Deterministic and stochastic methods combining while solving the problem of defectoscopy of an elastic rod
DOI:
https://doi.org/10.17721/1812-5409.2021/4.4Keywords:
harmonic rod oscillations, natural frequencies, flaw detection, Bootstrap-aggregated Regression TreesAbstract
The paper considers the problem of natural harmonic oscillations of an elastic rod with stress-free ends in the presence of one or a set of defects. Defects are modeled by the inhomogeneity of the Young's modulus. The location of the defects, their geometric size, which is considered small, and the change in elastic properties are the parameters of the defects. The analysis of natural frequency shifts caused by the defect of the rod is the subject of the study. The aim of the work is a mathematical substantiation for the construction of fast and stable algorithms for determining the defect parameters of elastic bodies by analyzing free oscillations. The paper uses and compares fundamentally different research methods. The first methods are classical mathematical methods of mechanics, applied to the analysis of deterministic systems and based on analytical studies combined with numerical implementation. In contrast, a composite machine learning meta-algorithm used in standard statistical classification and regression - Bootstrap-aggregated Regression Trees (BART) - is used to solve the inverse problem. When comparing the constructed algorithms, the statistical method Sampling was used, which allowed to quantify the accuracy and stability of the algorithms.
Pages of the article in the issue: 35 - 38
Language of the article: Ukrainian
References
KAPLUNOV, J., PRIKAZCHIKOV., D., SERGUSHOVA, O. (2016). Journal of Sound and Vibration, 366, p. 264–276. Available from: https://doi.org/10.1016/j.jsv.2015.12.008
RUBIO, L., FERNÁNDEZ-SÁEZ, J., MORASSI, A. (2015). The full nonlinear crack detection problem in uniform vibrating rods. Journal of Sound and Vibration, 339, p. 99–111. Available from: https://doi.org/10.1016/j.jsv.2014.11.011
SOLOVIEV A.N., PARINOV I.A., CHERPAKOV A.V., CHAIKA YU.A., ROZHKOV E.V. Analysis of oscillation forms at defect identification in node of truss based on finite element modeling (2018). Materials Physics and Mechanics, 37, p. 192-197.
ZRAZHEVSKY, G., ZRAZHEVSKA, V. Obtaining and investigation of the integral representation of solution and boundary integral equation for the non-stationary problem of thermal conductivity (2016). Eureka: Physics and Engineering, 6, p. 53–58. doi: 10.21303/2461-4262.2016.00216
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 (6), p. 1009-1026. doi: 10.1007/s10559-019-00211-x
ZRAZHEVSKY, G., ZRAZHEVSKA, V. (2020). The extension method for solving boundary value problems of the theory of oscillations of bodies with heterogeneity World Journal of Engineering Research and Technology 6 (2), p. 503-514.
ZRAZHEVSKY G.M., ZRAZHEVSKA V.F. (2021) Modeling of Finite Inhomogeneities by Discret Singularities. Journal of Computational and Applied Mathematics. 1 (135) р. 138-144.
Downloads
Published
How to Cite
Issue
Section
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).