Uses of new sensitivity and DAE solving methods in SMARTMOBILE for verified analysis of mechanical systems

Auer, E. ; Luther, W.

International Journal of Applied Mathematics and Computer Science, Tome 19 (2009) no. 3, pp. 455-467.

Résumé

Software for modeling and simulation (MSS) of mechanical systems helps to reduce production costs for industry. Usually, such software relies on (possibly erroneous) finite precision arithmetic and does not take into account uncertainty in the input data. The program SMARTMOBILE enhances the existing MSS MOBILE with verified techniques to provide a guarantee that the obtained results are correct and measure the influence of data uncertainty. In this paper, we outline the main features and functionalities of SMARTMOBILE. In particular, we focus on its use of newly developed methods for sensitivity analysis and DAE solving for several practically relevant mechanical systems.

Détail

Keywords: multibody systems, result verification, sensitivity, DAE, uncertainty
Mots-clés : układ wieloczłonowy, weryfikacja wyników, wrażliwość, niepewność

Bibliographie

[1] Auer, E. (2007). SmartMOBILE: A framework for reliable modeling and simulation of kinematics and dynamcis of mechanical systems, Ph.D. thesis, Universität Duisburg-Essen, Duisburg.

[2] Auer, E. and Luther, W. (2007). SMARTMOBILE-An environment for guaranteed multibody modeling and simulation, Proceedings of the 4th International Conference on Informatics in Control, Automation and Robotics ICINCO, Angers, France, pp. 109-116.

[3] Auer, E. and Luther, W. (2009). Numerical verification assessment in computational biomechanics, Proceedings of the Dagstuhl Seminar 08021: Numerical Validation in Current Hardware Architectures, Dagstuhl, Germany, Lecture Notes in Computer Science, Vol. 5492, Springer-Verlag, Berlin/Heidelberg, pp. 145-160.

[4] Auer, E., Tändl, M., Strobach, D. and Kecskeméthy, A. (2007). Toward validating a simplified muscle activation model in SMARTMOBILE, Proceedings of 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006), Duisburg, Germany, p. 7.

[5] Bell, B. M. (2006). Automatic differentiation software CppAD. http://www.coin-or.org/CppAD/.

[6] Bendsten, C. and Stauning, O. (1996). FADBAD, a flexible C++ package for automatic differentiation using the forward and backward methods, Technical Report 1996-x5-94, Technical University of Denmark, Lyngby.

[7] Berz, M. and Makino, K. (2006). COSY INFINITY 9.0. Programmer's manual, Technical Report MSUHEP 060803, Michigan State University, East Lansing, MI.

[8] Eble, I. (2007). Über Taylor-Modelle, Ph.D. thesis, Universität Karlsruhe, Karlsruhe.

[9] Griewank, A. (2000). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia, PA.

[10] Hammer, R., Hocks, M., Kulisch, U. and Ratz, D. (1995). C++ Toolbox for Verified Computing I-Basic Numerical Problems, Springer-Verlag, Heidelberg/New York, NY.

[11] Kecskeméthy, A. and Hiller, M. (1994). An object-oriented approach for an effective formulation of multibody dynamics, Computer Methods in Applied Mechanics and Engineering 115(3-4): 287-314.

[12] Knüppel, O. (1994). PROFIL/BIAS-A fast interval library, Computing 53(3-4): 277-287.

[13] Knuth, D. E. and Levy, S. (1993). The CWEB System of Structured Documentation, Addison-Wesley, Reading, MA.

[14] Krawczyk, R. (1969). Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken, Computing 4(3): 187-201.

[15] Lin, Y. and Stadtherr, M. A. (2006). Validated solution of initial value problems for ODEs with interval parameters, Proceeding of the NSF Workshop on Reliable Engineering Computing, Savannah, GA, USA.

[16] Nedialkov, N. and Pryce, J. (2007). Solving differential-algebraic equations by Taylor series (III): The DAETS code, Journal of Numerical Analysis, Industrial and Applied Mathematics 1(1): 1-30.

[17] Nedialkov, N. S. (2002). The design and implementation of an object-oriented validated ODE solver, Technical report, University of Toronto, Toronto.

[18] Rauh, A., Auer, E. and Hofer, E. P. (2007a). VALENCIA-IVP:A comparison with other initial value problem solvers, Proceedings of the 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2006), Duisburg, Germany, p. 36.

[19] Rauh, A., Auer, E., Minisini, J. and Hofer, E. P. (2007b). Extensions of VALENCIA-IVP for reduction of over estimation, for simulation of differential algebraic systems, and for dynamical optimization, PAMM 7(1): 1023001-1023002.

[20] Rauh, A., Minisini, J. and Hofer, E. P. (2009). Towards the development of an interval arithmetic environment for validated computer-aided design and verification of systems in control engineering, Proceedings of the Dagstuhl Seminar 08021: Numerical Validation in Current Hardware Architectures, Dagstuhl, Germany, Lecture Notes in Computer Science, Vol. 5492, Springer-Verlag, Berlin/Heidelberg, pp. 175-188.

[21] Schlesinger, S. (1979). Terminology for model credibility, Simulation 32(3): 103-104.

[22] Strobach, D., Kecskeméthy, A., Steinwender, G. and Zwick, B. (2005). A Simplified Approach for Rough Identification of Muscle Activation Profiles via Optimization and Smooth Profile Patches, CD Proceedings of the International ECCOMAS Thematic Conference on Advances in Computational Multibody Dynamics, ECCOMAS, Madrid, Spain.

[23] Tändl, M., Stark, T., Erol, N.E., Löer, F. and Kecskeméthy, A. (2009). An object-oriented approach to simulating human gait motion based on motion tracking, International Journal of Applied Mathematics and Computer Science 19(3): 469-483.