferred through the use of metrics called utility functions. Most of these metrics are based on functions of the posterior distribution. In this paper, the use of three utility functions (Bayesian D-posterior precision, Bayesian A-posterior precision, and Expected Information Gain) is investigated for the problem of sensor placement.The case study chosen consists of a beam with translational and rotational springs connected to the ground subject to an impulsive load. The goal of the analysis is to select the most informative position of a sensor in order to update the distribution of two uncertain physical parameters of the beam based on natural frequencies extracted using the Eigensystem Realization Algorithm. It is shown that for the case investigated, the three utility functions yield the same optimal sensor location.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Bayesian Frameworkmentioning

confidence: 99%

Section: Bayesian Frameworkmentioning

confidence: 99%

Section: Bayesian Frameworkmentioning

confidence: 99%

See 3 more Smart Citations

On the Investigation of the Effect of Population Uncertainty on Optimal Sensor Locations

Igea¹,

Chatzis²,

Cicirello³

2021

4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering

Self Cite

View full text Add to dashboard Cite

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Experimental model updating of slope considering spatially varying soil properties and dynamic loading

Wang,

Ouyang,

Fragkoulis

et al. 2024

Earthquake Engineering and Resilience

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The widespread threat posed by slope structure failures to human lives and property safety is widely acknowledged. Additionally, natural soil often displays spatial variability due to geological deposition and other factors. Therefore, predicting the seismic response of slopes subjected to ground motions and inversely analyzing the spatial distribution of soils remains an unresolved issue. In the present work, a shaking table experimental test is first designed and carried out, in which a soft‐soil slope dynamic system is established. To capture the seismic response of the soft‐soil slope, specifically the experimental characteristic of acceleration and soil pressure response in both spatial domain and time domain, a series of sensors were pre‐embedded in the slope. Subsequently, a model updating approach is proposed for slope seismic analysis that incorporates spatial variability of soil. In addition, to enhance computational efficiency, the dimensionality reduction of Karhunen–Loève expansion method is introduced to reduce inverse analysis parameters. On the basis of 34 samples collected from experimental data, it is shown that near‐fault pulse‐like ground motions deliver greater concentrated energy, causing more severe damage to slope structures, especially the topsoil layer. Furthermore, using data obtained from a shaking table test subjected to ground motion Recorded Sequence Number 158H1 from the Pacific Earthquake Engineering Research Center NGA‐West2 database as an example, it is also shown that the proposed approach demonstrates high accuracy in predicting the spatial distribution of the maximum shear modulus in soil slope dynamic systems. The present work not only addresses the challenges posed by mainshock–aftershock effects but also highlights the potential of model updating approaches to enhance the understanding of slope behavior under seismic loading conditions.

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Stochastic finite element model updating through Bayesian approach with unscented transform

Zhang

2022

Structural Contr & Hlth

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Finite element (FE) model updating is important and challenging. To address the issues of ill-conditioning and nonuniqueness, stochastic approaches have been developed for calibrating model parameters and associated uncertainties. Markov chain Monte Carlo (MCMC) methods have been widely used for stochastic model updating by providing a straightforward way to infer the posterior probability density function (PDF) using a sequence of random samples. However, the inherent nature relying on a large number of sampling points to approximate the posterior PDF of model parameters limits their application. In this paper, a Bayesian approach with unscented transform is investigated to perform stochastic model updating in a computational friendly way. Rather than using a large number of randomly chosen sampling points, the proposed approach selects a minimal set of sampling points to represent the PDF of model parameters. On the basis of the unscented transform, this approach effectively explores the distribution of measurements, from which model parameters and associated uncertainties are updated. Numerical simulation of a reinforced concrete beam is presented to show that the proposed approach can achieve similar model updating performance as the MCMC methods. The proposed Bayesian approach is further applied to update the FE model of a real-world cable-stayed bridge and provide quantitative assessment of the predication accuracy.

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Sampling methods for solving Bayesian model updating problems: A tutorial

Cited by 91 publications

References 187 publications

On the Investigation of the Effect of Population Uncertainty on Optimal Sensor Locations

On the Investigation of the Effect of Population Uncertainty on Optimal Sensor Locations

Experimental model updating of slope considering spatially varying soil properties and dynamic loading

Stochastic finite element model updating through Bayesian approach with unscented transform

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