Abstract
The inverse mathematical modelling problem for a linear dynamic system is considered. The parameter and initial condition identification were reduced to an optimization problem. The proposed approach is based on the simultaneous estimation of linear differential equation coefficients and initial condition vector coordinates. The mathematical model is determined by the vector of equation parameters and the state coordinate of the model. The initial value problem solution is required to fit the sample data. The complexity and multimodality of criterion for the reduced problem leads to the implementation of an efficient optimization technique. The meta-heuristic optimization algorithm called Co-Operation of Biology Related Algorithms (COBRA) was used for this purpose. Its high efficiency had been proven in previous studies. Investigation results show that COBRA is a high-performance and reliable technique for current extremum problem class solving. The usefulness of the proposed approach is confirmed with the investigation results based on experiments made for different sample characteristics and different dynamic systems.
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References
Fang, Y., Wu, H., Zhu, L.-X.: A two-stage estimation method for random coefficient differential equation models with application to longitudinal HIV dynamic data. Stat. Sinica 21(3), 1145–1170 (2011)
Wu, H., Xue, H., Kumar, A.: Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research. Biometrics 68, 344–352 (2012)
Brunel, N.J.-B.: Parameter estimation of ODE’s via nonparametric estimators. Electronic J. Stat. 2, 1242–1267 (2008)
Peifer, M., Timmer, J.: Parameter estimation in ordinary differential equations for biochemical processes using the method of multiple shooting. IET Syst. Biol. 1, 78–88 (2007)
Ryzhikov, I., Semenkin, E.: Evolutionary strategies algorithm based approaches for the linear dynamic system identification. In: Tomassini, M., Antonioni, A., Daolio, F., Buesser, P. (eds.) ICANNGA 2013. LNCS, vol. 7824, pp. 477–484. Springer, Heidelberg (2013)
Wang, J., Zhou, B., Zhou, S.: An improved Cuckoo search optimization algorithm for the problem of chaotic systems parameter estimation. Comput. Intell. Neurosci. 2016, Article ID 2959370, 8 (2016)
Sun, J., Palade, V., Cai, Y., Fang, W., Wu, X.: Biochemical systems identification by a random drift particle swarm optimization approach. BMC Bioinform. 15(Suppl. 6), S1 (2014)
Parmar, G., Prasad, R., Mukherjee, S.: Order reduction of linear dynamic systems using stability equation method and GA. Int. J. Comput. Inf. Eng. 1(1), 26–32 (2007)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, pp. 1942–1948 (1995)
Yang, C., Tu, X., Chen, J.: Algorithm of marriage in honey bees optimization based on the wolf pack search. In: International Conference on Intelligent Pervasive Computing, pp. 462–467 (2007)
Yang, X.S.: Firefly algorithms for multimodal optimization. In: 5th Symposium on Stochastic Algorithms, Foundations and Applications, pp. 169–178 (2009)
Yang, X.S., Deb, S.: cuckoo search via levy flights. In: World Congress on Nature & Biologically Inspired Computing, IEEE Publications, USA, pp. 210–214 (2009)
Yang, X.-S.: A new metaheuristic bat-inspired algorithm. In: González, J.R., Pelta, D.A., Cruz, C., Terrazas, G., Krasnogor, N. (eds.) NICSO 2010. SCI, vol. 284, pp. 65–74. Springer, Heidelberg (2010)
Akhmedova, S., Semenkin, E.: Co-operation of biology related algorithms. In: IEEE Congress on Evolutionary Computation, pp. 2207–2214 (2013)
Akhmedova, S., Semenkin, E.: Co-operation of biology related algorithms meta-heuristic in ANN-Based classifiers design. In: IEEE World Congress on Computational Intelligence, pp. 867—873 (2014)
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Research is performed with the financial support of the Russian Foundation of Basic Research, the Russian Federation, contract â„–20 16-01-00767, dated 03.02.2016.
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Ryzhikov, I., Semenkin, E., Akhmedova, S. (2016). Linear ODE Coefficients and Initial Condition Estimation with Co-operation of Biology Related Algorithms. In: Tan, Y., Shi, Y., Niu, B. (eds) Advances in Swarm Intelligence. ICSI 2016. Lecture Notes in Computer Science(), vol 9712. Springer, Cham. https://doi.org/10.1007/978-3-319-41000-5_23
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DOI: https://doi.org/10.1007/978-3-319-41000-5_23
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