Application of BPOE and CVaR in the determination of optimal controls of round plate oscillations

Authors

DOI:

https://doi.org/10.17721/1812-5409.2023/2.16

Keywords:

control, vibration of plate, bPOE, CVaR

Abstract

The work is devoted to the modeling of forced mono harmonic oscillations of a circular plate on active supports in order to determine the optimal location of the minimum number and optimal controls of supports, which ensure the deviation from the given shape of the wave motion of the plate surface with the required accuracy. It was assumed that the plate contains an ensemble of small inhomogeneities (defects) with unknown geometric and physical characteristics. Defects were modeled by high-order singularities, which ensure the equivalence of the boundary value problem solution with specified accuracy to a given power of a small parameter, which is the characteristic area of the regions of individual defects. Stochastic optimization is chosen as the main method of problem research. The probability of exceeding the rms deviation of the oscillation form of the controlled plate from the given wave profile (probability of failure) is considered as a criterion of optimality. The formation of a quantitative characteristic of the probability of failure was carried out by constructing scenarios with generated defects with random characteristics. It is proposed to use the risk measures bPOE and CVaR, which are quasi-convex with respect to random variables.

Pages of the article in the issue: 112 - 115

Language of the article: Ukrainian

References

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ZRAZHEVSKY, G.M, & ZRAZHEVSKA V.F. (2021) Modelyuvannya skinchennykh neodnoridnostey dyskretnymy osoblyvostyamy. Zhurnal obchyslyuvalʹnoyi ta prykladnoyi matematyky. 1(135). p. 138-144.

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Published

2023-12-23

How to Cite

Zrazhevsky, G. M., & Zrazhevska, V. F. (2023). Application of BPOE and CVaR in the determination of optimal controls of round plate oscillations. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (2), 112–115. https://doi.org/10.17721/1812-5409.2023/2.16

Issue

Section

Differential equations, mathematical physics and mechanics