Abstract
The main objective of nonlinear dynamic system identification is to model the behaviour of the systems under analysis from input-output signals. To approach this problem, the Laguerre-Volterra network architecture combines the connectionist approach with Volterra-based processing to achieve good performance when modeling high-order nonlinearities, while retaining interpretability of the system’s characteristics. In this research we assess the performances of three metaheuristics in the optimization of Laguerre-Volterra Networks using synthetic input-output data, a task in which only the simulated annealing metaheuristic was previously evaluated.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alataris, K., Berger, T., Marmarelis, V.: A novel network for nonlinear modeling of neural systems with arbitrary point-process inputs. Neural Networks 13(2), 255–266 (2000)
Allgöwer, F., Zheng, A.: Nonlinear Model Predictive Control, vol. 26. Birkhäuser, Basel (2012)
de Assis, L.S., Junior, J.R.d.P., Tarrataca, L., Haddad, D.B.: Efficient Volterra systems identification using hierarchical genetic algorithms. Appl. Soft Comput. 85, 105745 (2019)
Brooks, D.G., Verdini, W.A.: Computational experience with generalized simulated annealing over continuous variables. Am. J. Math. Manag. Sci. 8(3–4), 425–449 (1988)
Chon, K.H., Holstein-Rathlou, N.H., Marsh, D.J., Marmarelis, V.Z.: Comparative nonlinear modeling of renal autoregulation in rats: Volterra approach versus artificial neural networks. IEEE Trans. Neural Networks 9(3), 430–435 (1998)
Costa, V.O.: Metaheuristics for Laguerre-Volterra networks optimization (2020). https://github.com/vctrop/metaheuristics_for_Laguerre-Volterra_networks_optimization/tree/BRACIS2020
Friedman, M.: The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Am. Stat. Assoc. 32(200), 675–701 (1937)
Geng, K., Marmarelis, V.: Methodology of recurrent Laguerre-Volterra network for modeling nonlinear dynamic systems. IEEE Trans. Neural Netw. Learn. Syst. 28, 1–13 (2016)
Geng, K., et al.: Mechanism-based and input-output modeling of the key neuronal connections and signal transformations in the CA3-CA1 regions of the hippocampus. Neural Comput. 30(1), 149–183 (2018)
Geng, K., et al.: Multi-input, multi-output neuronal mode network approach to modeling the encoding dynamics and functional connectivity of neural systems. Neural Comput. 31(7), 1327–1355 (2019)
Gurusamy, S.: Metaheuristic algorithms for the identification of nonlinear systems and multivariable PID controller tuning. Ph.D. thesis, Kalasalingam Academy of Research and Education, Krishnankoil, India (2017)
Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117(4), 500 (1952)
Hu, E.Y., Yu, G., Song, D., Bouteiller, C.J.M., Berger, W.T.: Modeling nonlinear synaptic dynamics: a Laguerre-Volterra network framework for improved computational efficiency in large scale simulations. In: 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), pp. 6129–6132 (2018)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN 1995 – International Conference on Neural Networks, vol. 4, pp. 1942–1948. IEEE (1995)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Korenberg, M.J., Hunter, I.W.: The identification of nonlinear biological systems: Volterra kernel approaches. Ann. Biomed. Eng. 24(2), A250–A268 (1996). https://doi.org/10.1007/BF02648117
Locatelli, M.: Simulated annealing algorithms for continuous global optimization. In: Pardalos, P.M., Romeijn, H.E. (eds.) Handbook of Global Optimization. NOIA, vol. 62, pp. 179–229. Springer, Boston (2002). https://doi.org/10.1007/978-1-4757-5362-2_6
Marmarelis, P.Z., Marmarelis, V.Z.: Analysis of physiological signals. In: Analysis of Physiological Systems. CBM, pp. 11–69. Springer, Boston (1978). https://doi.org/10.1007/978-1-4613-3970-0_2
Marmarelis, V.Z.: Identification of nonlinear biological systems using Laguerre expansions of kernels. Ann. Biomed. Eng. 21(6), 573–589 (1993). https://doi.org/10.1007/BF02368639
Marmarelis, V.Z.: Modeling methology for nonlinear physiological systems. Ann. Biomed. Eng. 25(2), 239–251 (1997). https://doi.org/10.1007/BF02648038
Marmarelis, V.Z.: Nonlinear Dynamic Modeling of Physiological Systems, vol. 10. Wiley, Hoboken (2004)
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953)
Mitsis, G.D., Poulin, M.J., Robbins, P.A., Marmarelis, V.Z.: Nonlinear modeling of the dynamic effects of arterial pressure and co2 variations on cerebral blood flow in healthy humans. IEEE Trans. Biomed. Eng. 51(11), 1932–1943 (2004)
Mitsis, G.D., Zhang, R., Levine, B., Marmarelis, V.: Modeling of nonlinear physiological systems with fast and slow dynamics. II. Application to cerebral autoregulation. Ann. Biomed. Eng. 30(4), 555–565 (2002). https://doi.org/10.1114/1.1477448
Nemenyi, P.: Distribution-free multiple comparisons. Ph.D. thesis, Princeton University, New Jersey, United States (1963)
Nourani, Y., Andresen, B.: A comparison of simulated annealing cooling strategies. J. Phys. A Math. Gen. 31(41), 8373 (1998)
Ogura, H.: Estimation of wiener kernels of a nonlinear system by means of digital Laguerre filters and their fast algorithm. In: Nonlinear Signal and Image Processing, pp. 855–858. IEEE (1995)
Oliphant, T.E.: A Guide to NumPy, vol. 1. Trelgol Publishing, New York (2006)
Palm, G., Pöpel, B.: Volterra representation and wiener-like identification of nonlinear systems: scope and limitations. Q. Rev. Biophys. 18(2), 135–164 (1985)
Poli, R., Kennedy, J., Blackwell, T.: Particle swarm optimization. Swarm Intell. 1(1), 33–57 (2007). https://doi.org/10.1007/s11721-007-0002-0
Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence, pp. 69–73 (1998)
Socha, K., Dorigo, M.: Ant colony optimization for continuous domains. Eur. J. Oper. Res. 185(3), 1155–1173 (2008)
Stützle, T., et al.: Parameter adaptation in ant colony optimization. In: Hamadi, Y., Monfroy, E., Saubion, F. (eds.) Autonomous Search, pp. 191–215. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21434-9_8
Terpilowski, M.: scikit-posthocs: Pairwise multiple comparison tests in Python. J. Open Source Softw. 4(36), 1169 (2019). https://doi.org/10.21105/joss.01169
Vanderbilt, D., Louie, S.G.: A Monte Carlo simulated annealing approach to optimization over continuous variables. J. Comput. Phys. 56(2), 259–271 (1984)
Virtanen, P., et al.: SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 17, 261–272 (2020)
Volterra, V.: Theory of Functionals and of Integral and Integro-Differential Equations. Blackie & Son, London (1930)
Watanabe, A., Stark, L.: Kernel method for nonlinear analysis: identification of a biological control system. Math. Biosci. 27(1), 99–108 (1975)
Yang, X., Deb, S., Fong, S., He, X., Zhao, Y.: From swarm intelligence to metaheuristics: nature-inspired optimization algorithms. Computer 49, 52–59 (2016)
Yang, Y.S., Chang, W.D., Liao, T.L.: Volterra system-based neural network modeling by particle swarm optimization approach. Neurocomputing 82, 179–185 (2012)
Yazid, E., Liew, M.S., Parman, S., Kurian, V.J.: Improving the modeling capacity of Volterra model using evolutionary computing methods based on Kalman smoother adaptive filter. Appl. Soft Comput. 35, 695–707 (2015)
Ye, H., Luo, W., Li, Z.: Convergence analysis of particle swarm optimizer and its improved algorithm based on velocity differential evolution. Comput. Intell. Neurosci. 2013, 384125 (2013)
Zhang, Y., Rong, Y., Yan, C., Liu, J., Wu, X.: Kernel estimation of Volterra using an adaptive artificial bee colony optimization and its application to speech signal multi-step prediction. IEEE Access 7, 49048–49058 (2018)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Costa, V.O., Müller, F.M. (2020). Evaluation of Metaheuristics in the Optimization of Laguerre-Volterra Networks for Nonlinear Dynamic System Identification. In: Cerri, R., Prati, R.C. (eds) Intelligent Systems. BRACIS 2020. Lecture Notes in Computer Science(), vol 12319. Springer, Cham. https://doi.org/10.1007/978-3-030-61377-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-61377-8_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-61376-1
Online ISBN: 978-3-030-61377-8
eBook Packages: Computer ScienceComputer Science (R0)