A modified discrete least-squares method for optimal solutions in inverse problems

40th AIAA Aerospace Sciences Meeting and Exhibit

Volumn , Issue , 2002, Pages

  Frankel, J I ^a   Keyhani, M ^a   Taira, K ^a  

^a UNIVERSITY OF TENNESSEE   (United States)

Author keywords

Error estimation; Heating cooling rate data; Instrument models; Inverse analysis; Least squares method; Norms; Radial basis functions; V curve analysis

Indexed keywords

AEROSPACE ENGINEERING; DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; ERRORS; ESTIMATION; FORECASTING; HEAT FLUX; LEAST SQUARES APPROXIMATIONS; OPTIMAL SYSTEMS; RADIAL BASIS FUNCTION NETWORKS; THERMOCOUPLES; TRANSIENT ANALYSIS;

CURVE ANALYSIS; HEATING/COOLING RATE; INSTRUMENT MODELS; INVERSE ANALYSIS; LEAST SQUARES METHODS; NORMS; RADIAL BASIS FUNCTIONS;

INVERSE PROBLEMS;

EID: 85088758876     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2002-657     Document Type: Conference Paper

References (25)

1. Beck, J.V., Blackwell, B., and St. Glair, Jr., C.R., Inverse Heat Conduction, Wiley, NY, 1985.
2. Trujillo, D.M., and Busby, H.R., Practical Inverse Analysis in Engineering, CRC Press, Boca Raton, FL, 1997.
3. Kurpisz, K. and Nowak, A.J., Inverse Thermal Problems, Computational Mechanics Publications, Southampton, UK, 1995.
4. Frankel, J.I., and Keyhani, M., "Inverse Heat Conduction: The Need of-Data for Design and Diagnostic Purposes", 18th IASTED International Conference on Modelling, Identification and Control, Innsbruck, Austria, Feb. 15-18, 1999.
5. Frankel, J.I. and Keyhani, M., "A New Approach for Solving Inverse Solidification Design Problems", Numerical Heat Transfer, Part B, Vol. 30, No. 2, 1996, pp. 161-177.
6. Mendenhall, W., and R.L. Scheaffer, Mathematical Statistics with Applications, Duxbury Press, North Scituate, MA, 1973.
7. Maron, M.J., Numerical Analysis, 2nd ed., MacMillan Publishing Company, New York, 1987.
8. Gerald, C.F., and P.O. Wheatley, Applied Numerical Analysis, 6th ed., Addison-Wesley, Reading, MA, 1999.
9. Doebelin, E.O., Measurement Systems, Revised Edition, McGraw-Hill Book Company, New York, 1975.
10. Delves, L.M. and Mohamed, J.L., Computational Methods for Integral Equations, Cambridge University Press, Cambridge, 1988.
11. Wing, G.M. A Primer on Integral Equations of the First Kind, SIAM, Philadelphia, PA, 1991.
12. Frankel, J. L, Osborne, G.E., and Keyhani, M., "Thermal Design Aspects in Inverse Heat Conduction", Third International Conference on Dynamic System Identification and Inverse Problems, Moscow, Russia, May 30-June 5, 1998.
13. Osborne, G.E., Frankel, J.I., and Keyhani, M., "The Function Decomposition and its Application in Thermal Inverse Analysis", International Mechanical Engineering Congress and Exhibition, Anaheim, CA, Nov. 15-20, 1998.
14. Hardy, R.L., "Theory and Applications of the Multiquadric-Biharmonic Method", Computers Math. Applic., vol. 19, Nos. 8,9, 1990, pp. 163-208.
15. Frankel, J. L, "Direct Least-Square Solutions to Integral Equations Containing Discrete Data", J. Thermophysics and Heat Transfer, Vol. 10, No. 1, 1996, pp. 182-186.
16. Finlayson, B.A. "The Method of Weighted Residuals and Variational Principles", Academic Press, New York, 1972.
17. Frankel, J. L, "Cumulative Variable Formulation to Transient Conductive and Radiative Transport in Participating Media", AIAA Journal of Thermophysics and Heat Transfer, Vol. 9, No. 2, 1995, pp. 210-218.
18. Frankel, J. L, and Osborne, G.E., "A New Time Treatment for Solving Partial Integro-Differential Equations of Radiative Transport", IMA Journal of Numerical Analysis, Vol. 19. 1999, pp. 91-103.
19. Frankel, J. L, and Keyhani, M., "A Global Time Treatment for Inverse Heat Conduction Problems", J. Heat Transfer, Vol. 119, No. 4, 1997, pp.673-683.
20. Bender, C.M., and Orszag, S.A., Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978.
21. Taylor, A.E., and Lay, D. C., Introduction to Functional Analysis, 2nd ed, Kreiger Publishing Company, Malabar, FL, 1986.
22. Frankel, J. L, "Advanced Diagnostic Analyses and Inverse Heat Conduction", ICME 2000, Shanghai, China, November 20-22, 2000.
23. Hansen, P.C., and D. P. O'leary, "The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems", UMIACS-TR-91-142 (CS-TR-2781), University of Maryland, College Park, MD, 1991
24. Taira, K., J.I. Frankel, and M. Keyhani, "Metric Analysis for the Modified Discrete Least-Squares Method", 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 14-17, 2002
25. Frankel J. L, B. Vick, and M.N. Ozisik, "Flux Formulation in Hyperbolic Heat Conduction", J. Applied Physics, vol. 58, No. 9, 1985, pp.3340-3345.