Application of BPOE and CVaR in the determination of optimal controls of round plate oscillations
DOI:
https://doi.org/10.17721/1812-5409.2023/2.16Keywords:
control, vibration of plate, bPOE, CVaRAbstract
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
ROCKAFELLAR, T. & ROYSET, J. O. (2010) On buffered failure probability in design and optimization of structures. Reliability Engineering and System Safety. 95. p. 499 - 510.
ZRAZHEVSKY, G., GOLODNIKOV, A. & URYASEV, S. (2019) Mathematical Methods to Find Optimal Control of Oscillations of a Hinged Beam (Deterministic Case). Cybernetics and Systems Analysis. 55. p. 1009-1026.
ZRAZHEVSKY, G., GOLODNIKOV, A. & URYASEV, S. (2020) Application of Buffered Probability of Exceedance in Reliability Optimization Problems. Cybernetics and Systems Analysis. 56. p. 476-484.
ZRAZHEVSKY, G.M, ZRAZHEVSKA V.F. & GOLODNIKOV, A.N. (2022) Developing a Model for a Modulating Mirror Fixed on Active Supports. Deterministic Problem. Cybernetics and systems analysis. 58. p. 707-712.
ZRAZHEVSKY, G.M, & ZRAZHEVSKA V.F. (2021) Modelyuvannya skinchennykh neodnoridnostey dyskretnymy osoblyvostyamy. Zhurnal obchyslyuvalʹnoyi ta prykladnoyi matematyky. 1(135). p. 138-144.
MAFUSALOV, A. & URYASEV, S. (2018) Buffered probability of exceedance: mathematical properties and optimization. SIAM. J. Optim. 28. p. 1077-1103.
ROCKAFELLAR, R.T. & URYASEV S. (2000) Optimization of conditional value-at-risk The Journal of Risk. 2 (3). р. 21-41.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 G. M. Zrazhevsky, V. F. Zrazhevska
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
