Mixed Gaussian Process and State-Space Approach for Fatigue ...

Fig. 6 Crack growth curve from the hybrid model.CONCLUSIONThe hybrid state space andGaussian Process (SS-GP) modelgives a better prediction of cracklength evolution and crackgrowth rate compared to both aphysics based “pure” state spacemodel and a data driven “pure”GP model. The hybrid model notonly implicitly incorporatesuncertainty into physics basedstate space model but also avoidsexponential error accumulationdue to the Paris type formulation.ACKNOWLEDGEMENTThis research was supported by the Air Force Office of Scientific Research, grant number:FA9550-06-1-0309, with Technical Monitor Dr. Victor GiurgiutiuREFERENCES1. Schwabache, M.A. 2005. “A Survey of Data-Driven Prognostics,” presented at theInfotech@Aerospace AIAA Conference, September 26-29, 2005.2. Ghonem, H., and Dore, S. 1987, “Experimental Study of the Constant Probability Crack GrowthCurves Under Constant Amplitude Loading ,” Engineering Fracture Mechanics., 27(1):1-253. Suresh, S. 1991, Fatigue of Materials, Cambridge University Press, Cambridge, U.K4. Newman, J.C., Jr. 1982, "Prediction of fatigue crack growth under variable-amplitude andspectrum loading using a closure model". ASTM STP 761: 255-2775. Newman, J.C. Jr. 1984. A crack-opening stress equation for fatigue crack growth. InternationalJournal of Fracture 24, R131–R135.6. Newman, J.C. Jr.1992. FASTRAN-II – A Fatigue Crack Growth Structural Analysis Program.NASA Technical Memorandum 104159, Langley Research Center.7. Harter, J.A. 1999, AFGROW Users’ Guide and Technical Manual. Report No. AFRL-VA-WP-1999-3016, Air force Research Laboratory.8. Ray, A., Patankar, R.P.,2001, “Fatigue Crack Growth Under Variable Amplitude Loading-Part-I:Model Formulation in State-Space Setting,” J. of Applied Mathematical Modeling, pp. 979-994.9. Ray, A., Patankar, R.P.,2001, “Fatigue Crack Growth Under Variable Amplitude Loading-Part-II:Code Development and Model Validation,” J. of Applied Mathematical Modeling, pp. 995-1013.10. Patankar, R., Qu, R. 2005, “Validation of the state-space model of fatigue crack growth in ductilealloys under variable-amplitude load via comparison of the crack-opening stress data,” Int J. ofFracture., 131(4):337-34911. QU, R. 1 ; Patankar, R. P.; Rao, M. D. 2006, “A third-order state-space model for fatigue crackgrowth ”, Fatigue Fract Engng Mater Struct, 29(12):1045-105512. Haque, M.E., and Sudhakari,K.V.,2001, “ANN based prediction model for fatigue crack growthin DP steel,” Fatigue Fract Engng Mater Struct., 23, 63–68.13. Hidetoshi, F.., D.. Mackay, and H. Bhadeshia. 1996, “Bayesian Neural Network Analysis of FatigueCrack Growth Rate in Nickel Base Supper alloys” ISIJ International., 36(11): 1373-1 382.14. MacKay, D. J. C. 1997, “Gaussian processes - a replacement for supervised neural networks?”Tutorial lecture notes for NIPS,1-32.15. MacKay, D. 1998, Introduction to Gaussian processes. In C. M. Bishop, editor, Neural Networksand Machine Learning, volume 168 of NATO ASI Series, pages 133-165. Springer, Berlin.16. Rasmussen, C., and C. Williams.2006, Gaussian Processes for Machine Learning. The MIT Press,Cambridge, MA, 2006.17. ASTM Standards, 1981, ASTM E 399-81, PART-10.