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Application of buffered probability of exceedance in reliability optimization problems. (English. Russian original) Zbl 1454.74123
Cybern. Syst. Anal. 56, No. 3, 476-484 (2020); translation from Kibern. Sist. Anal. 2020, No. 3, 152-162 (2020).
Summary: We propose an approach to solving the problem of optimizing the reliability of complex systems using Buffered Probability of Exceedance (bPOE). As a research subject, we consider the model of optimal control of oscillations of a hinged beam with random defects. This example shows that minimizing bPOE in reliability optimization problems is more preferable than minimizing the classical probability of exceedance.
MSC:
74M05 Control, switches and devices (“smart materials”) in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74P10 Optimization of other properties in solid mechanics
74S60 Stochastic and other probabilistic methods applied to problems in solid mechanics
93E20 Optimal stochastic control
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References:
[1] G. M. Zrazhevsky, “Determination of the optimal parameters of the beam waveform actuation,” Bulletin of Taras Shevchenko National University of Kyiv, Ser. Physics & Matematics, Issue 3, 138-141 (2013). · Zbl 1289.74084
[2] Zrazhevsky, G.; Golodnikov, A.; Uryasev, S., Mathematical methods to find optimal control of oscillations of a hinged beam (Deterministic case), Cybern. Syst. Analysis, 55, 6, 1009-1026 (2019) · Zbl 07190727
[3] Rockafellar, R. T.; Royset, J. O., On buffered failure probability in design and optimization of structures, Reliability Engineering & System Safety, 95, 5, 499-510 (2010)
[4] R. T. Rockafellar, “Convexity and reliability in engineering optimization,” in: Proc. of the 9th Intern. Conf. on Nonlinear Analysis and Convex Analysis (Chiangrai, Thailand) (2015), pp. 1-10.
[5] Rockafellar, R. T.; Royset, J. O., Random variables, monotone relations, and convex analysis, Mathematical Programming, 148, 1-2, 297-331 (2014) · Zbl 1330.60009
[6] Mafusalov, Alexander; Uryasev, Stan, Buffered Probability of Exceedance: Mathematical Properties and Optimization, SIAM Journal on Optimization, 28, 2, 1077-1103 (2018) · Zbl 1395.90191
[7] Norton, Matthew; Uryasev, Stan, Maximization of AUC and Buffered AUC in binary classification, Mathematical Programming, 174, 1-2, 575-612 (2018) · Zbl 1421.90099
[8] Donnell, LH, Beams, Plates, and Shells (1976), New York: McGraw-Hill Book Company, New York
[9] S. Timoshenko asnd S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-hill Book Company, New York (1959). · Zbl 0114.40801
[10] Rockafellar, R. Tyrrell; Uryasev, Stan, The fundamental risk quadrangle in risk management, optimization and statistical estimation, Surveys in Operations Research and Management Science, 18, 1-2, 33-53 (2013)
[11] Rockafellar, R. Tyrrell; Uryasev, Stanislav, Optimization of conditional value-at-risk, The Journal of Risk, 2, 3, 21-41 (2000)
[12] Rockafellar, RT; Uryasev, S., Conditional Value-at-Risk for general loss distributions, J. of Banking and Finance, 26, 7, 1443-1471 (2002)
[13] AORDA Portfolio Safeguard (PSG). URL: http://www.aorda.com/html/PSG_Help_HTML/index.html?bpoe.htm.
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