Abstract
In this paper, a Multi-fidelity optimization method via information fusion with uncertainty (MFOIFU) is proposed. MFOIFU combines prediction uncertainty of kriging and model uncertainty, aiming at reducing computational cost of optimization and guaranteeing reliability of the optima. Firstly, the uncertainty of Low-fidelity (LF) and High-fidelity (HF) models is confirmed, respectively. After that, the optimal estimation theory of Kalman filter is employed to fuse information from LF and HF models. Then, the fused model is optimized and a distinctive updating strategy is presented to supplement feasible solutions. The newly introduced MFOIFU is verified through eight benchmark examples. Results showed that MFOIFU has some advantages over the Single high-fidelity optimization (SHO) method and some of the well-established multi-fidelity methods on computational expense and optimization efficiency. Finally, the MFOIFU method is successfully applied to the shell structure design of an Autonomous underwater vehicle (AUV).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. V. Queipo, R. T. Haftka, S. Wei, T. Goel, R. Vaidyanathan and P. K. Tucker, Surrogate-based analysis and optimization, Progress in Aerospace Sciences, 41 (1) (2005) 1–28.
A. I. J. Forrester and A. J. Keane, Recent advances in surrogate-based optimization, Progress in Aerospace Sciences, 45 (1) (2009) 50–79.
A. I. J. Forrester, A. Sóbester and A. J. Keane, Multifidelity optimization via surrogate modelling, Proceedings of the Royal Society a-Mathematical Physical and Engineering Sciences, 463 (2088) (2007) 3251–3269.
A. Bekasiewicz and S. Koziel, Rapid simulation-driven design of UWB antennas using surrogate-based optimization, IEEE International Symposium on Antennas and Propagation & Usnc/ursi National Radio Science Meeting IEEE (2015) 2003–2004.
E. Iuliano and E. A. Pérez, Application of surrogate-based global optimization to aerodynamic design, Springer International Publishing (2016).
X. Li, B. Huang, T. Chen, Y. Liu, S. Qiu and J. Zhao, Combined experimental and computational investigation of the cavitating flow in an orifice plate with special emphasis on surrogate-based optimization method, Journal of Mechanical Science & Technology, 31 (1) (2017) 269–279.
X. Zhao, B. Huang, T. Chen, G. Wang, D. Gao and J. Zhao, Numerical simulations and surrogate-based optimization of cavitation performance for an aviation fuel pump, Journal of Mechanical Science & Technology, 31 (2) (2017) 705–716.
J. Zheng, H. Qiu and H. Feng, The variable fidelity optimization for simulation-based design: A review, International Conference on Computer Supported Cooperative Work in Design IEEE (2012) 289–294.
Y. Kuya, K. Takeda, X. Zhang and A. I. J. Forrester, Multifidelity surrogate modeling of experimental and computational aerodynamic data sets, AIAA Journal, 49 (2) (2011) 289–298.
Z. H. Han and S. Görtz, Hierarchical Kriging model for variable-fidelity surrogate modeling, AIAA Journal, 50 (9) (2012) 1885–1896.
A. March and K. Willcox, Provably convergent multifidelity optimization algorithm not requiring high-fidelity derivatives, AIAA Journal, 50 (5) (2012) 1079–1089.
A. March and K. Willcox, Constrained multifidelity optimization using model calibration, Structural & Multidisciplinary Optimization, 46 (1) (2012) 93–109.
J. Zheng, X. Shao, L. Gao, P. Jiang, Z. Li and J. Zheng, A hybrid variable-fidelity global approximation modelling method combining tuned radial basis function base and Kriging correction, Journal of Engineering Design, 24 (8) (2013) 604–22.
N. M. Alexandrov, R. M. Lewis, C. R. Gumbert, L. L. Green and P. A. Newman, Approximation and model management in aerodynamic optimization with variablefidelity models, Journal of Aircraft, 38 (6) (2001) 1093–1101.
N. M. Alexandrov and R. M. Lewis, Optimization with variable-fidelity models applied to wing design, ICASE (1999).
M. Eldred, A. Giunta and S. Collis, Second-order corrections for surrogate-based optimization with model hierarchies, 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY: American Institute of Aeronautics and Astronautics Inc (2004) 1754–1768.
S. Gano, J. Renaud and B. Sanders, Hybrid variable fidelity optimization by using a Kriging-based scaling function, AIAA Journal, 43 (11) (2005) 2422–2430.
G. Sun, G. Li, S. Zhou, W. Xu, X. Yang and Q. Li, Multifidelity optimization for sheet metal forming process, Structural & Multidisciplinary Optimization, 44 (1) (2011) 111–24.
S. E. Gano, Simulation-based design using varible fidelity optimization, The University of Notre Dame, Notre Dame, IN (2006).
Z. H. Han, S. Görtz and R. Zimmermann, Improving variable-fidelity surrogate modeling via gradient-enhanced Kriging and a generalized hybrid bridge function, Aerospace Science and Technology, 25 (1) (2013) 177–189.
S. H. Son and D. H. Choi, The effects of scale factor and correction on the multi-fidelity model, Journal of Mechanical Science & Technology, 30 (5) (2016) 2075–2081.
L. Leifsson and S. Koziel, Multi-fidelity design optimization of transonic airfoils using shape-preserving response prediction, Procedia Computer Science, 1 (1) (2010) 1311–1320.
L. Leifsson and S. Koziel, Variable-fidelity aerodynamic shape optimization. computational optimization, methods and algorithms, Springer Berlin Heidelberg (2011) 179–210.
S. Koziel and L. Leifsson, Multi-fidelity airfoil shape optimization with adaptive response prediction, AIAA Aviation Technology, Integration, and Operations (2013).
L. Leifsson and S. Koziel, Aerodynamic shape optimization by variable-fidelity computational fluid dynamics models: A review of recent progress, Journal of Computational Science, 10 (2015) 45–54.
S. Ulaganathan et al., Building accurate radio environment maps from multi-fidelity spectrum sensing data, Wireless Networks (2015).
P. M. Zadeh, A. Mehmani and A. Messac, High fidelity multidisciplinary design optimization of a wing using the interaction of low and high fidelity models, Optimization and Engineering (2015).
G. N. Absi and S. Mahadevan, Multi-fidelity approach to dynamics model calibration, Mechanical Systems and Signal Processing, 68–69 (2016) 189–206.
F. Fusi, P. M. Congedo, A. Guardone and G. Quaranta, Robust optimization of a helicopter rotor airfoil using multi-fidelity approach. advances in evolutionary and deterministic methods for design, Optimization and Control in Engineering and Sciences, 36 (2015) 385–99.
B. Liu, S. Koziel and Q. Zhang, A multi-fidelity surrogate-model-assisted evolutionary algorithm for computationally expensive optimization problems, Journal of Computational Science, 12 (2016) 28–37.
L. Leifsson, S. Koziel, Y. Tesfahunegn and A. Bekasiewicz, Fast multi-objective aerodynamic optimization using space-mapping-corrected multi-fidelity models and Kriging interpolation, Springer Proceedings in Mathematics & Statistics, 153 (2016) 55–73.
L. W. T. Ng and K. E. Willcox, Multifidelity approaches for optimization under uncertainty, International Journal for Numerical Methods in Engineering, 100 (2014) 746–772.
H. Dong, B. Song, P. Wang and S. Huang, Multi-fidelity information fusion based on prediction of Kriging, Structural & Multidisciplinary Optimization, 51 (2015) 1267–1280.
J. Yi, X. Li, M. Xiao, J. Xu and L. Zhang, Construction of nested maximin designs based on successive local enumeration and modified novel global harmony search algorithm, Engineering Optimization, 49 (1) (2017) 161–180.
S. N. Lophaven, DACE — A MATLAB Kriging Toolbox — Version 2.0 (2002).
A. I. J. Forrester, A. Sóbester and A. J. Keane, Multifidelity optimization via surrogate modelling, Proceedings of the Royal Society A, 463 (2088) (2007) 3251–3269.
R. M. Lewis and S. G. Nash, A multigrid approach to the optimization of systems governed by differential equations, AIAA Paper (2000) 2000–4890.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Jaewook Lee
Chengshan Li was born in 1991. He received his bachelor’s and master’s degrees in Northwestern Polytechnical University (NWPU), China, in 2014 and 2016, respectively. He is currently working toward the Ph.D. degree at NWPU. His research interests include surrogate-based optimization, multifidelity optimization and multidisciplinary optimization.
Peng Wang was born in 1978. He received his M.S. and Ph.D. degrees in Northwestern Polytechnical University (NWPU), China, in 2004 and 2008, respectively. He is currently a Professor of NWPU. His research interests are general design of Autonomous Underwater Vehicle (AUV), multidisciplinary optimization, High-precision shape design, Drag-reducing and noise-reducing technique.
Rights and permissions
About this article
Cite this article
Li, C., Wang, P. & Dong, H. Kriging-based multi-fidelity optimization via information fusion with uncertainty. J Mech Sci Technol 32, 245–259 (2018). https://doi.org/10.1007/s12206-017-1225-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-017-1225-7