Polynomial Regression Approaches Using Derivative Information for Uncertainty Quantification

Roderick, Oleg; Anitescu, Mihai; Fischer, Paul

doi:10.13182/nse08-79

Cited by 79 publications

(53 citation statements)

References 21 publications

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“…In aerospace engineering, a surrogate model for lift as a function of freestream parameters may be constructed in order to predict lift for a variety of flight conditions [14]. For nuclear engineering simulations, a safety metric such as peak fuel temperature can be represented by a surrogate model approximating the relationship between the safety metric and input physical parameters, such as crosssections, thermal conductivities, or heat transfer coefficients [22]. This relationship can then be used to estimate the uncertainty in the safety metric due to uncertain physical parameters.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, we proposed using information about the gradient ∇ x J( x) in the construction of the surrogate in order to reduce the number of baseline samples needed. Specifically, we constructed a surrogate by using a least squares polynomial regression approach that used both function and gradient values from J [22,23]. All the n x components of the gradient can be obtained by adjoint approaches at a cost that is at most five times [8], and, in many circumstances, substantially fewer times [22], the cost of one evaluation of J( x).…”

Section: Introductionmentioning

confidence: 99%

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Gradient-Enhanced Universal Kriging for Uncertainty Propagation

Lockwood

Anitescu

2012

Nuclear Science and Engineering

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In this work, we investigate the issue of providing a statistical model for the response of a computer model-described nuclear engineering system, for use in uncertainty propagation. The motivation behind our approach is the need for providing an uncertainty assessment even in the circumstances where only a few samples are available. Building on our recent work in using a regression approach with derivative information for approximating the system response, we investigate the ability of a universal gradientenhanced Kriging model to provide a means for inexpensive uncertainty quantification. The universal Kriging model can be viewed as a hybrid of polynomial regression and Gaussian process regression. For this model, the mean behavior of the surrogate is determined by a polynomial regression, and deviations from this mean are represented as a Gaussian process. Tests with explicit functions and nuclear engineering models show that the universal gradient-enhanced Kriging model provides a more accurate surrogate model when compared to either regression or ordinary Kriging models. In addition we investigate the ability of the Kriging model to provide error predictions and bounds for regression models.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gradient-Enhanced Universal Kriging for Uncertainty Propagation

Lockwood

Anitescu

2012

Nuclear Science and Engineering

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“…In contrast to most other common reduction methods so far used in nonlinear time-integration, it does not require a current state of deformation of the system and continuous basis updates, thus the projection basis can be fully pre-computed based on the linear system. Furthermore there are also similar well-established techniques of second-order enhancements in other fields of computational engineering such as uncertainty quantification [23].…”

Section: Introductionmentioning

confidence: 98%

Nonlinear frequency response analysis of structural vibrations

2014

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In this paper we present a method for nonlinear frequency response analysis of mechanical vibrations of 3-dimensional solid structures. For computing nonlinear frequency response to periodic excitations, we employ the wellestablished harmonic balance method. A fundamental aspect for allowing a large-scale application of the method is model order reduction of the discretized equation of motion. Therefore we propose the utilization of a modal projection method enhanced with modal derivatives, providing second-order information. For an efficient spatial discretization of continuum mechanics nonlinear partial differential equations, including large deformations and hyperelastic material laws, we use the isogeometric finite element method, which has already been shown to possess advantages over classical finite element discretizations in terms of higher accuracy of numerical approximations in the fields of linear vibration and static large deformation analysis. With several computational examples, we demonstrate the applicability and accuracy of the modal derivative reduction method for nonlinear static computations and vibration analysis. Thus, the presented method opens a promising perspective on application of nonlinear frequency analysis to large-scale industrial problems.

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“…One method for overcoming this limitation is the incorporation of gradient information into the training of the surrogate. 13,17,18,[23][24][25] When adjoint methods are employed, this gradient may be evaluated with a cost approximately equal to the simulation of the physical problem. [26][27][28] By incorporating derivative values, the cost associated with training an accurate surrogate can be greatly reduced.…”

Section: Introductionmentioning

confidence: 99%

Mixed Aleatory/Epistemic Uncertainty Quantification for Hypersonic Flows via Gradient-Based Optimization and Surrogate Models

Lockwood

Anitescu

Mavriplis

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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The use of optimization for the propagation of mixed epistemic/aleatory uncertainties is demonstrated within the context of hypersonic flows. Specifically, this work focuses on strategies applicable for models where input parameters can be divided into a set of variables containing only aleatory uncertainties and a set with epistemic uncertainties. With the input parameters divided in this way, uncertainty due to the epistemic variables is propagated via a constrained optimization approach, while the uncertainty due to aleatory variables is propagated via sampling. A statistics-of-intervals approach is proposed in which the constrained optimization results are treated as a random variable and multiple optimizations are performed to quantify the aleatory uncertainty. In order to reduce the total number of optimizations required, a surrogate is employed to model the variation of the optimization results with respect to the aleatory variables, and exhaustive sampling is performed on this surrogate to determine the desired statistics. The properties of the statistics-of-intervals approach are demonstrated by using the Fay-Riddell stagnation heating correlations and compared with a competing method based on uncertain optimization. Additionally, the statistics-of-intervals approach is demonstrated for mixed epistemic/aleatory uncertainty quantification on a real gas computational fluid dynamic simulation.

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Polynomial Regression Approaches Using Derivative Information for Uncertainty Quantification

Cited by 79 publications

References 21 publications

Gradient-Enhanced Universal Kriging for Uncertainty Propagation

Gradient-Enhanced Universal Kriging for Uncertainty Propagation

Nonlinear frequency response analysis of structural vibrations

Mixed Aleatory/Epistemic Uncertainty Quantification for Hypersonic Flows via Gradient-Based Optimization and Surrogate Models

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