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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\textit{G. M. Zrazhevsky} et al., Cybern. Syst. Anal. 56, No. 3, 476--484 (2020; Zbl 1454.74123); translation from Kibern. Sist. Anal. 2020, No. 3, 152--162 (2020)

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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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