A residual-based Gaussian process model framework for finite element model updating

SUMMARYThis paper proposes an efficient metamodeling approach for UQ of complex system based on Gaussian process model (GPM). The proposed GPM-based method is able to efficiently and accurately calculate the mean and variance of model outputs with uncertain parameters specified by arbitrary probability distributions. Due to the use of GPM, the closed form expressions of mean and variance can be derived by decomposing high-dimensional integrals into one-dimensional integrals. This paper details on how to efficiently compute the one-dimensional integrals. When the parameters are either uniformly-or normally distributed, the one-dimensional integrals can be analytically evaluated, while when parameters do not follow normal or uniform distributions, this paper adopts the effective Gaussian quadrature technique for the fast computation of the one-dimensional integrals. As a result, the developed GPM method is able to calculate mean and variance of model outputs in an efficient manner independent of parameter distributions. The proposed GPM method is applied to a collection of examples. And its accuracy and efficiency is compared with Monte Carlo simulation (MCS), which is used as benchmark solution. Results show that the proposed GPM method is feasible and reliable for efficient UQ of complex systems in terms of the computational accuracy and efficiency.

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“…When parameter x follows normal or uniform distributions, the aforementioned integral may be analytically evaluated ; see as follows:

\begin{matrix} I & = \int N_{x} (ζ, ϑ^{2}) p (x) dx \\ = \{\begin{matrix} \int {scriptN}_{x} ((), ζ, ϑ^{2}) {scriptN}_{x} ((), ξ, θ^{2}) dx & if x \sim scriptN ((), ξ, θ^{2}), \\ \frac{1}{(\overset{x}{false} - \underset{x}{false})} \int {scriptN}_{x} ((), ζ, ϑ^{2}) dx & if x \sim scriptU (\overset{x}{false}, \underset{x}{false}) . \end{matrix} \\ = \{\begin{matrix} {scriptN}_{ζ} ((), ξ, ϑ^{2} + θ^{2}) & if x \sim scriptN ((), ξ, θ^{2}), \\ \frac{1}{(\overset{x}{false} - \underset{x}{false})} ([], normalΦ ((), \frac{\overset{x}{false} - ζ}{ϑ}) - normalΦ ((), \frac{\underset{x}{false} - ζ}{ϑ})) & if x \sim scriptU (\overset{x}{false}, \underset{x}{false}) \end{matrix} \end{matrix}

…”

Section: Efficient Uncertainty Quantification Using Gpmmentioning

confidence: 99%

“…When parameter x follows normal or uniform distributions, the aforementioned integral may be analytically evaluated [1,32]; see as follows:…”

Section: Analytical Solutionmentioning

confidence: 99%

An efficient metamodeling approach for uncertainty quantification of complex systems with arbitrary parameter probability distributions

Wan

Ren

Todd

2016

Int. J. Numer. Meth. Engng

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“…The application of hybrid GA has obvious advantages over the classic GA method. When updating the high-fidelity FE model of the complex bridge structure, the high-resolution FE model is constructed on the platform of the FE packages, whereas the advanced optimization techniques, such as the GA method, can be easily implemented in numerical software such as MATLAB (Wan and Ren 2015). Sanayei et al (2015) and Sipple and Sanayei (2014) developed a frequencyresponse function-based parameter-estimation method for model calibration of a full-scale bridge; they then developed a robust multipleresponse structural parameter-estimation method for the automated FE model updating.…”

Section: Introductionmentioning

confidence: 99%

Structural Identification of a Concrete-Filled Steel Tubular Arch Bridge via Ambient Vibration Test Data

Zhou

Zhang

et al. 2017

J. Bridge Eng.

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Structural identification (St-Id) is an effective structural evaluation approach for health monitoring and performance-based engineering. However, various uncertainties may significantly influence the reliability of St-Id. This paper presents ambient vibration measurements to develop a baseline model for a newly constructed arch bridge over Hongshui River in Guangxi, China. In this study, modal parameter identification was performed using the random decrement (RD) technique together with the complex mode indicator function (CMIF) algorithm, and the results were compared with those from stochastic subspace identification (SSI). First, a three-dimensional (3D) finite-element (FE) model was constructed to obtain the analytical frequencies and mode shapes. Then, the FE model of the arch bridge was tuned to minimize the difference between the analytical and experimental modal properties. Three artificial intelligence algorithms were used to calibrate uncertain parameters: the simple genetic algorithm (SGA), the simulated annealing algorithm (SAA), and the genetic annealing hybrid algorithm (GAHA). The simulation results showed that GAHA exhibited the best performance in mathematic function tests among the three methods and that the large-scale arch bridge could be efficiently calibrated using a hybrid strategy that combines SGA and SAA. To verify the admissibility of the calibration procedure, a sensitivity analysis was performed for the Young's modulus of the steel members, and the relative error for the static deformation of the bridge deck was determined. Finally, to verify the accuracy of the results, a multimodel updating method based on Bayesian statistical detection was analyzed for further validation. Through a detailed St-Id study using precise modeling, operational modal analysis (OMA), and the artificial intelligence algorithms, the authors confirmed the accuracy of the updated FE model for further structural performance prediction.

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“…Three kinds of metamodel are widely been used: response surface methodology (RSM), Kriging method and radial basis function (RBF), and they have been well studied in some fields, such as structural static model updating [12], structural dynamic model updating based on modal parameters [13], structural damage identification [14,15], structural reliability analysis [16]. Some researcher also gave the comparison [17,18] and recommendation [19] of the main metamodels.…”

Section: Introductionmentioning

confidence: 99%

Structural dynamic model updating based on Kriging model using frequency response data

Wang¹,

Wang²,

Zhao³

2016

J. vibroeng.

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Metamodel technique is attracting more and more attention in structural dynamic model updating. In this paper, an attempt is made to explore the effectiveness of Kriging method for acceleration frequency response function based model updating. A Kriging model is constructed based on the input variables selected by F-test method specially, which is applied to the results of design of experiment. The response of design of experiment is obtained based on the errors between acceleration response curves of analytical model and experimental model. Two examples of representative structure are discussed, the comparison of updated results of different metamodel shows that a less error of updated results can be obtained based on Kriging model, and the updated analytical model has a good prediction capability. It can be concluded that the Kriging model is suitable for the frequency response function based model updating.

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A residual-based Gaussian process model framework for finite element model updating

Cited by 57 publications

References 31 publications

An efficient metamodeling approach for uncertainty quantification of complex systems with arbitrary parameter probability distributions

An efficient metamodeling approach for uncertainty quantification of complex systems with arbitrary parameter probability distributions

Structural Identification of a Concrete-Filled Steel Tubular Arch Bridge via Ambient Vibration Test Data

Structural dynamic model updating based on Kriging model using frequency response data

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