Abstract
The response correction techniques described in Chap. 6 utilized explicit formulation where the relationship between the high-fidelity model and the surrogate is quantified by a number of parameters that need to be extracted in order to identify the model. In this chapter, we focus on nonparametric methods, where the relationship between the low- and high-fidelity models is identified, or better said, directly extracted from the model responses; however, it is not explicitly given by any formula. In particular, in the optimization context, the surrogate model prediction may be obtained by tracking the response changes of the low-fidelity model and applying these changes to the known high-fidelity model response at a certain reference design. The formulation of nonparametric techniques is generally more complex and involves more restrictive assumptions regarding their applicability. However, these methods are normally characterized by a better generalization capability than the parametric techniques (cf. Chap. 6). The particular techniques described in this chapter are adaptive response correction, adaptive response prediction, and shape-preserving response prediction. We provide their formulations and illustrate their performance using design problems that involve airfoil shapes, and microwave devices, as well as antenna structures.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abbott, I.H., and Von Doenhoff, A.E., Theory of Wing Sections, Dover Publications, 1959.
Agilent ADS (2011), Agilent Technologies, 1400 Fountaingrove Parkway, Santa Rosa, CA 95403–1799.
Bandler, J.W., Biernacki, R.M., Chen, S.H., Grobelny, P.A., Hemmers, R.H., (1994) Space mapping technique for electromagnetic optimization. IEEE Trans. Microwave Theory Tech. 42, 2536–2544.
Bandler, J.W., Cheng, Q.S., Gebre-Mariam, D.H., Madsen, K., Pedersen, F., Søndergaard, J. (2003) EM-based surrogate modeling and design exploiting implicit, frequency and output space mappings. IEEE Int. Microwave Symp. Digest, Philadelphia, PA, pp. 1003–1006.
Chen, Z.N. (2008) Wideband microstrip antennas with sandwich substrate. IET Microw. Ant. Prop., vol. 2, pp. 538–546.
Cheng, Q.S., Bandler, J.W., Koziel, S., Bakr, M.H., and Ogurtsov, S. (2010) The state of the art of microwave CAD: EM-based optimization and modeling. Int. J. RF and Microwave Computer-Aided Eng., vol. 20, no. 5, pp. 475–491.
Conn, A.R., Gould, N.I.M., Toint, P.L. (2000) Trust Region Methods. MPS-SIAM Series on Optimization.
CST Microwave Studio (2013). CST AG, Bad Nauheimer Str. 19, D-64289 Darmstadt, Germany.
Dielectric resonator filter, Examples (2011) CST Microwave Studio, ver. 2011, CST AG, Bad Nauheimer Str. 19, D-64289 Darmstadt, Germany.
em TM Version 12.54 (2010), Sonnet Software, Inc., 100 Elwood Davis Road, North Syracuse, NY 13212, USA.
FEKO (2008), Suite 5.4, EM Software & Systems-S.A. (Pty) Ltd, 32 Techno Lane, Technopark, Stellenbosch, 7600, South Africa.
Forrester, A.I.J., Keane, A.J. (2009) Recent advances in surrogate-based optimization, Prog. in Aerospace Sciences, 45, pp. 50−79.
Guan, X., Ma, Z., Cai, P., Anada, T., and Hagiwara, G. (2008) A microstrip dual-band bandpass filter with reduced size and improved stopband characteristics. Microwave and Opt. Tech. Lett., 50, pp. 618–620.
Hsieh, M.Y., and Wang, S.M. (2005) Compact and wideband microstrip bandstop filter. IEEE Microwave and Wireless Component Letters, vol. 15, no. 7, pp. 472–474.
Journel, A.G., Huijbregts, Ch.J. (1981) Mining Geostatistics. Academic Press.
Kolda, T.G., Lewis, R.M., Torczon, V. (2003). Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev., 45, pp. 385−482.
Koziel, S., Bandler, J.W., Madsen, K. (2006) A space mapping framework for engineering optimization: theory and implementation. IEEE Trans. Microwave Theory Tech., 54. 3721-3730.
Koziel, S., Bandler, J.W., Madsen, K. (2006b) Theoretical justification of space-mapping-based modeling utilizing a data base and on-demand parameter extraction. IEEE Trans. Microwave Theory Tech., vol. 54, no. 12, pp. 4316-4322.
Koziel, S., Bandler, J.W., Madsen, K. (2009a) Space mapping with adaptive response correction for microwave design optimization. IEEE Trans. Microwave Theory Tech., 57, pp. 478–486.
Koziel, S. (2010a) Shape-preserving response prediction for microwave design optimization. IEEE Trans. Microwave Theory and Tech., 58, pp. 2829–2837.
Koziel, S., (2010c) Multi-fidelity multi-grid design optimization of planar microwave structures with Sonnet. International Review of Progress in Applied Computational Electromagnetics, Tampere, Finland, 719–724.
Koziel, S. (2010d) Improved microwave circuit design using multipoint-response-correction space mapping and trust regions. Int. Symp. Antenna Technology and Applied Electromagnetics, ANTEM 2010, Ottawa, Canada.
Koziel, S. (2010e) Shape-preserving response prediction for microwave circuit modeling. IEEE MTT-S Int. Microwave Symp. Dig., Anaheim, CA, pp. 1660–1663.
Koziel, S. (2010g) Computationally efficient multi-fidelity multi-grid design optimization of microwave structures. Applied Computational Electromagnetics Society Journal, 25, 578–586.
Koziel, S., and Leifsson, L. (2012a) Multi-fidelity airfoil shape optimization with adaptive response prediction.AIAA/ISSMO Multidisciplinary Analysis and Optimization Conf.
Koziel, S., and Leifsson, L. (2012c) Adaptive Response Correction for Surrogate-Based Airfoil Shape Optimization. 30th AIAA Applied Aerodynamics Conference, New Orleans, Louisiana, June 25–28.
Koziel, S., and Leifsson, L. (2013c) Surrogate-Based Aerodynamic Shape Optimization by Variable-Resolution Models. AIAA Journal, vol. 51, no. 1, pp. 94–106.
Koziel, S., Ogurtsov, S. (2011d) Bandwidth enhanced design of dielectric resonator antennas using surrogate-based optimization. IEEE Int. Symp. Antennas Prop., Spokane, WA, July 3–8.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Koziel, S., Leifsson, L. (2016). Nonparametric Response Correction Techniques. In: Simulation-Driven Design by Knowledge-Based Response Correction Techniques. Springer, Cham. https://doi.org/10.1007/978-3-319-30115-0_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-30115-0_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30113-6
Online ISBN: 978-3-319-30115-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)