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

Wan, Hua‐Ping; Ren, Wei‐Xin; Todd, Michael D.

doi:10.1002/nme.5305

Cited by 33 publications

(24 citation statements)

References 37 publications

(56 reference statements)

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“…To reduce the computational burden, the GP metamodel is used to map the relationship between the LBS and the longitudinal displacements under the thermal effects. GP metamodel is fully characterized by the mean and covariance functions. In the following, it considers the zero‐mean function and squared exponential covariance function expressed by

C ((), boldx, x^{'}) = η^{2} \exp ([], - \frac{1}{2} \sum_{k = 1}^{d} {(\frac{x_{k} - x_{k}^{'}}{{normalℓ}_{k}})}^{2}),

where x k and

x_{k}^{'}

are the k th component of x and x ′, respectively; d is the length of x ; η 2 is the signal variance; and ℓ is the characteristic length scale.…”

Section: Lbs Identification Using Metamodel‐based Model Updatingmentioning

confidence: 99%

“…To reduce the computational burden, the GP metamodel is used to map the relationship between the LBS and the longitudinal displacements under the thermal effects. GP metamodel [29][30][31] is fully characterized by the mean F I G U R E 8 Displacement versus temperature of the bridge deck on April 15, 2006 (a-d) and covariance functions. In the following, it considers the zero-mean function and squared exponential covariance function 32…”

Section: Gp Metamodelmentioning

confidence: 99%

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Condition analysis of expansion joints of a long‐span suspension bridge through metamodel‐based model updating considering thermal effect

Xia

Wan

et al. 2020

Struct Control Health Monit

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Summary Expansion joints of bridges are vulnerable to damage due to the thermal expansion and contraction, vehicle traffic, and so forth. Currently, the temperature–displacement relationship model may be the only qualitative method for condition evaluation of bridge expansion joints using the field monitoring data. The quantitative assessment based on the finite element model updating techniques is heavy computational burden and time consuming. Therefore, a Gaussian process (GP) metamodel‐based model updating method is proposed in this study and performed for the quantitative identification on the boundary condition of the expansion joints of Jiangyin Suspension Bridge using the long‐term displacement and temperature monitoring data. At first, the relationship between the longitudinal boundary stiffness (LBS) and structural temperature is formulated on the basis of thermal effects of the bridge deck. The range of LBS is approximately estimated by the regression coefficients from 1‐year monitoring data and is used as initial bounds for the subsequent model updating procedure. The GP metamodel is formulated to map the relationship between the LBS and the longitudinal displacements under the thermal effects. The LBS identification of the Jiangyin Suspension Bridge is performed within the fast‐running GP metamodel. The results show that the longitudinal displacements using the updated LBS are in good agreement with the measurements, which verifies the effectiveness of GP metamodel‐based model updating method in identifying the LBS of the long‐span suspension bridge.

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C ((), boldx, x^{'}) = η^{2} \exp ([], - \frac{1}{2} \sum_{k = 1}^{d} {(\frac{x_{k} - x_{k}^{'}}{{normalℓ}_{k}})}^{2}),

where x k and

x_{k}^{'}

are the k th component of x and x ′, respectively; d is the length of x ; η 2 is the signal variance; and ℓ is the characteristic length scale.…”

Section: Lbs Identification Using Metamodel‐based Model Updatingmentioning

confidence: 99%

“…To reduce the computational burden, the GP metamodel is used to map the relationship between the LBS and the longitudinal displacements under the thermal effects. GP metamodel [29][30][31] is fully characterized by the mean F I G U R E 8 Displacement versus temperature of the bridge deck on April 15, 2006 (a-d) and covariance functions. In the following, it considers the zero-mean function and squared exponential covariance function 32…”

Section: Gp Metamodelmentioning

confidence: 99%

Condition analysis of expansion joints of a long‐span suspension bridge through metamodel‐based model updating considering thermal effect

Xia

Wan

et al. 2020

Struct Control Health Monit

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“…where 〈•,•〉 defines the inner product; and δ mn represents the Kronecker delta that is one if m = n and zero otherwise. More details regarding formulation of the univariate orthogonal polynomials are referred to (Wan et al, 2017a).…”

Section: Analytical Gsa Using Pcementioning

confidence: 99%

Comprehensive sensitivity analysis of rotational stability of a super-deep underground spherical structure considering uncertainty

Wan

Zheng

Luo

et al. 2020

Advances in Structural Engineering

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Jiangmen Underground Neutrino Observatory central detector is located 700 m below the ground and also submerged into an ultrapure water pool. The main structure of the Jiangmen Underground Neutrino Observatory central detector is a hybrid spherical shell that is vulnerable to rotation under the buoyancy effect. The influences of the model parameters on the rotational stability of this complex and unique structure are investigated. Since the model parameters are inevitably subjected to many sources of uncertainties (e.g. manufacturing tolerances and geometrical imperfections), the parameter uncertainty is taken into account. In addition, linear and nonlinear rotational stabilities of this super-deep underground spherical structure are also under consideration. Specifically, the critical loading multiplier is used as the evaluation indicator of linear rotational stability and the load proportionality factor- θ curve is considered as the evaluation indicator of nonlinear rotational stability. The sensitivity of linear and nonlinear rotational stabilities to uncertain parameters is systematically studied in terms of univariate and multivariate global sensitivity analyses. The univariate global sensitivity analysis is able to evaluate the effects of uncertain parameters on each evaluation indicator, whereas multivariate global sensitivity analysis enables to assess the global influence of uncertain parameters on all evaluation indicators. A polynomial chaos expansion surrogate model is utilized to replace the time-consuming simulation model for analytical implementation of the univariate and multivariate global sensitivity analyses. The present polynomial chaos expansion-based univariate and multivariate global sensitivity analyses effectively and efficiently reveal the sensitivity of the rotational stability of this super-deep underground spherical structure to uncertain parameters, and provide a practical method for comprehensive sensitivity analysis of similar structures.

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“…Metamodelling techniques have recently shown great potential with respect to efficiency and accuracy in reliability analysis. The main idea of metamodelling is to firstly build a metamodel (also termed as response surfaces, or surrogate models), such as Kriging, support vector machines, and polynomial chaos expansions, based on a group of samples of input variables, also named as the training samples, and their model responses. Then classical reliability methods are adopted to assess failure probabilities by replacing the original model with the obtained metamodel.…”

Section: Introductionmentioning

confidence: 99%

A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations

Pan

Liu

et al. 2020

Num Anal Meth Geomechanics

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Summary Polynomial chaos expansions (PCEs) have been widely employed to estimate failure probabilities in geotechnical engineering. However, PCEs suffer from two deficiencies: (a) PCE coefficients are solved by the least‐square minimization method which easily causes overfitting issues; (b) building a high order PCE is often computationally expensive. In order to overcome the aforementioned drawbacks, the Bayesian regression technique is employed to evaluate PCE coefficients, which not only provides a sparse solution but also avoids overfitting. With the aid of the predictive means and variances given by Bayesian analysis, a learning function is proposed to sequentially select the most informative samples that are critical to build a PCE. This sequential learning scheme can highly enhance the computational efficiency of PCEs. Besides, importance sampling (IS) is incorporated into the sequential learning (SL)‐PCEs to deal with geotechnical problems with small failure probabilities. The proposed method of SL‐PCE‐IS is applied to three illustrative examples, which shows that the improved PCE method is more effective and efficient than the common PCEs method, leading to accurate estimations of small failure probabilities using fewer training samples.

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

Cited by 33 publications

References 37 publications

Condition analysis of expansion joints of a long‐span suspension bridge through metamodel‐based model updating considering thermal effect

Condition analysis of expansion joints of a long‐span suspension bridge through metamodel‐based model updating considering thermal effect

Comprehensive sensitivity analysis of rotational stability of a super-deep underground spherical structure considering uncertainty

A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations

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