Abstract
This chapter introduces performance-driven modeling using principal component analysis. The keystone of the technique is in spanning the surrogate model domain by the selected principal components of the reference points. This allows for a reduction of the model dimensionality, a consequence of which is an improved scalability of the surrogate in terms of the dependence between the model predictive power and the number of training data samples. Because the domain is essentially an affinely transformed unity hypercube, both the design of experiments (in particular, uniform sampling) and surrogate model optimization are straightforward. Depending on the setup, the discussed approach may be competitive to previously discussed methods in terms of the computational cost of surrogate model construction. Application case studies and benchmarking against conventional data-driven modeling methods but also nested kriging are given as well.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Chen, Y.-C., Chen, S.-Y., & Hsu, P. (2006). Dual-band slot dipole antenna fed by a coplanar waveguide. Proceedings of IEEE International Symposium on Antennas and Propagation (ISAP). Singapore. pp. 3589–3592.
Jolliffe, I. T. (2002). Principal component analysis (2nd ed.). New York: Springer.
Khandelwal, M. K., Kanaujia, B. K., & Kumar, S. (2017). Defected ground structure: Fundamentals, analysis, and applications in modern wireless trends. International Journal of Antennas and Propagation, 2017, 2018527, 22 pages.
Kleijnen, J. P. C. (2009). Kriging metamodeling in simulation: A review. European Journal of Operational Research, 192(3), 707–716.
Koziel, S. (2017). Low-cost data-driven surrogate modeling of antenna structures by constrained sampling. IEEE Antennas and Wireless Propagation Letters, 16, 461–464.
Koziel, S., & Bekasiewicz, A. (2016). Rapid simulation-driven multi-objective design optimization of decomposable compact microwave passives. IEEE Transactions on Microwave Theory and Techniques, 64(8), 2454–2461.
Koziel, S., & Pietrenko-Dabrowska, A. (2019). Performance-based nested surrogate modeling of antenna input characteristics. IEEE Transactions on Antennas and Propagation, 67(5), 2904–2912.
Koziel, S., & Sigurðsson, A. T. (2018). Triangulation-based constrained surrogate modeling of antennas. IEEE Transactions on Antennas and Propagation, 66(8), 4170–4179.
Koziel, S., Bekasiewicz, A., Kurgan P., & Bandler, J. W. (2015). Expedited multi-objective design optimization of miniaturized microwave structures using physics-based surrogates. IEEE MTT-S International Microwave Symposium. Phoenix. pp. 1–3.
Koziel, S., Sigurðsson, A. T., & Szczepanski, S. (2018). Uniform sampling in constrained domains for low-cost surrogate modeling of antenna input characteristics. IEEE Antennas and Wireless Propagation Letters, 17(1), 164–167.
Liu, Z., Yang, M., & Li, W. (2016a). A sequential Latin hypercube sampling method for metamodeling. In L. Zhang, X. Song, & Y. Wu (Eds.), Theory, methodology, tools and applications for modeling and simulation of complex systems (AsiaSim 2016, Communication in Computer and Information Science) (Vol. 643, pp. 176–185). New York: Springer.
Liu, Y., Shi, Y., Zhou, Q., & Xiu, R. (2016b). A sequential sampling strategy to improve the global fidelity of metamodels in multi-level system design. Structural and Multidisciplinary Optimization, 53(6), 1295–1313.
Pietrenko-Dabrowska, A., & Koziel, S. (2019). Numerically efficient algorithm for compact microwave device optimization with flexible sensitivity updating scheme. International Journal of RF and Microwave Computer-Aided Engineering, 29(7), e21714.
Queipo, N. V., Haftka, R. T., Shyy, W., Goel, T., Vaidynathan, R., & Tucker, P. K. (2005). Surrogate-based analysis and optimization. Progress in Aerospace Sciences, 41(1), 1–28.
Sim, C. Y. D., Chang, M. H., & Chen, B. Y. (2014). Microstrip-fed ring slot antenna design with wideband harmonic suppression. IEEE Transactions on Antennas and Propagation, 62(9), 4828–4832.
Ye, K. Q. (1998). Orthogonal column latin hypercubes and their application in computer experiments. Journal of the American Statistical Association, 93, 1430–1439.
Ying, M., & Sun, M. (2017). Some feasibility sampling procedures in interval methods for constrained global optimization. Journal of Global Optimization, 67(1–2), 379–397.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Koziel, S., Pietrenko-Dabrowska, A. (2020). Constrained Modeling Using Principal Component Analysis. In: Performance-Driven Surrogate Modeling of High-Frequency Structures. Springer, Cham. https://doi.org/10.1007/978-3-030-38926-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-38926-0_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-38925-3
Online ISBN: 978-3-030-38926-0
eBook Packages: EngineeringEngineering (R0)