Efficient uncertainty propagation for parameterized p-box using sparse-decomposition-based polynomial chaos expansion

Liu, H.B.; Jiang, Chao; Xiao, Zhao

doi:10.1016/j.ymssp.2019.106589

Cited by 30 publications

(9 citation statements)

References 46 publications

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“…Constructed p-box for input variables, uncertainty in response could be propagated with a variety of approaches, such as nested Monte Carlo sampling (MCS) (Ferson and Ginzburg, 1996), optimization method (Liu et al, 2018), polynomial chaos expansion (Xiu and Karniadakis, 2003;Liu et al, 2020), etc. Usually, an efficient surrogate model is needed in uncertainty propagation for reducing the computational cost.…”

Section: Uq For Correlated Variablesmentioning

confidence: 99%

Uncertainty quantification for correlated variables combining p-box with copula upon limited observed data

Shen

Zang

Chen

et al. 2022

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PurposeFor fast calculation of complex structure in engineering, correlations among input variables are often ignored in uncertainty propagation, even though the effect of ignoring these correlations on the output uncertainty is unclear. This paper aims to quantify the inputs uncertainty and estimate the correlations among them acorrding to the collected observed data instead of questionable assumptions. Moreover, the small size of the experimental data should also be considered, as it is such a common engineering problem.Design/methodology/approachIn this paper, a novel method of combining p-box with copula function for both uncertainty quantification and correlation estimation is explored. Copula function is utilized to estimate correlations among uncertain inputs based upon the observed data. The p-box method is employed to quantify the input uncertainty as well as the epistemic uncertainty associated with the limited amount of the observed data. Nested Monte Carlo sampling technique is adopted herein to ensure that the propagation is always feasible. In addition, a Kriging model is built up to reduce the computational cost of uncertainty propagation.FindingsTo illustrate the application of this method, an engineering example of structural reliability assessment is performed. The results indicate that it may significantly affect output uncertainty whether to quantify the correlation among input variables. Furthermore, an additional advantage for risk management is obtained in this approach due to the separation of aleatory and epistemic uncertainties.Originality/valueThe proposed method takes advantage of p-box and copula function to deal with the correlations and limited amount of the observed data, which are two important issues of uncertainty quantification in engineering. Thus, it is practical and has the ability to predict accurate response uncertainty or system state.

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Section: Uq For Correlated Variablesmentioning

confidence: 99%

Uncertainty quantification for correlated variables combining p-box with copula upon limited observed data

Shen

Zang

Chen

et al. 2022

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“…The training set is generated for an auxiliary input vector X and least angle regression (LARS) is used for training. In case of parametric p-boxes, it is proposed in (Liu et al, 2020) to model the sparse PCE coefficients a α as quadratic polynomial functions of the parameters θ of the p-box and using a double-loop sampling for the propagation.…”

Section: Polynomial Chaos Expansions and Kriging Modelsmentioning

confidence: 99%

Engineering analysis with probability boxes: A review on computational methods

et al. 2021

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The consideration of imprecise probability in engineering analysis to account for missing, vague or incomplete data in the description of model uncertainties is a fast-growing field of research. Probability-boxes (p-boxes) are of particular interest in an engineering context, since they offer a mathematically straightforward description of imprecise probabilities, as well as allow for an intuitive visualisation. In essence, p-boxes are defined via lower and upper bounds on the cumulative distribution function of a random variable whose exact probability distribution is unknown. However, the propagation of p-boxes on model inputs towards bounds on probabilistic measures describing the uncertainty on the model responses is numerically still very demanding, and hence is subject of intensive research. In order to provide an overview on the available methods, this paper gives a state-of-the art review for the modelling and propagation of p-boxes with a special focus on structural reliability analysis.

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“…Here is a short list of methods currently being developed for the reduction of computational cost in imprecise probability models, in particular, for imprecise random fields: Approximations by inner and outer bounds [2,3,57,64]; propagation methods for p-boxes [11,12,48,62,63]; methods employing polynomial chaos expansion [31,43,52]; probability plots, an enhancement of the first order reliability method (FORM) proposed by [26]. A very efficient method appears to be advanced line sampling [8,56] that intertwines the two required loops and can reduce M and N simultaneously.…”

Section: Numerical Aspectsmentioning

confidence: 99%

Random set solutions to elliptic and hyperbolic partial differential equations

Karakašević,

Oberguggenberger

2021

Preprint

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The past decades have seen increasing interest in modelling uncertainty by heterogeneous methods, combining probability and interval analysis, especially for assessing parameter uncertainty in engineering models. A unifying mathematical framework admitting the combination of a wide range of such methods is the theory of random sets, describing input and output of a structural model by set-valued random variables. The purpose of this paper is to highlight the mathematics behind this approach. The modelling and computational implications are discussed and demonstrated with the help of prototypical partial differential equations-a scalar elliptic equation from elastostatics and hyperbolic systems arising in elastodynamics.

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Efficient uncertainty propagation for parameterized p-box using sparse-decomposition-based polynomial chaos expansion

Cited by 30 publications

References 46 publications

Uncertainty quantification for correlated variables combining p-box with copula upon limited observed data

Uncertainty quantification for correlated variables combining p-box with copula upon limited observed data

Engineering analysis with probability boxes: A review on computational methods

Random set solutions to elliptic and hyperbolic partial differential equations

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