Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-29T16:57:16.497Z Has data issue: false hasContentIssue false

Cumulative global metamodels with uncertainty — a tool for aerospace integration

Published online by Cambridge University Press:  03 February 2016

P. H. Reisenthel
Affiliation:
Nielsen Engineering & Research, California, USA
J. F. Love
Affiliation:
Nielsen Engineering & Research, California, USA
D. J. Lesieutre
Affiliation:
Nielsen Engineering & Research, California, USA
R. E. Childs
Affiliation:
Nielsen Engineering & Research, California, USA

Abstract

The integration of multidisciplinary data is key to supporting decisions during the development of aerospace products. Multidimensional metamodels can be automatically constructed using limited experimental or numerical data, including data from heterogeneous sources. Recent progress in multidimensional response surface technology, for example, provides the ability to interpolate between sparse data points in a multidimensional parameter space. These analytical representations act as surrogates that are based on and complement higher fidelity models and/or experiments, and can include technical data from multiple fidelity levels and multiple disciplines. Most importantly, these representations can be constructed on-the-fly and are cumulatively enriched as more data become available. The purpose of the present paper is to highlight applications of these cumulative global metamodels (CGM), their ease of construction, and the role they can play in aerospace integration. A simple metamodel implementation based on a radial basis function network is presented. This model generalises multidimensional data while simultaneously furnishing an estimate of the uncertainty on the prediction. Four examples are discussed. The first two illustrate the efficiency of surrogate-based design/optimisation. The third applies CGM concepts to a data fusion application. The last example is used to visualise extrapolation uncertainty, based on computational fluid dynamics data.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society 2006 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Burman, J., Papila, N., Shyy, W. and Gebart, B.R., Assessment of response surface-based optimisation techniques for unsteady flow around bluff bodies, AIAA 2002-5596.Google Scholar
2. Deloach, R. and Erickson, G.E., Low-order response surface modeling of wind-tunnel data over truncated inference subspaces, AIAA 2003-0456.Google Scholar
3. Forrester, A.I.J., Bressloff, N.W. and Keane, A.J., Response surface model evolution, AIAA 2003-4089.Google Scholar
4. Hirokawa, N., Fujita, K. and Iwase, T., Voronoi diagram based blending of quadratic response surfaces for cumulative global optimisation, AIAA 2002-5460.Google Scholar
5. Knill, D.L., Giunta, A., Baker, C.A., Grossman, B., Mason, W.H., Haftka, R.T. and Watson, L.T., Response surface models combining linear and Euler aerodynamics for supersonic transport design, J Aircr, January-February 1999, 36, (1), pp 7586.Google Scholar
6. Krishnamurphy, T., Response surface approximation with augmented and compactly supported radial basis functions, AIAA 2003-1748.Google Scholar
7. Papila, N., Shyy, W., Griffin, L. and Dorney, D.J., Shape optimisation of supersonic turbines using response surface and neural network methods, AIAA 2001-1065.Google Scholar
8. Walker, E.L., Statistical calibration and validation of a homogeneous ventilated wall-interference correction method for the National Transonic Facility, NASA TP-2005-213947.Google Scholar
9. Rais-Rohani, M. and Singh, M.N., Efficient response surface approach for reliability estimation of composite structures, AIAA 2002-5604.Google Scholar
10. Vittal, S. and Hajela, P., Confidence intervals for reliability estimated using response surface methods, AIAA 2002 5475.Google Scholar
11. Jones, D.R., Schonlau, M. and Welch, W.J., Efficient global optimisation of expensive black-box functions, J Global Opt, 1998, 13, pp 455492.Google Scholar
12. Sobester, A., Leary, S.J. and Keane, A.J., On the design of optimisation strategies based on global response surface approximation models, J Global Opt, 2005, 33, (1), pp 3159.Google Scholar
13. Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vaidyanathan, R. and Tucker, P.K., Surrogate-based analysis and optimisation, Progress in Aerospace Sciences, 2005, 41, pp 128.Google Scholar
14. Poggio, T. and Girosi, F., Network for approximation and learning, Proc IEEE, September 1990, 78, (9), pp 14811497.Google Scholar
15. Raeth, P.G., Gustafson, S.C., Little, G.R. and Puterbaugh, T.S., Stretch and hammer neural networks for n-dimensional data generalisation, Air Force Wright Laboratory Report WL-TR-91-1146, 1992.Google Scholar
16. Vapnik, V.N., The Nature of Statistical Learning Theory. Springer, 1995.Google Scholar
17. Gunn, S.R., Structural modelling with sparse kernels, Proceedings of the 13th IFAC Symposium on System Identification, Rotterdam, Netherlands, 2003.Google Scholar
18. Gramacy, R.B., Lee, H.K.H. and Macready, W., Parameter space exploration with Gaussian process trees, Proceedings of the International Conference on Machine Learning, Omnipress and ACM Digital Library, 2004, pp 353360.Google Scholar
19. Friedman, J.H., Multivariate adaptive regression splines, The Annals of Statistics, 1991, 19, (1), pp 167.Google Scholar
20. Rodman, L.C., Reisenthel, P.H. and Childs, R.E., An automated documentation and reporting system for CFD, AIAA 2002-0986.Google Scholar
22. Zeldin, B.A. and Meade, A.J., Integrating experimental data and mathematical models in simulation of physical systems, AIAA J, 1998, 35, (11), pp 17871790.Google Scholar
23. Matheron, G., Principles of geostatistics, Economic Geology, 1963, 58, pp 12461266.Google Scholar
24. Cressie, N., The origins of Kriging, Mathematical Geology, 1990, 22, (3), pp 239252.Google Scholar
25. Sacks, J., Welch, W.J., Mitchell, T.J. and Wynn, H.P., Design and analysis of computer experiments, Statistical Science, 1989, 4, pp 409435.Google Scholar
26. Orr, M., Optimising the widths of radial basis functions, Proceedings of the Fifth Brazilian Symposium on Neural Networks, Belo Horizonte, Brazil, 1998.Google Scholar
27. Pottmann, M. and Seborg, D.E., Identification of non-linear processes using reciprocal multiquadric functions, J Process and Control, 1992, 2, (4), pp 189203.Google Scholar
28. Hardy, R.L., Multiquadric equations of topography and other irregular surfaces, J Geophys. Res, 1971, 76, (8), pp 19051915.Google Scholar
29. Franke, R., Scattered data interpolation: Test of some methods, Math of Comp, 1982, 38, (157), pp 181200.Google Scholar
30. Orr, M.J.L., Regularisation in the selection of radial basis function centres, Neural Computation, 1995, 7, (3), pp 606623.Google Scholar
31. Strang, G., Linear Algebra and Its Applications, Academic Press, New York, USA, 1980, p 142.Google Scholar
32. Norton, J.P., An Introduction to Identification, Academic Press, New York, USA, 1986, pp 87119.Google Scholar
33. Strickland, J.H., Axisymmetric bluff-body flow: a vortex solver for thin shells, Sandia Report SAND91-2760, 1992.Google Scholar
34. Pediroda, V., Poloni, C. and Clarich, A., A fast and robust adaptive methodology for airfoil design under uncertainties based on game theory and self-organising-map theory, AIAA 2006-1472.Google Scholar
35. Childs, R.E., Reisenthel, P.H., Rose, J. and Maly, J., Large asymmetric launch vehicle payload fairing, NEAR TR 611, 2005.Google Scholar
36. Buning, P.G., Jespersen, D.C., Pulliam, T.H., Klopfer, G.H., Chan, W.M., Slotnick, J.P., Krist, S.E. and Renze, K.J., Overflow user’s manual version 1.8r, NASA Ames Research Center, 2000.Google Scholar
37. Chan, W.M. and Steger, J.L., Enhancements of a three-dimensional hyperbolic grid generation scheme, Appl Math and Comput, 1992, 51, pp 181205.Google Scholar
38. Giunta, A.A., Wojtkiewicz, S.F. and Eldred, M.S., Overview of modern design of experiments methods for computational simulations,’ AIAA 2003-0649.Google Scholar
39. Audet, C. and Dennis, J.E., A pattern search filter method for nonlinear programming without derivatives, SIAM J Optim, 2004, 14, (4), pp 9801010.Google Scholar
40. Kolda, T.G., Lewis, R.M. and Torczon, V., Optimisation by direct search: new perspectives on some classical and modern methods, SIAM Review, 2003, 45, (3), pp 385482.Google Scholar
41. Lesieutre, D.J., Love, J.F. and Dillenius, M.F.E., MISL3 aerodynamic analysis for finned vehicles with axisymmetric bodies, NEAR TR 561, 2004.Google Scholar