Direct and Adjoint Sensitivity Analysis of Ordinary Differential Equation Multibody Formulations

Journal of Computational and Nonlinear Dynamics - Tập 10 Số 1 - 2015
Daniel Dopico1, Yitao Zhu1, Adrian Sandu2, Corina Sandu3
1Advanced Vehicle Dynamics Laboratory and Computational Science Laboratory, Departments of Mechanical Engineering and Computer Science, Virginia Tech, Blacksburg, VA 24061 e-mail:
2Computational Science Laboratory, Department of Computer Science, Virginia Tech, Blacksburg, VA 24061 e-mail:
3Advanced Vehicle Dynamics Laboratory, Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061

Tóm tắt

Sensitivity analysis of multibody systems is essential for several applications, such as dynamics-based design optimization. Dynamic sensitivities, when needed, are often calculated by means of finite differences. This procedure is computationally expensive when the number of parameters is large, and numerical errors can severely limit its accuracy. This paper explores several analytical approaches to perform sensitivity analysis of multibody systems. Direct and adjoint sensitivity equations are developed in the context of Maggi's formulation of multibody dynamics equations. The approach can be generalized to other formulations of multibody dynamics as systems of ordinary differential equations (ODEs). The sensitivity equations are validated numerically against the third party code fatode and against finite difference solutions with real and complex perturbations.

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Tài liệu tham khảo

1989, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations

1998, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations

1982, Dynamic Analysis of Plane Mechanisms With Lower Pairs in Basic Coordinates, Mech. Mach. Theory, 17, 397, 10.1016/0094-114X(82)90032-5

1982, Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Mechanical Systems, J. Mech. Des., 104, 247

1994, Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge

1979, Applied Optimal Design: Mechanical and Structural Systems

2002, Adjoint Sensitivity Analysis for Differential-Algebraic Equations: Algorithms and Software, J. Comput. Appl. Math., 149, 171, 10.1016/S0377-0427(02)00528-9

2003, Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution, SIAM J. Sci. Comput., 24, 1076, 10.1137/S1064827501380630

1985, Optimal Design of Mechanical Systems With Constraint Violation Stabilization Method, J. Mech., Trans. Autom. Des., 107, 493, 10.1115/1.3260751

1987, Design Sensitivity Analysis of Dynamic Systems, Computer Aided Optimal Design: Structural and Mechanical Systems

1992, Sensitivity Analysis of Constrained Multibody Systems, Arch. Appl. Mech., 62, 181, 10.1007/BF00787958

1992, Analyzing and Optimizing Multibody Systems, Mech. Struct. Mach., 20, 67, 10.1080/08905459208905161

1997, Optimization of Multibody Dynamics Using Object Oriented Programming and a Mixed Numerical-Symbolic Penalty Formulation, Mech. Mach. Theory, 32, 161, 10.1016/S0094-114X(96)00037-7

1997, Sensitivity Analysis of Rigid-Flexible Multibody Systems, Multibody Syst. Dyn., 1, 303, 10.1023/A:1009790202712

1997, Efficient Sensitivity Analysis of Large-Scale Differential-Algebraic Systems, Appl. Numer. Math., 25, 41, 10.1016/S0168-9274(97)00050-0

2002, Analytical Fully-Recursive Sensitivity Analysis for Multibody Dynamic Chain Systems, Multibody Syst. Dyn., 8, 1, 10.1023/A:1015867515213

2004, Order-(n+m) Direct Differentiation Determination of Design Sensitivity for Constrained Multibody Dynamic Systems, Struct. Multidisc. Optim., 26, 171, 10.1007/s00158-003-0336-1

2007, Second Order Adjoint Sensitivity Analysis of Multibody Systems Described by Differential-Algebraic Equations, Multibody Syst. Dyn., 18, 599, 10.1007/s11044-007-9080-4

2006, Stabilized Index-1 Differential-Algebraic Formulations for Sensitivity Analysis of Multi-body Dynamics, Proc. Inst. Mech. Eng., Part K, 220, 141

2009, Sensitivity Analysis of Flexible Multibody Systems Using Composite Materials Components, Int. J. Numer. Methods Eng., 77, 386, 10.1002/nme.2417

2010, An Efficient Direct Differentiation Approach for Sensitivity Analysis of Flexible Multibody Systems, Multibody Syst. Dyn., 23, 121, 10.1007/s11044-009-9176-0

2013, Symbolic Sensitivity Analysis of Multibody Systems, Multibody Dynamics. Computational Methods and Applications, 123

2012, fatode: A Library for Forward, Adjoint, and Tangent Linear Integration of ODEs

2011, Efficient Solution of Maggi's Equations, ASME J. Comput. Nonlinear Dyn., 7, 021003

1988, A Modified Lagrangian Formulation for the Dynamic Analysis of Constrained Mechanical Systems, Comput. Methods Appl. Mech. Eng., 71, 183, 10.1016/0045-7825(88)90085-0

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Journal of Computational and Nonlinear Dynamics

Tập 10 Số 1

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