Potential of neural networks for maximum displacement predictions in railway beams on frictionally damped foundations


Since the use of finite element (FE) simulations for the dynamic analysis of railway beams on frictionally damped foundations are (i) very time consuming, and (ii) require advanced know-how and software that go beyond the available resources of typical civil engineering firms, this paper aims to demonstrate the potential of Artificial Neural Networks (ANN) to effectively predict the maximum displacements and the critical velocity in railway beams under moving loads. Four ANN-based models are proposed, one per load velocity range ([50, 175] ∪ [250, 300] m/s; ]175, 250[ m/s) and per displacement type (upward or downward). Each model is function of two independent variables, a frictional parameter and the load velocity. Among all models and the 663 data points used, a maximum error of 5.4 % was obtained when comparing the ANN- and FE-based solutions. Whereas the latter involves an average computing time per data point of thousands of seconds, the former does not even need a millisecond. This study was an important step towards the development of more versatile (i.e., including other types of input variables) ANN-based models for the same type of problem.


Abambres M, Corrêa R, Pinto da Costa A, Simões F (2019). Potential of neural networks for maximum displacement predictions in railway beams on frictionally damped foundations. engrXiv (January), 1-62, doi: http://doi.org/10.31224/osf.io/m3b7j

Anderson D, Hines EL, Arthur SJ, Eiap EL (1997). Application of Artificial Neural Networks to the Prediction of Minor Axis Steel Connections. Computers & Structures, 63(4):685-692.

Authors (2018). ANN development + final testing datasets [Data set]. Zenodo. http://doi.org/10.5281/zenodo.1445912

Aymerich F, Serra M (1998). Prediction of fatigue strength of composite laminates by means of neural networks. Key Eng. Materials, 144(September):231–240.

Bai Z, Huang G, Wang D, Wang H, Westover M (2014). Sparse extreme learning machine for classification. IEEE Transactions on Cybernetics, 44(10):1858–70.

Beyer W, Liebscher M, Beer M, Graf W (2006). Neural Network Based Response Surface Methods - A Comparative Study, 5th German LS-DYNA Forum, October 2006, 29-38, Ulm.

Bhaskar R, Nigam A (1990). Qualitative physics using dimensional analysis. Artificial Intelligence, 45(1-2):111–73.

Castro Jorge P, Pinto da Costa A, Simões FMF (2015). Finite element dynamic analysis of finite beams on a bilinear foundation under a moving load. Journal of Sound and Vibration, 346(June):328–44, doi: 10.1016/j.jsv.2014.12.044.

Castro Jorge P, Simões FMF, Pinto da Costa A (2015). Dynamics of beams on non-uniform nonlinear foundations subjected to moving loads. Computers and Structures, 148(February):26–34, doi: 10.1016/j.compstruc.2014.11.002.

Developer (2018a). Negative wmax (v = [50, 175] ∪ [250, 300] m/s) [Data set]. Zenodo, http://doi.org/10.5281/zenodo.1462150

Developer (2018b). Negative wmax (v = ]175, 250[ m/s) [Data set]. Zenodo, http://doi.org/10.5281/zenodo.1469207

Developer (2018c). Positive wmax (v = [50, 175] ∪ [250, 300] m/s) [Data set]. Zenodo, http://doi.org/10.5281/zenodo.1469879

Developer (2018d). Positive wmax (v = ]175, 250[ m/s) [Data set]. Zenodo, http://doi.org/10.5281/zenodo.1470854

Dimitrovová Z, Rodrigues AFS (2012). Critical velocity of a uniformly moving load. Advances in Engineering Software, 50(August):44–56, doi: 10.1016/j.advengsoft.2012.02.011.

Flood I (2008). Towards the next generation of artificial neural networks for civil engineering. Advanced Engineering Informatics, 228(1):4-14.

Frýba L (1972). Vibration of solids and structures under moving loads. Groningen: Noordhoff International Publishing.

Glocker C (2001). Set-Values force laws. Lecture notes in applied and computational mechanics. Berlin, Heidelberg: Springer, ISBN 978-3-540-41436-0.

Haykin SS (2009). Neural networks and learning machines, Prentice Hall/Pearson, New York.

Hern A (2016). Google says machine learning is the future. So I tried it myself. Available at: www.theguardian.com/technology/2016/jun/28/all (Accessed: 2 November 2016).

Hertzmann A, Fleet D (2012). Machine Learning and Data Mining, Lecture Notes CSC 411/D11, Computer Science Department, University of Toronto, Canada.

Jean M (1999). The non-smooth contact dynamics method. Computer Methods in Applied Mechanics and Engineering, 177(3-4):235–57, doi: 10.1016/S0045-7825(98)00383-1.

Kaynia A, Madshus C, Zackrisson P (2000). Ground vibration from high-speed trains: pre- diction and countermeasure. Journal of Geotechnical and Geoenvironmental Engineering, 126(6):531–7.

Madshus C, Kaynia A (2000). High-speed railway lines on soft ground: dynamic behaviour at critical train speed. Journal of Sound and Vibration, 231(3):689–701, doi: 10.1006/jsvi.1999.2647.

McCulloch WS, Pitts W (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5(4):115–133.

Moreau J (1994). Some numerical methods in multibody dynamics: application to granular materials. European Journal of Mechanics A/Solids, 13(4):94–114.

Prieto A, Prieto B, Ortigosa EM, Ros E, Pelayo F, Ortega J, Rojas I (2016). Neural networks: An overview of early research, current frameworks and new challenges. Neurocomputing, 214(November):242-268.

Researcher, The (2018). “Annsoftwarevalidation-report.pdf”, figshare, doi:10.6084/m9.figshare.6962873.

Studer C (2009). Numerics of unilateral contacts and friction – Lecture notes in applied and computational mechanics. Berlin, Heidelberg: Springer, ISBN 978-3-642-01099-6.

The Mathworks, Inc (2017). MATLAB R2017a, User’s Guide, Natick, USA.

Toscano Corrêa R, Pinto da Costa A, Simões FMF (2018). Finite element modelling of a rail resting on a Winkler-Coulomb foundation and subjected to a moving concentrated load. International Journal of Mechanical Sciences, 140(May):432-45, doi: 10.1016/j.ijmecsci.2018.03.022.

Wilamowski BM, Irwin JD (2011). The industrial electronics handbook: Intelligent Systems, CRC Press, Boca Raton.