Abstract
Many researchers have studied Multi-fidelity (MF) models to obtain the optimum solution efficiently when the time of analysis and evaluation is long. The MF model is a meta-model that combines High fidelity (HF) data, which requires large computational cost for evaluation; and Low fidelity (LF) data, which needs small computation cost but has low accuracy. Therefore, integrating HF and LF data with a scale factor and correction model is highly important in MF modeling. This study investigates the performance of the MF model in terms of definition and estimation. First, three different MF models are built: An LF model multiplied by the scale factor, an LF model combined with a correction model, and an LF model with both scale factor and correction model. Second, the effects of scale factor on the MF model are analyzed in terms of constant vs. linear and maximum likelihood estimation vs. least squares estimation. Finally, a correction model is built using two methods, namely, interpolation and regression, to assess the influence of the correction model on the MF model. To evaluate the MF model performance, several test problems are applied, and the root mean square error of each model is estimated as the accuracy measure. In conclusion, the characteristics of different types of MF models are summarized and guidelines for the generation of MF models are proposed to approximate closely the precise models.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. S. Eldred, A. A. Giunta and S. S. Collis, Second-order corrections for surrogate-based optimization with model hierarchies, Proc. of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York, USA (2004).
S. E. Gano and J. E. Renaud, Variable fidelity optimization using a Kriging based scaling function, Proc. of the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York, USA (2004).
Y. Goldfeld, K. Vervnne, J. Arbocz and F. V. Keulen, Multifidelity optimization of laminated conical shells for buckling, Structural and Multidisciplinary Optimization, 30 (2005) 128–141.
G. Sun, G. Li, S. Zhou, W. Xu, X. Yang and Q. Li, Multifidelity optimization for sheet metal forming process, Structural and Multidisciplinary Optimization, 44 (2011) 111–124.
D. Huang, T. T. Allen, W. I. Notz and R. A. Miller, Sequential Kriging optimization using multiple-fidelity evaluations, Structural and Multidisciplinary Optimization, 32 (2006) 369–382.
D. Rajnarayan, A. Haas and I. Kroo, A multifidelity gradient-free optimization method and application to aerodynamic design, Proc. of the 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Victoria, British Columbia, Canada (2008).
W. Chen, Y. Xiong, K. L. Tsui and S. Wang, A designdriven validation approach using bayesian prediction models, Journal of Mechanical Design, 130 (2008) 021101–1–021101-12.
S. Xiong, P. Z. G. Qian and C. F. J. Wu, Sequential design and analysis of high-accuracy and low-accuracy computer codes, Technometrics, 55 (1) (2013) 37–46.
Z. Qian, C. C. Seepersad, V. R. Joseph, J. K. Allen and C. F. J. Wu, Building surrogate models based on detailed and approximate simulations, Journal of Mechanical Design, 128 (2006) 668–677.
A. I. J. Forrester, A. Sobester and A. J. Keane, Multifidelity optimization via surrogate modelling, Proc. of The Royal Society A, 463 (2007) 3251–3263.
Y. Xiong, W. Chen and K. L. Tsui, A new variable-fidelity optimization framework based on model fusion and objective-oriented sequential sampling, Journal of Mechanical Design, 130 (2008) 111401–1–111401-9.
P. Z. G. Qian and C. F. J. Wu, Bayesian hierarchical modeling for integrating low-accuracy and high-accuracy experiments, Technometrics, 50 (2) (2008) 192–204.
S. H. Son, K. J. Cha and D. H. Choi, Performance comparison of existing multi-fidelity models, The 7th CJK Joint Symposium on Optimization of Structural and Mechanical Systems, Huangshan, June, China (2012).
S. H. Son, D. H. Park, K. J. Cha and D. H. Choi, Constrained global design optimization using a multi-fidelity model, 10th World Congress on Structural and Multidisciplinary Optimization, Orland, Florida, USA (2013).
C. Currin, T. Mitchell, M. Morris and D. Ylvisaker, A Bayesian approach to the design and analysis of computer experiments, Technical Report 6498, Oak Ridge National Laboratory (1998).
J. S. Park, Tuning complex computer codes to data and optimal designs, Ph.D. Thesis, University of Illlinois, Champaign-Urbana (1991).
D. D. Cox, J. S. Park and C. E. Singer, A statistical method for tuning a computer code to a data base, Computational Statistics & Data Analysis, 37 (1) (2001) 77–92.
S. Xiong, P. Z. Qian and C. J. Wu, Sequential design and analysis of high-accuracy and low-accuracy computer codes, Technometrics, 55 (1) (2013) 37–46.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Gang-Won Jang
Seok-Ho Son obtained a B.S. in Mechanical Engineering from Hannam University in 2005. He went on to obtain an M.S. and Ph.D. from Hanyang University in 2007 and 2013, respecttively. Thereafter, he engaged in a post-doctoral fellowship also at Hanyang University. He is currently an R&D engineer at PIDOTECH, Inc. in Seoul, South Korea. His research interests are in the area of optimization techniques, including metamodeling techniques, efficient global optimization techniques and experiment design.
Dong-Hoon Choi received a B.S. in Mechanical Engineering from Seoul National University in 1975. He went on to obtain an M.S. from the Korea Advanced Institute of Science and Technology in 1977 and a Ph.D. from the University of Wisconsin–Madison in 1986. He is currently a professor at the School of Mechanical Engineering at Hanyang University in Seoul, South Korea and the director of the Center of Innovative Design Optimization Technology (iDOT). His research interests are in the area of optimization techniques, including developing multidisciplinary design and optimization methodology, improving optimization techniques to ensure optimum solution reliability, and enhancing approximation optimization technique, among others.
Rights and permissions
About this article
Cite this article
Son, SH., Choi, DH. The effects of scale factor and correction on the multi-fidelity model. J Mech Sci Technol 30, 2075–2081 (2016). https://doi.org/10.1007/s12206-016-0414-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-016-0414-0