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Research Papers

Direct Sensitivity Analysis of Multibody Systems: A Vehicle Dynamics Benchmark

[+] Author and Article Information
Alfonso Callejo

Department of Aerospace Engineering,
University of Maryland,
College Park, MD 20742
e-mail: callejo@umd.edu

Daniel Dopico

Laboratorio de Ingeniería Mecánica,
Universidade da Coruña,
Mendizábal s/n,
Ferrol 15403, Spain
e-mail: ddopico@udc.es

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 1, 2018; final manuscript received November 3, 2018; published online January 7, 2019. Assoc. Editor: Kyung Choi.

J. Comput. Nonlinear Dynam 14(2), 021004 (Jan 07, 2019) (9 pages) Paper No: CND-18-1250; doi: 10.1115/1.4041960 History: Received June 01, 2018; Revised November 03, 2018

Algorithms for the sensitivity analysis of multibody systems are quickly maturing as computational and software resources grow. Indeed, the area has made substantial progress since the first academic methods and examples were developed. Today, sensitivity analysis tools aimed at gradient-based design optimization are required to be as computationally efficient and scalable as possible. This paper presents extensive verification of one of the most popular sensitivity analysis techniques, namely the direct differentiation method (DDM). Usage of such method is recommended when the number of design parameters relative to the number of outputs is small and when the time integration algorithm is sensitive to accumulation errors. Verification is hereby accomplished through two radically different computational techniques, namely manual differentiation and automatic differentiation, which are used to compute the necessary partial derivatives. Experiments are conducted on an 18-degree-of-freedom, 366-dependent-coordinate bus model with realistic geometry and tire contact forces, which constitutes an unusually large system within general-purpose sensitivity analysis of multibody systems. The results are in good agreement; the manual technique provides shorter runtimes, whereas the automatic differentiation technique is easier to implement. The presented results highlight the potential of manual and automatic differentiation approaches within general-purpose simulation packages, and the importance of formulation benchmarking.

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Figures

Grahic Jump Location
Fig. 2

Static equilibrium dynamic response: wheel z-coordinates

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Fig. 3

Static equilibrium sensitivities: z-coordinate of chassis COG with respect to front and rear stiffness (ks), damping coefficient (cd), and natural length (l0)

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Fig. 4

Steering profile and chassis y-position

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Fig. 5

Lane change dynamic response: angular velocity of wheels

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Fig. 6

Static equilibrium sensitivities: z-coordinate of chassis COG with respect to front and rear stiffness (ks), damping coefficient (cd), and natural length (l0)

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