Research Papers

Dynamic Response Optimization of Complex Multibody Systems in a Penalty Formulation Using Adjoint Sensitivity

[+] Author and Article Information
Yitao Zhu

Advanced Vehicle Dynamics Laboratory and
Computational Science Laboratory,
Department of Mechanical Engineering and
Department of Computer Science,
Virginia Tech,
Blacksburg, VA 24061
e-mail: yitao7@vt.edu

Daniel Dopico

Advanced Vehicle Dynamics Laboratory and
Computational Science Laboratory,
Department of Mechanical Engineering and
Department of Computer Science,
Virginia Tech,
Blacksburg, VA 24061
e-mail: ddopico@vt.edu

Corina Sandu

Advanced Vehicle Dynamics Laboratory,
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: csandu@vt.edu

Adrian Sandu

Computational Science Laboratory,
Department of Computer Science,
Virginia Tech,
Blacksburg, VA 24061
e-mail: sandu@cs.vt.edu

1Corresponding author.

Manuscript received October 29, 2014; final manuscript received January 10, 2015; published online February 11, 2015. Assoc. Editor: Rudranarayan Mukherjee.

J. Comput. Nonlinear Dynam 10(3), 031009 (May 01, 2015) (9 pages) Paper No: CND-14-1268; doi: 10.1115/1.4029601 History: Received October 29, 2014; Revised January 10, 2015; Online February 11, 2015

Multibody dynamics simulations are currently widely accepted as valuable means for dynamic performance analysis of mechanical systems. The evolution of theoretical and computational aspects of the multibody dynamics discipline makes it conducive these days for other types of applications, in addition to pure simulations. One very important such application is design optimization for multibody systems. In this paper, we focus on gradient-based optimization in order to find local minima. Gradients are calculated efficiently via adjoint sensitivity analysis techniques. Current approaches have limitations in terms of efficiently performing sensitivity analysis for complex systems with respect to multiple design parameters. To improve the state of the art, the adjoint sensitivity approach of multibody systems in the context of the penalty formulation is developed in this study. The new theory developed is then demonstrated on one academic case study, a five-bar mechanism, and on one real-life system, a 14 degree of freedom (DOF) vehicle model. The five-bar mechanism is used to validate the sensitivity approach derived in this paper. The full vehicle model is used to demonstrate the capability of the new approach developed to perform sensitivity analysis and optimization for large and complex multibody systems with respect to multiple design parameters with high efficiency.

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Haug, E., and Arora, J., 1978, “Design Sensitivity Analysis of Elastic Mechanical Systems,” Comput. Meth. Appl. Mech. Eng., 15(1), pp. 35–62. [CrossRef]
Haug, E., Wehage, R., and Mani, N., 1984, “Design Sensitivity Analysis of Largescale Constrained Dynamic Mechanical Systems,” ASME J. Mech. Trans. Autom. Des., 106(2), pp. 156–162. [CrossRef]
Krishnaswami, P., and Bhatti, M., 1984, “A General Approach for Design Sensitivity Analysis of Constrained Dynamic Systems,” ASME J. Mech. Trans. Autom. Des., pp. 84–132.
Haug, E., 1987, Computer Aided Optimal Design: Structural and Mechanical Systems, C. A. M.Soares, ed., Vol. 27 (NATO ASI Series. Series F, Computer and Systems Sciences), Springer-Verlag, Berlin, Germany.
Chang, C., and Nikravesh, P., 1985, “Optimal Design of Mechanical Systems With Constraint Violation Stabilization Method,” J. Mech. Trans. Autom. Des., 107(4), pp. 493–498. [CrossRef]
Pagalday, J., and Avello, A., 1997, “Optimization of Multibody Dynamics Using Object Oriented Programming and a Mixed Numerical-Symbolic Penalty Formulation,” Mech. Mach. Theory, 32(2), pp. 161–174. [CrossRef]
Haug, E., Wehage, R., and Barman, N., 1981, “Design Sensitivity Analysis of Planar Mechanism and Machine Dynamics,” ASME J. Mech. Des., 103(3), pp. 560–570. [CrossRef]
Bestle, D., and Seybold, J., 1992, “Sensitivity Analysis of Constrained Multibody Systems,” Arch. Appl. Mech., 62, pp. 181–190.
Bestle, D., and Eberhard, P., 1992, “Analyzing and Optimizing Multibody Systems,” Mech. Struct. Mach., 20(1), pp. 67–92. [CrossRef]
Dias, J., and Pereira, M., 1997, “Sensitivity Analysis of Rigid-Flexible Multibody Systems,” Multibody Sys. Dyn., 1, pp. 303–322. [CrossRef]
Feehery, W. F., Tolsma, J. E., and Barton, P. I., 1997, “Efficient Sensitivity Analysis of Large-Scale Differential-Algebraic Systems,” Appl. Numer. Math., 25(1), pp. 41–54. [CrossRef]
Anderson, K. S., and Hsu, Y., 2002, “Analytical Fully-Recursive Sensitivity Analysis for Multibody Dynamic Chain Systems,” Multibody Sys. Dyn., 8(1), pp. 1–27. [CrossRef]
Anderson, K., and Hsu, Y., 2004, “Order-(n+m) Direct Differentiation Determination of Design Sensitivity for Constrained Multibody Dynamic Systems,” Struct. Multidiscip. Optim., 26(3–4), pp. 171–182. [CrossRef]
Ding, J.-Y., Pan, Z.-K., and Chen, L.-Q., 2007, “Second Order Adjoint Sensitivity Analysis of Multibody Systems Described by Differential-Algebraic Equations,” Multibody Sys. Dyn., 18, pp. 599–617. [CrossRef]
Schaffer, A., 2006, “Stabilized Index-1 Differential-Algebraic Formulations for Sensitivity Analysis of Multi-Body Dynamics,” Proc. Inst. Mech. Eng. Part K: J. Multi-Body Dyn., 220(3), pp. 141–156. [CrossRef]
Neto, M. A., Ambrosio, J. A. C., and Leal, R. P., 2009, “Sensitivity Analysis of Flexible Multibody Systems Using Composite Materials Components,” Int. J. Numer. Meth. Eng., 77(3), pp. 386–413. [CrossRef]
Bhalerao, K., Poursina, M., and Anderson, K., 2010, “An Efficient Direct Differentiation Approach for Sensitivity Analysis of Flexible Multibody Systems,” Multibody Sys. Dyn., 23(2), pp. 121–140. [CrossRef]
Banerjee, J. M., and McPhee, J., 2013, “Multibody Dynamics. Computational Methods and Applications,” Symbolic Sensitivity Analysis of Multibody Systems, Vol. 28 (Computational Methods in Applied Sciences), Springer, Brussels, Belgium, pp. 123–146.
Brenan, K., Campbell, S., and Petzold, L., 1989, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, New York. [CrossRef]
Ascher, U., and Petzold, L., 1998, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, Society for Industrial and Applied Mathematics, Philadelphia, PA. [CrossRef]
Dopico, D., Zhu, Y., Sandu, A., and Sandu, C., 2014, “Direct and Adjoint Sensitivity Analysis of ODE Multibody Formulations,” ASME J. Comput. Nonlinear Dyn., 10(1), p. 011012. [CrossRef]
Jalon, J. G. D., and Bayo, E., 1994, Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge, Springer-Verlag, New York.
Bayo, E., García de Jalon, J., and Serna, M., 1988, “A Modified Lagrangian Formulation for the Dynamic Analysis of Constrained Mechanical Systems,” Comput. Meth. Appl. Mech. Eng., 71(2), pp. 183–195. [CrossRef]
Garcia de Jalon, J., and Bayo, E., 1994, Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge, Springer-Verlag, New York.
Zhu, C., Byrd, R. H., Lu, P., and Nocedal, J., 1997, “Algorithm 778: L-BFGS-B: Fortran Subroutines for Large-Scale Bound-Constrained Optimization,” ACM Trans. Math. Softw., 23(4), pp. 550–560. [CrossRef]
Cao, Y., Li, S., Petzold, L., and Serban, R., 2003, “Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution,” SIAM J. Sci. Comput., 24(3), pp. 1076–1089. [CrossRef]
Frik, S., Leister, G., and Schwartz, W., 1993, “Simulation of the IAVSD Road Vehicle Benchmark Bombardier Iltis With Fasim, Medyna, Neweul and Simpack,” Veh. Syst. Dyn., 22(suppl), pp. 215–253. [CrossRef]
Rodríguez, P. L., Mántaras, D. Á., and Vera, C., 2004, Ingeniería del automóvil: sistemas y comportamiento dinámico, Thomson, Madrid, Spain.


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Fig. 1

Five-bar mechanism

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Fig. 2

The Bombardier Iltis vehicle. Adapted from Ref. [27].

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Fig. 3

Topology of the multibody vehicle model

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Fig. 4

Left front suspension system

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Fig. 5

The modified speed bumps test

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Fig. 6

The evolutions of the parameters of chassis vertical acceleration

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Fig. 7

Dynamic response of chassis vertical acceleration




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