Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging

Kleijnen, J.P.C.; Beers, W.C.M. van; Nieuwenhuyse, Inneke Van

doi:10.2139/ssrn.1763726

Cited by 21 publications

(22 citation statements)

References 25 publications

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“…It is a widely used statistical measure which can help to decide the subsequent function evaluations in global optimisation. 39,40,41 Here "global optimisation" refers to that (i) first, the method guarantees to find the global optimum when the number of iterations tends to infinity 55 ; and (ii) the search is not limited to a local region of the current point. Although in practice, the number of iterations is always finite, the capability of searching globally gives rise to higher probability of finding the global optimum, when compared with the traditional gradient-based optimisation methods.…”

Section: Maximising Expected Improvementmentioning

confidence: 99%

“…The kriging method is to be used for meta-modelling. The principle of expected improvement (EI), a measure for global optimisation [39][40][41] , is utilised to formulate the calibration into an optimisation problem. However, in previous studies, EI was developed assuming a Gaussian process meta-model for the output (response) of the underlying simulation model; this is not applicable to calibration problems in which the objective is to minimise the sum of squared errors.…”

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confidence: 99%

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Kriging meta‐model assisted calibration of computational fluid dynamics models

et al. 2016

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Computational fluid dynamics (CFD) is a simulation technique widely used in chemical and process engineering applications. However, computation has become a bottleneck when calibration of CFD models with experimental data (also known as model parameter estimation) is needed. In this research, the kriging meta-modelling approach (also termed Gaussian process) was coupled with expected improvement (EI) to address this challenge. A new EI measure was developed for the sum of squared errors (SSE) which conforms to a generalised chi-square distribution and hence existing normal distribution-based EI measures are not applicable. The new EI measure is to suggest the CFD model parameter to simulate with, hence minimising SSE and improving match between simulation and experiments. The usefulness of the developed method was demonstrated through a case study of a single-phase flow in both a straight-type and a convergent-divergent-type annular jet pump, where a single model parameter was calibrated with experimental data.Keywords: Calibration, computational fluid dynamics, expected improvement, Gaussian process, parameter estimation Correspondence concerning this article should be addressed to Tao Chen at t.chen@surrey.ac.uk. 2 IntroductionComputational fluid dynamics (CFD) simulations are usually large complex computer programs representing real life fluid systems. The complexity of such simulations can make them quite a herculean task to solve, with the run time associated with the simulation being of great concern. Such simulation run time could be for hours or days.1,2 In addition, large scale or complex systems usually place a great demand on computer memory. 3 Computation is especially a problem when the CFD simulation is required to run for a large number of times, for example when sensitivity analysis is carried out 1,4 , or the models are used within a certain optimisation problem. 4,5 Of particular interest in this research project is calibration of CFD models (also known as model parameter estimation), which can be cast into an optimisation problem.CFD model calibration can be defined as the process of adjusting numerical or physical parameters in the CFD model which, on obtaining the optimal values 6 , helps to improve agreement with experimental data. 7,8,9 The parameters in this context are typically turbulence model coefficients or turbulence model choice. The default values given by CFD software providers for turbulence parameters may apply only in standard circumstances. In this paper, calibration is formulated as an optimisation problem to minimise the mismatch between simulated and experimental outputs (responses). The calibration process may need tens to hundreds of simulation runs to evaluate the objective function, the sum of squared errors (where the errors quantify the differences between the simulated and the experimental outputs) over the region of interest, a requirement that is often infeasible for CFD.These difficulties faced by CFD simulations have led to the application of meta-modelling, whi...

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Section: Maximising Expected Improvementmentioning

confidence: 99%

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confidence: 99%

Kriging meta‐model assisted calibration of computational fluid dynamics models

et al. 2016

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“…Under nondegeneracy conditions (for more technical details, see, e.g., Bull, 2011), it is possible to prove that unexplored regions, which have large σðcÞ, will be sooner or later sampled by maximizing the expected improvement. Therefore, the domain is densely sampled everywhere in infinite time and global convergence is guaranteed (Jones, 2001;Kleijnen et al, 2012). Global convergence cannot be achieved in a finite number of evaluations unless additional information on the regularity of the problem is available, e.g., a global Lipschtiz constant for the loss function.…”

Section: Efficient Global Optimizationmentioning

confidence: 99%

Efficient global optimization of reservoir geomechanical parameters based on synthetic aperture radar-derived ground displacements

et al. 2016

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When large volumes of fluids are removed from or injected into underground formations for, e.g., hydrocarbon and water production, CO 2 storage, gas storage, and geothermal energy exploitation, monitoring of surface deformations coupled to numerical modeling improves our understanding of reservoir behavior. The ability to accurately simulate surface displacements, however, is often impaired by limited information on reservoir geometry, waterdrive strength, and fluid-geomechanical parameters characterizing the geologic formations of interest. We have investigated the ability of efficient global optimization (EGO) to reduce the parameter uncertainties usually affecting geomechanical modeling. EGO is used to identify the parameter set that minimizes the difference in land displacements obtained from synthetic aperture radar (SAR)-derived measurements and 3D geomechanical modeling. We have tested the approach on the Tengiz giant oil field, Kazakhstan, where large uncertainties affect our knowledge of geomechanical parameters and pore pressure evolution. SqueeSAR on ENVISAT and RADARSAT-1 images acquired between 2004 and 2007 provided a set of high-precision, high-areal-density subsidence measurements of the test site. Based on the available information, a 3D geomechanical model of the reservoir has been developed using the elastoplastic finite-element code GEPS3D. Our results indicated that EGO efficiently identifies the global optimum in the parameter space, yielding a significant reduction in the difference between modeled and measured land subsidence. The match between simulated and SAR-measured horizontal displacements was developed as validation of the EGO calibration, which thus proved an effective and rather inexpensive method for the simultaneous management of several uncertainties and the reliable quantification of the rock properties.

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“…In this paper, we focus on problems where is continuous and is bounded by box constraints; for reasons explained in Section 3.1 , we discretize the function domain to obtain a finite set of points (as common in the literature; see, e.g., Frazier, Powell, and Dayanik, 2009;Van Nieuwenhuyse, 2012 , andSun, Hong, &Hu, 2014 ). Many methods are available for solving problem (1) with a finite set of points such as the ranking and selection (R&S) method (see Hong, Nelson, and Xu, 2015 , for a review).…”

Section: Introductionmentioning

confidence: 99%

Comparison of Kriging-Based Methods for Simulation Optimization with Heterogeneous Noise

2015

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a b s t r a c tIn this article we investigate the unconstrained optimization (minimization) of the performance of a system that is modeled through a discrete-event simulation. In recent years, several algorithms have been proposed which extend the traditional Kriging-based simulation optimization algorithms (assuming deterministic outputs) to problems with noise. Our objective in this paper is to compare the relative performance of a number of these algorithms on a set of well-known analytical test functions, assuming different patterns of heterogeneous noise. We also apply the algorithms to a popular inventory test problem. The conclusions and insights obtained may serve as a useful guideline for researchers aiming to apply Kriging-based algorithms to solve engineering and/or business problems, and may be useful in the development of future algorithms.

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Expected Improvement in Efficient Global Optimization Through Bootstrapped Kriging

Cited by 21 publications

References 25 publications

Kriging meta‐model assisted calibration of computational fluid dynamics models

Kriging meta‐model assisted calibration of computational fluid dynamics models

Efficient global optimization of reservoir geomechanical parameters based on synthetic aperture radar-derived ground displacements

Comparison of Kriging-Based Methods for Simulation Optimization with Heterogeneous Noise

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