ANALYSIS AND DATA PROCESSING SYSTEMS

Abstract
The paper discusses discrete-continuous (hybrid) systems and simulation tools. New hybrid models for analyzing systems in the time and spatial domain are proposed. Operation behavior of such systems is described by partial differential equations of the parabolic type with some constraints. A generalized classification of hybrid behavior types based on the causes of event occurrence and on the results of a regime change is also suggested. A new architecture of the software tool based on the CSSL standard for modeling an extended class of event-continuous systems is developed. The separation of the model frame and the experiment frame in the tool environment is shown. The software package is unified to the models in the purpose and object-oriented input languages. The model frame includes an original internal representation of computational models in the terminology of hybrid systems providing a possibility of a generalized specification, storage and processing of computational tasks. The experiment frame prepares and executes a computational model. The LISMA_PDE language for the specification of computer models is developed. It is inherited from the LISMA language with added blocks for recording partial differential equations and boundary conditions. The developed language grammar is classified and the unambiguity of the generative grammar is proved. Means for implementing the lexical analyzer and syntactic parser are found. The correctness of the proposed approach is constructively proved on test problems. We propose a hybrid approach to the description and analysis of system dynamics problems. The simulation of the production and trading system in terms of hybrid models is made. A hybrid problem with partial differential equations which describes the dynamics the ozone concentration of ozone in the stratosphere is considered.

 

References
1. Maler O., Manna Z., Pnueli A. From timed to hybrid systems. Real-Time: theory in practice. Berlin, Springer, 1992, pp. 447–484.

2. Harel D. Statecharts: a visual formalism for complex systems. Science of Computer Programming, 1987, vol. 8, pp. 231–274.

3. Esposito J., Kumar V., Pappas G.J. Accurate event detection for simulating hybrid systems. Hybrid systems: computation and control (HSCC). Berlin, New York, Springer, 2001, pp. 204–217.

4. Novikov E.A., Shornikov Yu.V. Komp'yuternoe modelirovanie zhestkikh gibridnykh sistem [Computer simulation of stiff hybrid systems]. Novosibirsk, NSTU Publ., 2012. 451 p.

5. Senichenkov Yu.B. Chislennoe modelirovanie gibridnykh sistem [Numerical simulation of hybrid systems]. St. Petersburg, Polytechnic University Publ., 2004. 206 p.

6. Backstrom G. Simple deformation and vibration by finite element analysis. Malmö, GB Publishing, 2012. 322 p.

7. Claudel C.G., Bayen A.M. Solutions to switched Hamilton-Jacobi Equations and conservation laws using hybrid components. Hybrid Systems: Computation and Control, 2008, vol. 4981, pp. 101–115.

8. Breitenecker F. Development of simulation software – from simple ode modelling to structural dynamic systems. Proceedings of 22^nd European Conference on Modelling and Simulation, ECMS 2008, Nicosia, Cyprus, 3–6 June 2008, pp. 5–22.

9. Shornikov Yu.V., Bessonov A.V. Komponenty yadra programmnogo kompleksa “ISMA 2015” [The components of core of "ISMA 2015" software]. The Certificate on official registration of the computer program. N 2015617235, 2015. (In Russian, unpublished).

Komponenty yadra programmnogo kompleksa «ISMA 2015» : svidetel'stvo o gosudarstvennoi registratsii programmy dlya EVM № 2015617235 / Yu.V. Shornikov, A.V. Bessonov. – M.: Federal'naya sluzhba po intellektual'noi sobstvennosti, patentam i tovarnym znakam, 2015.

10. Shornikov Yu.V., Bessonov A.V. Unifitsirovannyi podkhod k komp'yuternomu modelirovaniyu gibridnykh sistem [The unified approach to computer simulation of hybrid systems]. Informatsionnye tekhnologii modelirovaniya i upravleniya – Information technology of modeling and control, 2015, vol. 3 (93), pp. 286–298.

11. Shornikov Yu.V., Bessonov A.V., Myssak M.S., Dostovalov D.N. Instrumental analysis of hybrid systems with PDE. International Journal of Mathematics and Computers in Simulation, 2015, vol. 9, pp. 85–93.

12. Shornikov Yu.V., Bessonov A.V. Komponenta spetsifikatsii modelei gibridnykh sistem na yazyke LISMA_PDE [Component for specification of hybrid systems in the LISMA_PDE language]. The Certificate on official registration of the computer program. N 2015617191, 2015. (In Russian, unpublished).

13. Aho A.V., Ullman J.D. The Theory of parsing, translation and compiling. Englewood Cliffs, New Jersey, Prentice-Hall, 1972–1973. 1002 p. (Russ. ed.: Akho A.V., Ul'man Dzh. Teoriya sintaksicheskogo analiza, perevoda i kompilyatsii. Moscow, Mir Publ., 1978. 612 p.).

15. Adzievski K., Siddiqi A.H. Introduction to partial differential equations for scientists and engineers using mathematica. Boca Raton, Florida, CRC Press, 2014. 648 p.

16. Martin M.M., ed. Introduction to software for chemical engineers. Boca Raton, Florida, CRC Press, 2014, pp. 367–453.

17. Soares R.P., Secchi A.R. EMSO: a new environment for modelling, simulation and optimization. Computer Aided Chemical Engineering, 2003, vol. 14, pp. 947–952.

18. Piela P.C., Epperly T.G., Westerberg K.M., Westerberg A.W. ASCEND: an object-oriented computer environment for modeling and analysis: The modeling language. Computers & Chemical Engineering, 1991, vol. 15, iss. 1, pp. 53–72.

19. Forrester J.W. Industrial dynamics. Cambridge, Massachusetts, MIT Press, 1961. 464 p. (Russ. ed.: Forrester Dzh. Osnovy kibernetiki predpriyatiya. Moscow, Progress Publ., 1971. 340 p.).

20. Brown P.N., Hindmarsh A.C. Matrix free methods in the solution of stiff systems of ODEs. San Francisco, Lawrence Livermore National Laboratory, 1983. 38 p.