Abstract
Mathematical tools are proposed for the optimization of chemical compositions of alloys and technological parameters of their processing during the development of new steel grades under considerable uncertainty. By reason of uncertainty, statistical models for mechanical properties of new alloys are used in optimization problems. Particularly, CVaR is used to estimate the right tail of CVN (Charpy V-Notch impact on toughness) distribution. This implies the use of nonconcave (convex) objective functions in maximization problems. Mathematical methods are proposed for solving maximization problems.
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References
A. Golodnikov, Y. Macheret, A. Trindade, S. Uryasev, and G. Zrazhevsky, “Optimization of composition and processing parameters for the development of steel alloys: A statistical model-based approach,” Journal of Industrial and Management Optimization, 3, No. 3, 489–501 (2007).
A. Golodnikov, Y. Macheret, A. Trindade, S. Uryasev, and G. Zrazhevsky, “Statistical modeling of composition and processing parameters for alloy development,” Modeling and Simulation in Material Science and Engineering, 13, No. 4, 633–644 (2005).
G. Zrazhevsky, A. Golodnikov, S. Uryasev, and A. Zrazhevsky, “Advanced statistical tools for modeling of composition and processing parameters for alloy development,” in: A. Migdalas and A. Karakitsiou (eds.), Optimization, Control, and Applications in the Information Age, Springer Proceedings in Mathematics & Statistics (2015), pp. 393–413.
W. R. Corowin and A. M. Houghland, “Effect of specimen size and material condition on the Charpy impact properties of 9Cr-1Mo-V-Nb steel,” in: The Use of Small-Scale Specimens for Testing Irradiated Material, ASTM STP 888 (Philadelphia, PA) (1986), pp. 325–338.
E. Lucon, R. Chaouadi, A. Fabry, J.-L. Puzzolante, and E. Valle, “Characterizing material properties by the use of full-size and sub-size Charpy tests,” in: T. Siewert and M. P. Manahan (eds.), Pendulum Impact Testing: A Century of Progress, ASTM STP 1380, American Society for Testing and Materials, West Conshohocken, PA (1999), pp. 146–163.
R. Koenker and G. Bassett, “Regression quantiles,” Econometrica, 46, No. 1, 33–50 (1978).
R. T. Rockafellar and S. Uryasev, “Conditional Value-at-Risk for general loss distributions,” Journal of Banking and Finance, 26, No. 7, 1443–1471 (2002),
R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton (NJ) (1970).
J. H. Friedman and N. I. Fisher, “Bump-hunting in high-dimensional data,” Statistics and Computing, 9, 123–143 (1999).
S. I. Gass, Linear Programming: Methods and Applications, 5th Edition, McGraw-Hill, New York (1985).
H. M. Markowitz, “Portfolio selection,” Journal of Finance, 7, No. 1, 77–91 (1952).
A. P. Goldren and T. B. Cox, AMAX Report, CPR-2, AMAX Materials Research Center, Ann Arbor, MI (1986).
A. A. Zhiglyavskii and A. G. Zhilinskas, Search Methods for Global Extrema [in Russian], Nauka, Moscow (1991).
E. Hansen, Global Optimization Using Interval Analysis, Dekker, New York (1992).
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*The study is carried out with financial support from the European Office of Aerospace Research and Development, grant P-590/EOARD 133063.
Translated from Kibernetika i Sistemnyi Analiz, No. 4, July–August, 2016, pp. 118–133.
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Zrazhevsky, G.M., Golodnikov, A.N., Uryasev, S.P. et al. Optimization Techniques to Obtain the Best Combination of Alloy Strength and Toughness* . Cybern Syst Anal 52, 600–612 (2016). https://doi.org/10.1007/s10559-016-9862-x
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DOI: https://doi.org/10.1007/s10559-016-9862-x