Numerical solution of beam equation using neural networks and evolutionary optimization tools |
Babaei, Mehdi
(Department of Civil Engineering, University of Bonab)
Atasoy, Arman (Department of Civil Engineering, Istanbul Rumeli University) Hajirasouliha, Iman (Department of Civil & Structural Engineering, The University of Sheffield) Mollaei, Somayeh (Department of Civil Engineering, University of Bonab) Jalilkhani, Maysam (Department of Civil Engineering, Urmia University of Technology) |
1 | Eberhart, R. and Kennedy, J. (1995), "Particle swarm optimization", Proceedings of the IEEE International Conference on Neural Networks, Perth, WA, Australia, November. |
2 | Yentis, R. and Zaghloul, M. (1996), "VLSI implementation of locally connected neural network for solving partial differential equations", IEEE T. Circ. Syst. I, 43(8), 687-690. https://doi.org/10.1109/81.526685. DOI |
3 | Lee, H. and Kang I.S. (1990), "Neural algorithm for solving differential equations", J. Comput. Phys., 91(1), 110-131. https://doi.org/10.1016/0021-9991(90)90007-N. DOI |
4 | Luh, G.C., Lin, C.Y. and Lin, Y.S. (2011), "A binary particle swarm optimization for continuum structural topology optimization", Appl. Soft Comput., 11(2), 2833-2844. https://doi.org/10.1016/j.asoc.2010.11.013. DOI |
5 | Mojtabaei, S.M., Hajirasouliha, I., Ye, J. (2021), "Optimization of cold-formed steel beams for best seismic performance in bolted moment connections", J. Constr. Steel Res., 181, 106621. https://doi.org/10.1016/j.jcsr.2021.106621. DOI |
6 | Nabian, M.A. and Meidani, H. (2019). "A deep learning solution approach for high-dimensional random differential equations", Probabilist. Eng. Mech., 57, 14-25. https://doi.org/10.1016/j.probengmech.2019.05.001. DOI |
7 | Parastesh, H., Mojtabaei, S.M., Taji, H., Hajirasouliha, I. and Sabbagh, A.B. (2021), "Constrained optimization of anti-symmetric cold-formed steel beam-column sections", Eng. Struct., 228, 111452. https://doi.org/10.1016/j.engstruct.2020.111452. DOI |
8 | Sun, H., Hou, M., Yang, Y., Zhang, T., Weng, F. and Han, F. (2019). "Solving partial differential equation based on Bernstein neural network and extreme learning machine algorithm", Neural Process. Lett., 50(2), 1153-1172. https://doi.org/10.1007/s11063-018-9911-8. DOI |
9 | Phan, D.T., Mojtabaei, S.M., Hajirasouliha, I., Ye, J. and Lim, J.B.P (2020), "Coupled element and structural level optimisation framework for cold-formed steel frames", J. Constr. Steel Res., 168, 105867. https://doi.org/10.1016/j.jcsr.2019.105867. DOI |
10 | Sirignano, J. and Spiliopoulos, K. (2018), "DGM: A deep learning algorithm for solving partial differential equations", J. Comput. Phys., 375, 1339-1364. https://doi.org/10.1016/j.jcp.2018.08.029. DOI |
11 | Yadav, N., Yadav, A. and Kumar, M. (2015), An Introduction to Neural Network Methods for Differential Equations, Springer, Netherlands. |
12 | Magill, M., Qureshi, F., and de Haan, H.W. (2018), "Neural networks trained to solve differential equations learn general representations", Adv. Neural Inform. Process. Syst., 1097-1105. https://arxiv.org/abs/1807.00042. |
13 | Omondi, A.R. and Rajapakse J.C. (2006), FPGA Implementations of Neural Networks, Springer, Boston, MA. https://doi.org/10.1007/0-387-28487-7. DOI |
14 | Schmidhuber, J. (2015), "Deep learning in neural networks: An overview", Neural Networks, 61, 85-117. https://doi.org/10.1016/j.neunet.2014.09.003. DOI |
15 | Sivanandam, S.N. and Deepa, S.N. (2008), Introduction to genetic algorithms, Springer, Berlin, Heidelberg, Germany. |
16 | Van Milligen, B.P., Tribaldos, V. and Jimenez, J.A. (1995), "Neural network differential equation and plasma equilibrium solver", Phys. Rev. Lett., 75(20), 3594. https://doi.org/10.1103/PhysRevLett.75.3594. DOI |
17 | Babaei, M. and Sheidaii, M.R. (2014), "Automated optimal design of double-layer latticed domes using particle swarm optimization", Struct. Multidiscip. O., 50(2), 221-235. https://doi.org/10.1007/s00158-013-1042-2. DOI |
18 | Ye, J., Hajirasouliha, I., Becque, J. and Eslami, A. (2016). "Optimum design of cold-formed steel beams using particle swarm optimisation method", J. Constr. Steel Res., 122, 80-93. https://doi.org/10.1016/j.jcsr.2016.02.014. DOI |
19 | Babaei, M. (2013), "A general approach to approximate solutions of nonlinear differential equations using particle swarm optimization", Appl. Soft Comput., 13(7), 3354-3365. https://doi.org/10.1016/j.asoc.2013.02.005. DOI |
20 | Babaei, M. and Sheidaii, M.R. (2013), "Optimal design of double layer scallop domes using genetic algorithm", Appl. Mathem. Modelling, 37(4), 2127-2138. https://doi.org/10.1016/j.apm.2012.04.053. DOI |
21 | Berg, J. and Nystrom, K. (2018), "A unified deep artificial neural network approach to partial differential equations in complex geometries", Neurocomput., 317, 28-41. https://doi.org/10.1016/j.neucom.2018.06.056. DOI |
22 | Lagaris, I. E., Likas, A. and Fotiadis, D. (1998), "Artificial neural networks for solving ordinary and partial differential equations", IEEE T. Neural. Networ., 9(5), 987-1000. https://doi.org/10.1109/72.712178. DOI |
23 | Dissanayake, M. and Phan-Thien, N. (1994), "Neural-network-based approximations for solving partial differential equations", Commun. Numer. Meth. Eng., 10(3), 195-201. https://doi.org/10.1002/cnm.1640100303. DOI |
24 | Fang, Z., Roy, K., Chen, B., Sham, C.W., Hajirasouliha, I. and Lim, J.B. (2021), "Deep learning-based procedure for structural design of cold-formed steel channel sections with edge-stiffened and un-stiffened holes under axial compression", Thin Wall. Struct., 166, 108076. https://doi.org/10.1016/j.tws.2021.108076. DOI |
25 | Holland, J.H. (1992), Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, The MIT press, U.S. |
26 | Jafarian, A., Mokhtarpour, M. and Baleanu, D. (2017). "Artificial neural network approach for a class of fractional ordinary differential equation", Neural Comput. Appl., 28(4), 765-773. https://doi.org/10.1007/s00521-015-2104-8. DOI |
27 | Koza, J.R. (1992), Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT press, Cambridge, Massachusetts, London, England. |
28 | Ye, J., Becque, J., Hajirasouliha, I., Mojtabaei, S.M. and Lim, J.B.P. (2018). "Development of optimum cold-formed steel sections for maximum energy dissipation in uniaxial bending". Eng. Struct., 161, 55-67. https://doi.org/10.1016/j.engstruct.2018.01.070. DOI |