Abstract
Along with the development of surrogate models, there is a growing need to use surrogate models instead of computationally intensive simulations to estimate real system responses. Compared with individual surrogate models, the ensemble of surrogate models is gradually drawing more attention due to its better applicability and robustness. Thus, this paper proposes an adaptive median-based ensemble of surrogate models (MID-ESMs). At first, construct a reference model using the median of the predicted values of several surrogate models. Then an adaptive weight ensemble strategy is proposed based on the reference model to integrate global trends and local features. Thirty test functions and a practical engineering case are used to evaluate the model performance. In addition, this paper investigates the effect of homoscedasticity noise and test functions of different dimensions on the proposed model. The results demonstrate that MID-ESM has higher accuracy and robustness than individual surrogate models and other ensembles of surrogate models, offering better applicability in engineering problems.
Issue Section:
Technical Brief
References
1.
Han
, Z.-H.
, and Görtz
, S.
, 2012
, “Hierarchical Kriging Model for Variable-Fidelity Surrogate Modeling
,” AIAA J.
, 50
(9
), pp. 1885
–1896
. 2.
Qian
, J.
, Yi
, J.
, Cheng
, Y.
, Liu
, J.
, and Zhou
, Q.
, 2020
, “A Sequential Constraints Updating Approach for Kriging Surrogate Model-Assisted Engineering Optimization Design Problem
,” Eng. Comput.
, 36
(3
), pp. 993
–1009
. 3.
Jung
, Y.
, Kang
, K.
, Cho
, H.
, and Lee
, I.
, 2021
, “Confidence-Based Design Optimization for a More Conservative Optimum Under Surrogate Model Uncertainty Caused by Gaussian Process
,” ASME J. Mech. Des.
, 143
(9
), p. 091701
. 4.
Bouhlel
, M. A.
, and Martins
, J. R. R. A.
, 2018
, “Gradient-Enhanced Kriging for High-Dimensional Problems
,” Eng. Comput.
, 35
(1
), pp. 157
–173
. 5.
Chen
, Z.
, Peng
, S.
, Li
, X.
, Qiu
, H.
, Xiong
, H.
, Gao
, L.
, and Li
, P.
, 2015
, “An Important Boundary Sampling Method for Reliability-Based Design Optimization Using Kriging Model
,” Struct. Multidiscipl. Optim.
, 52
(1
), pp. 55
–70
. 6.
Jiang
, P.
, Zhang
, Y.
, Zhou
, Q.
, Shao
, X.
, Hu
, J.
, and Shu
, L.
, 2018
, “An Adaptive Sampling Strategy for Kriging Metamodel Based on Delaunay Triangulation and TOPSIS
,” Appl. Intell.
, 48
(6
), pp. 1644
–1656
. 7.
Hariri-Ardebili
, M. A.
, 2018
, “MCS-Based Response Surface Metamodels and Optimal Design of Experiments for Gravity Dams
,” Struct. Infrastruct. E
, 14
(12
), pp. 1641
–1663
. 8.
Chatterjee
, T.
, Chakraborty
, S.
, and Chowdhury
, R.
, 2017
, “A Critical Review of Surrogate Assisted Robust Design Optimization
,” Arch. Comput. Methods Eng.
, 26
(1
), pp. 245
–274
. 9.
Assari
, P.
, and Dehghan
, M.
, 2017
, “The Numerical Solution of Two-Dimensional Logarithmic Integral Equations on Normal Domains Using Radial Basis Functions With Polynomial Precision
,” Eng. Comput.
, 33
(4
), pp. 853
–870
. 10.
Liu
, X.
, Liu
, X.
, Zhou
, Z.
, and Hu
, L.
, 2021
, “An Efficient Multi-objective Optimization Method Based on the Adaptive Approximation Model of the Radial Basis Function
,” Struct. Multidiscipl. Optim.
, 63
(3
), pp. 1385
–1403
. 11.
Urquhart
, M.
, Ljungskog
, E.
, and Sebben
, S.
, 2020
, “Surrogate-Based Optimisation Using Adaptively Scaled Radial Basis Functions
,” Appl. Soft Comput.
, 88
, p. 106050
. 12.
Clarke
, S. M.
, Griebsch
, J. H.
, and Simpson
, T. W.
, 2004
, “Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses
,” ASME J. Mech. Des.
, 127
(6
), pp. 1077
–1087
. 13.
Jiang
, C.
, Cai
, X.
, Qiu
, H.
, Gao
, L.
, and Li
, P.
, 2018
, “A Two-Stage Support Vector Regression Assisted Sequential Sampling Approach for Global Metamodeling
,” Struct. Multidiscipl. Optim.
, 58
(4
), pp. 1657
–1672
. 14.
Prado
, D. R.
, López-Fernández
, J. A.
, Arrebola
, M.
, and Goussetis
, G.
, 2021
, “On the Use of the Angle of Incidence in Support Vector Regression Surrogate Models for Practical Reflectarray Design
,” IEEE Trans. Antennas Propag.
, 69
(3
), pp. 1787
–1792
. 15.
Lim
, D.
, Ong
, Y.-S.
, Jin
, Y.
, and Sendhoff
, B.
, 2007
, “A Study on Metamodeling Techniques, Ensembles, and Multi-Surrogates in Evolutionary Computation
,” Proceedings of the 9th Annual Conferences on Genetic Programming
, London, UK, July 7–11
, ACM
, pp. 1288
–1295
. 16.
Cheng
, K.
, and Lu
, Z.
, 2020
, “Structural Reliability Analysis Based on Ensemble Learning of Surrogate Models
,” Struct. Saf.
, 83
, p. 101905
. 17.
Goel
, T.
, Haftka
, R. T.
, Shyy
, W.
, and Queipo
, N. V.
, 2007
, “Ensemble of Surrogates
,” Struct. Multidiscipl. Optim.
, 33
(3
), pp. 199
–216
. 18.
Zerpa
, L. E.
, Queipo
, N. V.
, Pintos
, S.
, and Salager
, J.-L.
, 2005
, “An Optimization Methodology of Alkaline–Surfactant–Polymer Flooding Processes Using Field Scale Numerical Simulation and Multiple Surrogates
,” J. Pet. Sci. Eng.
, 47
(3
), pp. 197
–208
. 19.
Viana
, F. A. C.
, Haftka
, R. T.
, and Steffen
, V.
, 2009
, “Multiple Surrogates: How Cross-Validation Errors Can Help Us to Obtain the Best Predictor
,” Struct. Multidiscipl. Optim.
, 39
(4
), pp. 439
–457
. 20.
Acar
, E.
, and Rais-Rohani
, M.
, 2008
, “Ensemble of Metamodels With Optimized Weight Factors
,” Struct. Multidiscipl. Optim.
, 37
(3
), pp. 279
–294
. 21.
Ferreira
, W. G.
, and Serpa
, A. L.
, 2016
, “Ensemble of Metamodels: The Augmented Least Squares Approach
,” Struct. Multidiscipl. Optim.
, 53
(5
), pp. 1019
–1046
. 22.
Liu
, H.
, Xu
, S.
, Wang
, X.
, Meng
, J.
, and Yang
, S.
, 2016
, “Optimal Weighted Pointwise Ensemble of Radial Basis Functions With Different Basis Functions
,” AIAA J.
, 54
(10
), pp. 3117
–3133
. 23.
Zhang
, S.
, Pang
, Y.
, Liang
, P.
, and Song
, X.
, 2022
, “On the Ensemble of Surrogate Models by Minimum Screening Index
,” ASME J. Mech. Des.
, 144
(7
), p. 071707
. 24.
Acar
, E.
, 2010
, “Various Approaches for Constructing an Ensemble of Metamodels Using Local Measures
,” Struct. Multidiscipl. Optim.
, 42
(6
), pp. 879
–896
. 25.
Lee
, Y.
, and Choi
, D.-H.
, 2014
, “Pointwise Ensemble of Meta-models Using v Nearest Points Cross-Validation
,” Struct. Multidiscipl. Optim.
, 50
(3
), pp. 383
–394
. 26.
Zhang
, J.
, Yue
, X.
, Qiu
, J.
, Zhang
, M.
, and Wang
, X.
, 2021
, “A Unified Ensemble of Surrogates With Global and Local Measures for Global Metamodelling
,” Eng. Optim.
, 53
(3
), pp. 474
–495
. 27.
Ye
, Y.
, Wang
, Z.
, and Zhang
, X.
, 2020
, “An Optimal Pointwise Weighted Ensemble of Surrogates Based on Minimization of Local Mean Square Error
,” Struct. Multidiscipl. Optim.
, 62
(2
), pp. 529
–542
. 28.
Zhang
, J.
, Chowdhury
, S.
, and Messac
, A.
, 2012
, “An Adaptive Hybrid Surrogate Model
,” Struct. Multidiscipl. Optim.
, 46
(2
), pp. 223
–238
. 29.
Zhang
, J.
, Chowdhury
, S.
, Zhang
, J.
, Messac
, A.
, and Castillo
, L.
, 2013
, “Adaptive Hybrid Surrogate Modeling for Complex Systems
,” AIAA J.
, 51
(3
), pp. 643
–656
. 30.
Xueguan
, S.
, Liye
, L.
, Jieling
, L.
, Wei
, S.
, and Jie
, Z.
, 2018
, “An Advanced and Robust Ensemble Surrogate Model: Extended Adaptive Hybrid Functions
,” ASME J. Mech. Des.
, 140
(4
), p. 041402
. 31.
Stone
, M.
, 1974
, “Cross-Validation and Multinomial Prediction
,” Biometrika
, 61
(3
), pp. 509
–515
. 32.
Kaminsky
, A. L.
, Wang
, Y.
, and Pant
, K.
, 2021
, “An Efficient Batch K-Fold Cross-Validation Voronoi Adaptive Sampling Technique for Global Surrogate Modeling
,” ASME J. Mech. Des.
, 143
(1
), p. 011706
. 33.
Arlot
, S.
, and Celisse
, A.
, 2010
, “A Survey of Cross-Validation Procedures for Model Selection
,” Stat. Surv.
, 4
, pp. 40
–79
. 34.
Viana
, F. A. C.
, 2010
, SURROGATES Toolbox User’s Guide
, Gainesville, FL
.35.
Talgorn
, B.
, Le Digabel
, S.
, and Kokkolaras
, M.
, 2015
, “Statistical Surrogate Formulations for Simulation-Based Design Optimization
,” ASME J. Mech. Des.
, 137
(2
), p. 021405
. 36.
Gramacy
, R. B.
, and Lee
, H. K. H.
, 2010
, “Cases for the Nugget in Modeling Computer Experiments
,” Stat. Comput.
, 22
(3
), pp. 713
–722
. 37.
Mullur
, A. A.
, and Messac
, A.
, 2006
, “Metamodeling Using Extended Radial Basis Functions: A Comparative Approach
,” Eng. Comput.
, 21
(3
), pp. 203
–217
. 38.
Park
, J.-S.
, 1994
, “Optimal Latin-Hypercube Designs for Computer Experiments
,” J. Stat. Plan. Infer.
, 39
(1
), pp. 95
–111
. 39.
Ravikumar
, M.
, and Chattopadhyay
, A. J. C.
, 1999
, “Integral Analysis of Conveyor Pulley Using Finite Element Method
,” Comput. Struct.
, 71
(3
), pp. 303
–332
.Copyright © 2023 by ASME
You do not currently have access to this content.
