An adaptive hybrid surrogate model

Zhang, Jie; Chowdhury, Souma; Messac, Achille

doi:10.1007/s00158-012-0764-x

Cited by 121 publications

(54 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Hence, it can be applied to any kind of surrogate model including the hybrid models, such as Adaptive Hybrid Functions. 11 The proposed method adds infill points in the region of global optimum as well as in the location where the surrogate model has relatively high errors. The paper is organized as follows: Section II describes the formulation of the proposed methodology in detail.…”

Section: Research Objectivementioning

confidence: 99%

“…2 Popular surrogate modeling methods include Polynomial Response Surfaces, 3 Kriging, 4, 5 Moving Least Square, 6, 7 radial basis functions, 8 neural networks, 9 and hybrid surrogate modeling. 10,11 These methods have been applied to a wide range of disciplines, such as aerospace design, automotive design, chemistry, and material science. 12 The four main steps typically involved in constructing a surrogate model are: (a) choosing the appropriate method for performing the design of experiments (DoE); (b) evaluating the response of high fidelity simulation model at the sampling points; (c) determining the proper surrogate model to fit the responses in previous step; and (d) validating the accuracy of the surrogate model.…”

Section: A Surrogate-based Optimizationmentioning

confidence: 99%

See 1 more Smart Citation

Surrogate-Based Design Optimization with Adaptive Sequential Sampling

Mehmani¹,

Zhang²,

Chowdhury³

et al. 2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials ConferenceSelf Cite

11
0
7
0

View full text Add to dashboard Cite

In spite of the recent developments in surrogate modeling techniques, the low fidelity of these models often limits their use in practical engineering design optimization. When surrogate models are used to represent the behavior of a complex system, it is challenging to simultaneously obtain high accuracy over the entire design space. When such surrogates are used for optimization, it becomes challening to find the optimum/optima with certainty. Sequential sampling methods offer a powerful solution to this challenge by providing the surrogate with reasonable accuracy where and when needed. When surrogate-based design optimization (SBDO) is performed using sequential sampling, the typical SBDO process is repeated multiple times, where each time the surrogate is improved by addition of new sample points. This paper presents a new adaptive approach to add infill points during SBDO, called Adaptive Sequential Sampling (ASS). In this approach, both local exploitation and global exploration aspects are considered for updating the surrogate during optimization, where multiple iterations of the SBDO process is performed to increase the quality of the optimal solution. This approach adaptively improves the accuracy of the surrogate in the region of the current global optimum as well as in the regions of higher relative errors. Based on the initial sample points and the fitted surrogate, the ASS method adds infill points at each iteration in the locations of: (i) the current optimum found based on the fitted surrogate; and (ii) the points generated using cross-over between sample points that have relatively higher cross-validation errors. The Nelder and Mead Simplex method is adopted as the optimization algorithm. The effectiveness of the proposed method is illustrated using a series of standard numerical test problems.

show abstract

Section: Research Objectivementioning
confidence: 99%

Section: A Surrogate-based Optimizationmentioning
confidence: 99%

Surrogate-Based Design Optimization with Adaptive Sequential Sampling
Mehmani¹,
Zhang²,
Chowdhury³
et al. 2012
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials ConferenceSelf Cite
11
0
7
0
View full text Add to dashboard Cite

show abstract

“…Major surrogate modeling methods include Polynomial Response Surfaces, 2 Kriging, 3,4 Moving Least Square, 5,6 Radial Basis Functions (RBF), 7 Neural Networks, 8 and hybrid surrogate modeling. 9, 10 These methods have been applied to a wide range of disciplines, such as aerospace design, automotive design, chemistry, and material science. 11 The four main steps typically involved in constructing a surrogate model are:…”

Section: A Approximation Modelsmentioning
confidence: 99%

Quantifying Regional Error in Surrogates by Modeling its Relationship with Sample Density
Mehmani
¹
,
Chowdhury
²
,
Zhang
³

et al. 2013
54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
Self Cite
4
0
0
0
View full text Add to dashboard Cite

Approximation models (or surrogate models) provide an efficient substitute to expensive physical simulations and an efficient solution to the lack of physical models of system behavior. However, it is challenging to quantify the accuracy and reliability of such approximation models in a region of interest or the overall domain without additional system evaluations. Standard error measures, such as the mean squared error, the cross-validation error, and the Akaikes information criterion, provide limited (often inadequate) information regarding the accuracy of the final surrogate. This paper introduces a novel and model independent concept to quantify the level of errors in the function value estimated by the final surrogate in any given region of the design domain. This method is called the Regional Error Estimation of Surrogate (REES). Assuming the full set of available sample points to be fixed, intermediate surrogates are iteratively constructed over a sample set comprising all samples outside the region of interest and heuristic subsets of samples inside the region of interest (i.e., intermediate training points). The intermediate surrogate is tested over the remaining sample points inside the region of interest (i.e., intermediate test points). The fraction of sample points inside region of interest, which are used as intermediate training points, is fixed at each iteration, with the total number of iterations being pre-specified. The estimated median and maximum relative errors within the region of interest for the heuristic subsets at each iteration are used to fit a distribution of the median and maximum error, respectively. The estimated statistical mode of the median and the maximum error, and the absolute maximum error are then represented as functions of the density of intermediate training points, using regression models. The regression models are then used to predict the expected median and maximum regional errors when all the sample points are used as training points. Standard test functions and a wind farm power generation problem are used to illustrate the effectiveness and the utility of such a regional error quantification method.

show abstract

“…Building a metamodel involves two procedures: (1) employing design of experiments (DOEs) to sample the computer simulation; and (2) selecting an approximation model to represent the data and fit the model with the sampling data . Various metamodels have been developed, such as the polynomial model (Montgomery 2007), kriging model (Chen et al 2014;Li et al 2013), radial basis functions (RBF) (Fang and Horstemeyer 2006), multivariate adaptive regression splines (MARS) (Friedman 1991), support vector regression (Clarke, Griebsch, and Simpson 2005;, high-dimensional model representation (Shan and Wang 2010;Wang, Tang, and Li 2011;Hajikolaei and Wang 2012;Li, Wang, and Li 2012), and multisurrogate models (Zerpa et al 2005;Goel et al 2006;Zhang, Chowdhury, and Messac 2012;Zheng et al 2013), which combine some of the basic metamodels. *Corresponding author.…”

Section: Introductionmentioning
confidence: 99%

A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials
Wu
¹
,
Luo
²
,
Zhang
³

et al. 2014
Engineering Optimization
18
0
13
0
View full text Add to dashboard Cite

The accuracy of metamodelling is determined by both the sampling and approximation. This article proposes a new sampling method based on the zeros of Chebyshev polynomials to capture the sampling information effectively. First, the zeros of one-dimensional Chebyshev polynomials are applied to construct Chebyshev tensor product (CTP) sampling, and the CTP is then used to construct high-order multi-dimensional metamodels using the 'hypercube' polynomials. Secondly, the CTP sampling is further enhanced to develop Chebyshev collocation method (CCM) sampling, to construct the 'simplex' polynomials. The samples of CCM are randomly and directly chosen from the CTP samples. Two widely studied sampling methods, namely the Smolyak sparse grid and Hammersley, are used to demonstrate the effectiveness of the proposed sampling method. Several numerical examples are utilized to validate the approximation accuracy of the proposed metamodel under different dimensions.

show abstract

An adaptive hybrid surrogate model

Cited by 121 publications

References 38 publications

Surrogate-Based Design Optimization with Adaptive Sequential Sampling

Surrogate-Based Design Optimization with Adaptive Sequential Sampling

Quantifying Regional Error in Surrogates by Modeling its Relationship with Sample Density

A new sampling scheme for developing metamodels with the zeros of Chebyshev polynomials

Contact Info

Product

Resources

About