Hava Taşıt Modeli İçin Belirlenen Bant Genişliğinde Model İndirgeme Tekniklerinin Karşılaştırılması

Yıl 2020, Cilt: 7 Sayı: 2, 882 - 894, 31.05.2020

Onur Yılmaz Bilal Erol

https://doi.org/10.31202/ecjse.722370

Öz

Bu çalışma popüler iki model indirgeme tekniğinin başarımlarının karşılaştırılması üzerinedir. Bir hava taşıtının, büyük ölçekli sistem modeli zemin titreşim testi (Ground Vibration Test, (GVT)) uygulanarak elde edilmiştir. Titreşim tabanlı uygulamalarda doğal frekanslar oldukça önemlidir, tasarımcılar bilhassa bu frekanslara odaklanmayı hedeflemektedir. Bundan dolayı kestirilecek düşük dereceden modelin, orijinal sistemi bu frekansların etrafında benzer cevap vermesi gerekmektedir. Bunun gerçeklenmesi için, iki popüler yöntem olan frekans tabanlı model indirgeme (Frequency Weighted Balanced Model Reduction (FWBMR)) ile Rasyonel Krylov model indirgeme tekniklerine başvurulmuştur. Her iki metodun başarımları ele alınmış, ve bilhassa Rasyonel Krylov metodunun hava taşıt gövdesinin dalgalanma modeli üzerindeki esnekliği gösterilmiştir.

Anahtar Kelimeler

Sistem Modeli İndirgeme, Büyük Ölçekli Sistemler, Uçak Modeli, Sistem Tanımlama

A Comparative Study of Model Reduction Techniques for Specified Bandwidth on Aircraft

Öz

This paper presents a comparison of two popular model reduction techniques on an aircraft model. Large scale model of the aircraft is obtained via Ground Vibration Test(GVT). In vibration based applications, natural frequencies are important, designers aims to focus on especially these frequencies. Therefore reduced order model should be obtained adequately by approximating original system at interested frequencies. In order to perform this, two popular model reduction methods; Frequency Weighted Balanced Model Reduction (FWBMR) and Rational Krylov based model reduction methods are resorted in this paper. Effectiveness of these two methods are discussed, and specifically flexibility of Rational Krylov based method is demonstrated on body freedom flutter aircraft model.

Anahtar Kelimeler

Model Order reduction, Large Scale Systems, Aircraft Model

Kaynakça

• S. J. Loring, “General approach to the flutter problem,” SAE Transactions, pp. 345–356, 1941.
• A. C. Antoulas, D. C. Sorensen, and S. Gugercin, “A survey of model reduction methods for large-scale systems,” tech. rep., 2000.
• J. Gu, “Efficient model reduction methods for structural dynamics analyses.,” 2001.
• Z.-Q. Qu, Model order reduction techniques with applications in finite element analysis. Springer Science & Business Media, 2013.
• T. Lieu, C. Farhat, and M. Lesoinne, “Reduced-order fluid/structure modeling of a complete aircraft configuration,” Computer methods in applied mechanics and engineering, vol. 195, no. 41-43, pp. 5730–5742, 2006.
• D. Amsallem and C. Farhat, “Stabilization of projection-based reducedorder models,” International Journal for Numerical Methods in Engineering, vol. 91, no. 4, pp. 358–377, 2012.
• J. Kos, R. Maas, B. Prananta, M. Hounjet, and B. Eussen, “Structural dynamics model reduction and aeroelastic application to fighter aircraft,” 2009.
• B. Salimbahrami and B. Lohmann, “Order reduction of large scale secondorder systems using krylov subspace methods,” Linear Algebra and its Applications, vol. 415, no. 2-3, pp. 385–405, 2006.
• A. C. Antoulas, Approximation of large-scale dynamical systems, vol. 6. Siam, 2005.
• D. F. Enns, “Model reduction with balanced realizations: An error bound and a frequency weighted generalization,” in Decision and Control, 1984. The 23rd IEEE Conference on, IEEE, 1984.
• E. Grimme, Krylov projection methods for model reduction. PhD thesis, University of Illinois at Urbana Champaign, 1997.
• C. P. M. Chicunque, Linear, Parameter-Varying Control of Aeroservoelastic Systems. PhD thesis, University of Minnesota, 2015.
• A. Gupta, P. J. Seiler, and B. P. Danowsky, “Ground vibration tests on a flexible flying wing aircraft-invited,” in AIAA Atmospheric Flight Mechanics Conference, p. 1753, 2016.
• C. P. Moreno, A. Gupta, H. Pfifer, B. Taylor, and G. J. Balas, “Structural model identification of a small flexible aircraft,” in American Control Conference (ACC), 2014, pp. 4379–4384, IEEE, 2014.
• B. Moore, “Principal component analysis in linear systems: Controllability, observability, and model reduction,” IEEE transactions on automatic control, vol. 26, no. 1, pp. 17–32, 1981.
• Y. Liu and B. D. Anderson, “Singular perturbation approximation of balanced systems,” International Journal of Control, vol. 50, no. 4, pp. 1379– 1405, 1989.
• K. Glover, “All optimal hankel-norm approximations of linear multivariable systems and their l,?-error bounds,” International journal of control, vol. 39, no. 6, pp. 1115–1193, 1984.
• C.-A. Lin, T.-Y. Chiu, et al., “Model-reduction via frequency weighted balanced realization,” Control-Theory and Advanced Technology, vol. 8, no. 2, pp. 341–351, 1992.
• B. Lohmann and B. Salimbahrami, “Introduction to krylov subspace methods in model order reduction,” Methods and Applications in Automation, pp. 1–13, 2000.
• Z. Bai, “Krylov subspace techniques for reduced-order modeling of largescale dynamical systems,” Applied numerical mathematics, vol. 43, no. 1-2, pp. 9–44, 2002.