Finite element model updating using objective-consistent sensitivity-based parameter clustering and Bayesian regularization

Bartilson, Daniel Thomas; Jang, Jinwoo; Smyth, Andrew W.

doi:10.1016/j.ymssp.2018.05.024

Cited by 38 publications

(29 citation statements)

References 33 publications

(97 reference statements)

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“…To the authors' knowledge, this approach has not been previously used for evidence estimation in FE model updating and presents a step forward for deterministic model updating. Previous work by the authors implemented Bayesian regularization, but also optimized

β

, which is inappropriate for evidence estimation and model evidence comparison, as will be discussed below.…”

Section: Model Evidence Estimation and Bayesian Regularizationmentioning

confidence: 99%

“…At this stage, the optimal value of

β

can be found by evidence maximization, giving

β = false(m - γ false) false/ false(2 E_{r}^{MP} false)

, as in previous work, but this has several disadvantages. Foremost, the likelihood function will no longer be model‐independent since

β

will depend on the optimized model error

E_{r}^{MP}

.…”

Section: Model Evidence Estimation and Bayesian Regularizationmentioning

confidence: 99%

“…The utilized Levenberg–Marquardt algorithm is described in Algorithm 1, including the scheme for iteratively evaluating the hyperparameters

λ

α

, and

γ

. Further detail on this derivation is available in the authors' previous work …”

Section: Levenberg–marquardt Minimization Algorithmmentioning

confidence: 99%

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Sensitivity‐based singular value decomposition parametrization and optimal regularization in finite element model updating

Bartilson

Jang

Smyth

2020

Struct Control Health Monit

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Summary Model updating is used to reduce error between measured structural responses and corresponding finite element (FE) model outputs, which allows accurate prediction of structural behavior in future analyses. In this work, reduced‐order parametrizations of an underlying FE model are developed from singular value decomposition (SVD) of the sensitivity matrix, thereby improving efficiency and posedness in model updating. A deterministic error minimization scheme is combined with asymptotic Bayesian inference to provide optimal regularization with estimates for model evidence and parameter efficiency. Natural frequencies and mode shapes are targeted for updating in a small‐scale example with simulated data and a full‐scale example with real data. In both cases, SVD‐based parametrization is shown to have good or better results than subset selection with very strong results on the full‐scale model, as assessed by Bayes factor.

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β

, which is inappropriate for evidence estimation and model evidence comparison, as will be discussed below.…”

Section: Model Evidence Estimation and Bayesian Regularizationmentioning

confidence: 99%

“…At this stage, the optimal value of

β

can be found by evidence maximization, giving

β = false(m - γ false) false/ false(2 E_{r}^{MP} false)

, as in previous work, but this has several disadvantages. Foremost, the likelihood function will no longer be model‐independent since

β

will depend on the optimized model error

E_{r}^{MP}

.…”

Section: Model Evidence Estimation and Bayesian Regularizationmentioning

confidence: 99%

See 1 more Smart Citation

Sensitivity‐based singular value decomposition parametrization and optimal regularization in finite element model updating

Bartilson

Jang

Smyth

2020

Struct Control Health Monit

Self Cite

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“…Use of this model updating technique also determined an optimal set of model parameters of the FE model; this minimized the differences between the measured properties and those of the FE model. A detailed explanation as to how the FE bridge model considered in this study was modified can be found in the authors' previous work, which focuses on developing algorithmic tools for sensitivity‐based parameterization methods and model updating techniques. Most model updating techniques are based on an underlying assumption that sensor measurements are deterministic so that they are used to infer the state of a structure (parameters of an FE model).…”

Section: System Identification and Fe Model Of A Major Long‐span Bridgementioning

confidence: 99%

Data‐driven models for temperature distribution effects on natural frequencies and thermal prestress modeling

Jang

Smyth

2019

Struct Control Health Monit

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In vibration-based damage detection, it is fundamentally important to distinguish between changes in the dynamics of a structure and those related to environmental effects. Modal properties of structures are widely used as damage-sensitive features and indicate changes in physical properties due to structural damage or degradation. However, civil structures such as bridges are influenced by various operational and environmental conditions (such as traffic, wind, humidity, and, most importantly, temperature), and these variables also alter the modal properties of structures. Changes in modal properties caused by environmental effects can mask the effect of structural damage, resulting in unreliable structural damage assessments. It is thus fundamentally important to understand the relationship between environmental effects and modal properties. In this paper, a full-scale finite element (FE) model is used in a simulation-based study to investigate the effects of temperature distribution on natural frequencies. Two approaches for modeling the temperature effects on natural frequencies (thermal prestress imposed at an element level and temperature-dependent Young's modulus) are implemented in the FE model, and results are compared. Then, temperature profiles of the model are hypothetically simulated. These simulation results are used to develop a linear model and the three most popular machine learning models to reproduce the effects of temperature distribution on natural frequencies. Finally, a comprehensive comparison is made between the performances of these data-driven models. KEYWORDS machine learning, regression model, system identification, temperature effects on natural frequencies, thermal prestress Struct Control Health Monit. 2020;27:e2489.wileyonlinelibrary.com/journal/stc

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“…In structural vibration modal analysis, the eigenvalue (square of frequency) and eigenvector (mode shape) are the two important parameters and their sensitivities are often used in many engineering problems such as structural vibration control [1][2][3][4][5][6], optimization design [7][8][9], model updating [10][11][12][13][14] and damage identification [15][16][17]. From the current research literature, the calculation formula of eigenvalue sensitivity is simple, but the calculating formula for eigenvector sensitivity is complicated.…”

Section: Introductionmentioning

confidence: 99%

An Exact Method for Calculating the Eigenvector Sensitivities

Yang

Peng

2020

Applied Sciences

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Eigenvector sensitivities are often used in many engineering problems such as structural vibration control, optimization design, model updating and damage identification. So far, modal superposition method and Nelson’s method are the two main methods for exactly calculating eigenvector sensitivities. However, modal superposition method has a great limitation in applications because it needs all the eigenvectors in its calculation. Although Nelson’s method does not need to use all the eigenvectors, there is no unified sensitivity calculation formula for each eigenvector. In this paper, a new exact method for calculating the eigenvector sensitivity is proposed. The explicit expressions for the first-order and second-order sensitivities of eigenvectors are derived, and strict proof is given. The developed eigenvector sensitivity formulas are simple and convenient in programming. The proposed method is as powerful as Nelson’s method, but much more easy to use. Two numerical examples are used to demonstrate the proposed method and the results show that the developed eigenvector sensitivity formulas are exact and reliable.

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Finite element model updating using objective-consistent sensitivity-based parameter clustering and Bayesian regularization

Cited by 38 publications

References 33 publications

Sensitivity‐based singular value decomposition parametrization and optimal regularization in finite element model updating

Sensitivity‐based singular value decomposition parametrization and optimal regularization in finite element model updating

Data‐driven models for temperature distribution effects on natural frequencies and thermal prestress modeling

An Exact Method for Calculating the Eigenvector Sensitivities

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