Solving a system of nonlinear equations with the use of optimization methods in problems related to the wheel-rail contact

• Autorzy: Jureczko M. , Duda S.

Identyfikatory

DOI

10.17512/jamcm.2016.2.06

• Języki publikacji: EN

Abstrakty

EN

The article presents the methods for defining the geometry of the contact surface between a rigid wheel and a rigid rail. The calculation model that has been developed allowed for any arrangement of the wheel in relation to the rail. This allowed for the creation of a system of nonlinear equations, the solution of which allows one to determine the presumable wheel-rail contact points. The search for the solution of the system of strongly nonlinear equations was conducted using a few optimization methods. This allowed one to study both the selection of the starting point and the convergence of the method.

Słowa kluczowe

EN

wheel-rail contact; system of nonlinear equations; Newton's method; trust region method; Levenberg-Marquardt method; damped Newton’s method

PL

styk koło-szyna; układ równań nieliniowych; metoda Newtona; metoda Levenberg-Marquardt

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2016
• Tom: Vol. 15, nr 2
• Strony: 53--64
• Opis fizyczny: Bibliogr. 17 poz., rys., tab.

Twórcy

autor

Jureczko M.

• Institute of Theoretical and Applied Mechanics, Silesian University of Technology Gliwice, Poland

autor

Duda S.

• Institute of Theoretical and Applied Mechanics, Silesian University of Technology Gliwice, Poland

Bibliografia

• [1] Grosan C., Abraham A., A new approach for solving nonlinear equations systems, IEEE Transactions on Systems, Man, and Cybernetics - part A: Systems and Humans 2008, 38, 3, 698-714.
• [2] Nedzhibov G.H., A family of multi-point iterative methods for solving systems of nonlinear equations, Comput. Appl. Math. 2008, 222, 244-250.
• [3] Taheri S., Mammadov M., Solving systems of nonlinear equations using a globally convergent optimization algorithm, Global J. of Tech. and Optim. 2012, 3, 132-138.
• [4] Chapra S.C., Canale R.P., Numerical Methods for Engineers, 6th edition, McGraw-Hill Companies, 2010.
• [5] Yang Y.W., Cao W., Chung T., Morris J., Applied Numerical Methods Using Matlab®, John Wiley & Sons, 2005.
• [6] Kiusalaas J., Numerical Methods in Engineering with Matlab®, Cambridge University Press, 2009.
• [7] Jureczko M., Metody optymalizacji - przykłady zadań z rozwiązaniami i komentarzami, Wydawnictwo Pracowni Komputerowej Jacka Skalmierskiego, Gliwice 2009.
• [8] Quarteroni A., Saleri F., Scientific Computing with Matlab and Octave, 2nd edition, Springer, 2006.
• [9] Mathews J.H., Fink K.D., Numerical Methods Using Matlab, Prentice Hall, 1999.
• [10] Deuflhard P., A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting, Numerical Mathematics No 22, Springer -Verlag, 1974, 289-315.
• [11] Hagan M.T., Menhaj M.B., Training feedforward networks with the Marquardt algorithm, IEEE Trans. on Neural Networks 1994, 5, 6, 989-993.
• [12] Transtrum M.K., Sethna J.P., Improvements to the Levenberg-Marquardt algorithm for nonlinear least-squares minimization, Preprint submitted to Journal of Computational Physics, January 30, 2012.
• [13] Yuan Y.X., A review of trust region algorithms for optimization, ICM99: Proc. 4th Int. Congress on Industrial and Applied Mathematics, eds. J.M. Ball, J.C.R. Hunt, Oxford University Press 2000, 271-282.
• [14] Yuan Y.X., Recent advances in trust region algorithms, Math. Program., Ser. B 2015, 249-281.
• [15] Mortenson M.E., Geometric Modeling, Wiley, New York 1985.
• [16] Duda S., Modelowanie i symulacja numeryczna zjawisk dynamicznych w elektrycznych pojazdach szynowych. Monografia nr 405, Wydawnictwo Politechniki Śląskiej, Gliwice 2012.
• [17] Duda S., Numerical simulations of the wheel-rail traction forces using the electromechanical model of an electric locomotive, J. Theor. Appl. Mech. 2014, 52, 2, 395-404.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.