Space Mapping: The State of the Art

Bandler, J.W.; Cheng, Qingsha S.; Dakroury, S.A.; Mohamed, A.S.A.; Bakr, Mohamed H.; Madsen, Kaj; Søndergaard, Jacob

doi:10.1109/tmtt.2003.820904

Cited by 930 publications

(819 citation statements)

References 67 publications

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“…Instead of using Z c or Z d , which are output correction processes, we can employ an input correction, known as space mapping [4]. By distorting the locations of X c we can attempt to align the contours of the cheap function with those of the expensive function.…”

Section: Multi-fidelity Analysismentioning

confidence: 99%

Recent advances in surrogate-based optimization

Forrester

Keane

2009

Progress in Aerospace Sciences

1,875

954

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The evaluation of aerospace designs is synonymous with the use of long running and computationally intensive simulations. This fuels the desire to harness the efficiency of surrogate-based methods in aerospace design optimization. Recent advances in surrogate-based design methodology bring the promise of efficient global optimization closer to reality. We review the present state of the art of constructing surrogate models and their use in optimization strategies. We make extensive use of pictorial examples and, since no method is truly universal, give guidance as to each method's strengths and weaknesses.

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Section: Multi-fidelity Analysismentioning

confidence: 99%

Recent advances in surrogate-based optimization

Forrester

Keane

2009

Progress in Aerospace Sciences

1,875

954

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“…Our goal is to solve (1) where is a given objective function. We consider an optimization algorithm that generates a sequence of points 0,1,2, , and a family of surrogate models , so that (2) Let denote the response vector of the coarse model: less accurate than the fine model but much faster to evaluate.…”

Section: Multicoarse-model Space Mapping Optimization Letmentioning

confidence: 99%

“…We consider an optimization algorithm that generates a sequence of points 0,1,2, , and a family of surrogate models , so that (2) Let denote the response vector of the coarse model: less accurate than the fine model but much faster to evaluate. Standard SM [1], [2] assumes that models are constructed from the coarse model so that the misalignment between and the fine model is minimized. Let be a generic SM surrogate model, i.e., the coarse model composed with suitable SM transformations.…”

Section: Multicoarse-model Space Mapping Optimization Letmentioning

confidence: 99%

“…I T is well known [1], [2] that the performance of a space mapping (SM) optimization algorithm depends on the quality of the underlying coarse model, which should be as good a representation of the fine model to be optimized as possible but also significantly less expensive than the fine model. Under these conditions, an SM algorithm can reach a satisfactory solution after a few fine model evaluations.…”

Section: Introductionmentioning

confidence: 99%

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Space Mapping With Multiple Coarse Models for Optimization of Microwave Components

Koziel

Bandler

2008

IEEE Microw. Wireless Compon. Lett.

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Abstract-The performance of space mapping (SM) optimization algorithms depends primarily on the quality of the underlying coarse model. Models available in the microwave area can be cheap but inaccurate or accurate but too expensive. Here, we consider a multicoarse-model technique that allows us to combine the merits of both types of coarse models to substantially reduce the overall computational cost of optimization in comparison to traditional SM.Index Terms-Coarse model, engineering optimization, microwave design, space mapping (SM) optimization.

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“…Co-Kriging [61,62] and space-mapping [63,64] are two examples of surrogate-based methods that rely on MF simulations; mainly for optimization purposes. Multi-fidelity techniques for UQ purpose recently appeared in literature.…”

mentioning

confidence: 99%

Global sensitivity analysis via multi-fidelity polynomial chaos expansion

Palar

Zuhal

Shimoyama

et al. 2018

Reliability Engineering & System Safety

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The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this aspect is to quantify and rank the effects of input random variables and their combinations to the variance of the random output. In problems where the use of expensive computer simulations are required, metamodels are widely used to speed up the process of global sensitivity analysis. In this paper, a multi-fidelity framework for global sensitivity analysis using polynomial chaos expansion (PCE) is presented. The goal is to accelerate the computation of Sobol sensitivity indices when the deterministic simulation is expensive and simulations with multiple levels of fidelity are available. This is especially useful in cases where a partial differential equation solver computer code is utilized to solve engineering problems. The multi-fidelity PCE is constructed by combining the lowfidelity and correction PCE. Following this step, the Sobol indices are computed using this combined PCE. The PCE coefficients for both low-fidelity and correction PCE are computed with spectral projection technique and sparse grid integration. In order to demonstrate the capability of the proposed method for sensitivity analysis, several simulations are conducted. On the aerodynamic example, the multi-fidelity approach is able to obtain an accurate value of Sobol indices with 36.66% computational cost compared to the standard single-fidelity PCE for a nearly similar accuracy.

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Space Mapping: The State of the Art

Cited by 930 publications

References 67 publications

Recent advances in surrogate-based optimization

Recent advances in surrogate-based optimization

Space Mapping With Multiple Coarse Models for Optimization of Microwave Components

Global sensitivity analysis via multi-fidelity polynomial chaos expansion

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