1_2021_sen_7

Title of the article APPLICATION OF LOGISTIC REGRESSION IN CALCULATION OF DAMAGEABILITY OF SOLID DEFORMABLE BODY
Authors

MARMYSH Dzianis E., Ph. D. in Phys. and Math., Associate Professor of the Department of Theoretical and Applied Mechanics, Belarusian State University, Minsk, Republic of Belarus; Vice-dean of the Dalian University of Technology and Belarusian State University Joint Institute, Dalian University of Technology, Dalian, People’s Republic of China; This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section MECHANICS OF DEFORMED SOLIDS
Year 2021
Issue 1
Pages 46–53
Type of article RAR
Index UDK 539.3
DOI https://doi.org/10.46864/1995-0470-2020-1-54-46-53
Abstract The paper proposes a logistic regression model for estimating the damageability of a solid deformable body. A training sample is randomly generated from a uniform distribution over the area containing the dangerous volume. For linear separability of the training sample, a classifying kernel is used in the form of a radial basis function. The regression parameters were estimated using the maximum likelihood method, then the system of nonlinear equations was solved by the Newton–Raphson method. To determine the quality of the classifier, a ROC analysis was performed, which consists in constructing the ROC curve and calculating the area between the ROC curve and the specificity axis. For adequate assessment of the work, the logistic regression model is used to calculate the damage of a half-plane when a normally distributed load acts on its boundary. The paper also analyzes the stability of the model parameter estimation algorithms when generating a random sample of training sample.
Keywords mechanics of damageability, machine learning, logistic regression, logit model, discriminant function
  You can access full text version of the article.
Bibliography
  1. Vapnik V.N. The nature of statistical learning theory. New York, Springer, 1995. 314 p.
  2. Dreiseitl S., Ohno-Machado L. Logistic regression and artificial neural network classification models: a methodology review. Journal of biomedical informatics, 2003, vol. 35, pp. 352–359. DOI: 10.1016/S1532-0464(03)00034-0.
  3. Maalouf M. Logistic regression in data analysis: an overview. International journal of data analysis techniques and strategies, 2011, vol. 3, iss. 3, pp. 281–299. DOI: https://doi.org/10.1504/IJDATS.2011.041335.
  4. Niu L. A review of the application of logistic regression in educational research: common issues, implications, and suggestions. Educational review, 2020, vol. 72, iss. 1, pp. 41–67. DOI: https://doi.org/10.1080/00131911.2018.1483892.
  5. Sherbakov S.S., Sosnovskiy L.A. Mekhanika tribofaticheskikh sistem [Mechanics of tribo-fatigue systems]. Minsk, Belorusskiy gosudarstvennyy universitet Publ., 2011. 407 p. (in Russ.).
  6. Marmysh D.E. Chislennoe modelirovanie povrezhdaemosti silovoy sistemy [Numerical simulation of force system damage]. Teotericheskaya i prikladnaya mekhanika, 2017, no. 32, pp. 312–316 (in Russ.).
  7. Marmysh D.Е. Chislenno-analiticheskiy metod granichnykh elementov v ploskoy kontaktnoy zadache teorii uprugosti [Numerical-analytical method of boundary elements in a plane contact problem of the theory of elasticity]. Prilozhenie k zhurnalu “Izvestiya Natsionalnoy akademii nauk Belarusi”, 2013, vol. 3, pp. 42–46 (in Russ.).
  8. Hosmer D.W., Lemeshow S. Applied logistic regression. New York, Wiley, 2000. 375 p.
  9. Tyrsin A.N., Kostin K.K. Otsenivanie logisticheskoy regressii kak ekstremalnaya zadacha [Consideration of estimation of logistic regression as an optimization problem]. Tomsk state university journal of control and computer science, 2017, vol. 40, pp. 52–60 (in Russ.).
  10. Galin L.A. Kontaktnye zadachi teorii uprugosti [Contact problems of elasticity theory]. Moscow, Gosudarstvennoe izdatelstvo tekhniko-teoreticheskoy literatury Publ., 1953. 265 p. (in Russ.).
  11. Jonson K.L. Contact mechanics. Cambridge, Cambridge University Press, 1985. 510 p.
  12. Popov V.L. Contact mechanics and friction. Physical principles and applications. Berlin, Springer, 2010. 362 p. DOI: https://doi.org/10.1007/978-3-642-10803-7.
  13. Marmysh D.E. Skhodimost metoda analiticheskogo granichnogo elementa pri analize napryazhennogo sostoyaniya i sostoyaniya povrezhdaemosti sredy [Convergence of the analytical boundary element method in the analysis of the stress state and the damage state of the medium]. Teotericheskaya i prikladnaya mekhanika, 2020, no. 35, pp. 92–98 (in Russ.).
  14. Bishop C.M. Pattern recognition and machine learning. Singapore, Springer, 2006. 738 p.
  15. Phienthrakul T., Kijsirikul B. Evolutionary strategies for multi-scale radial basis function kernels in support vector machines. Soft computing, 2010, vol. 14, pp. 681–699. DOI: https://doi.org/10.1007/s00500-009-0458-5.
  16. Guo X.C., Yanga J.H., Wuac C.G., Wanga C.Y., Lianga Y.C. A novel LS-SVMs hyper-parameter selection based on particle swarm optimization. Neurocomputing, 2008, vol. 71, pp. 3211–3215. DOI: https://doi.org/10.1016/j.neucom.2008.04.027.
  17. Zweig M.H., Campbell G. ROC plots: a fundamental evaluation tool in clinical medicine. Clinical chemistry, 1993, vol. 39, iss. 4, pp. 561–577.
  18. Kumari R., Srivastava S.K. Machine learning: a review on binary classification. International journal of computer applications, 2017, vol. 160, iss. 7, pp. 11–15. DOI: https://doi.org/10.5120/ijca2017913083.
  19. Gaidyshev I.P. Otsenka kachestva binarnykh klassifikatorov [Quality assessment of binary classifiers]. Herald of Omsk university, 2016, vol. 1, pp. 14–17 (in Russ.).