Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems

Auer, Ekaterina; Luther, Wolfram

doi:10.2478/v10006-009-0037-z

Abstract

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.

References

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.
Search in Google Scholar
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.
Search in Google Scholar
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.
Search in Google Scholar
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.
Search in Google Scholar
Bell, B. M. (2006). Automatic differentiation software CppAD. http://www.coin-or.org/CppAD/
Search in Google Scholar
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.
Search in Google Scholar
Berz, M. and Makino, K. (2006). COSY INFINITY 9.0. Programmer's manual, Technical Report MSUHEP 060803, Michigan State University, East Lansing, MI.
Search in Google Scholar
Eble, I. (2007). Über Taylor-Modelle, Ph.D. thesis, Universität Karlsruhe, Karlsruhe.
Search in Google Scholar
Griewank, A. (2000). Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia, PA.
Search in Google Scholar
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.
Search in Google Scholar
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): 287-314.10.1016/0045-7825(94)90064-7
Search in Google Scholar
Knüppel, O. (1994). PROFIL/BIAS—A fast interval library, Computing 53(3-4): 277-287.10.1007/BF02307379
Search in Google Scholar
Knuth, D. E. and Levy, S. (1993). The CWEB System of Structured Documentation, Addison-Wesley, Reading, MA.
Search in Google Scholar
Krawczyk, R. (1969). Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken, Computing 4(3): 187-201.10.1007/BF02234767
Search in Google Scholar
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.
Search in Google Scholar
Nedialkov, N. and Pryce, J. (2007). Solving differential-agebraic equations by Taylor series (III): The DAETS code, Journal of Numerical Analysis, Industrial and Applied Mathematics 1(1): 1-30.
Search in Google Scholar
Nedialkov, N. S. (2002). The design and implementation of an object-oriented validated ODE solver, Technical report, University of Toronto, Toronto.
Search in Google Scholar
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. 36.10.1109/SCAN.2006.47
Search in Google Scholar
Rauh, A., Auer, E., Minisini, J. and Hofer, E. P. (2007b). Extensions of ValEncIA-IVP for reduction of overestimation, for simulation of differential algebraic systems, and for dynamical optimization, PAMM 7(1): 1023001-1023002.10.1002/pamm.200700022
Search in Google Scholar
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.
Search in Google Scholar
Schlesinger, S. (1979). Terminology for model credibility, Simulation 32(3): 103-104.10.1177/003754977903200304
Search in Google Scholar
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.10.1002/mawe.200500964
Search in Google Scholar
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): 469-483.10.2478/v10006-009-0038-y
Search in Google Scholar

Uses of New Sensitivity and Dae Solving Methods in SmartMobile for Verified Analysis of Mechanical Systems

Abstract

Paradigm

My account