Research Papers

Direct and Adjoint Sensitivity Analysis of Ordinary Differential Equation Multibody Formulations

[+] Author and Article Information
Daniel Dopico

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

Yitao Zhu

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

Adrian Sandu

Computational Science Laboratory,
Department of Computer Science,
Virginia Tech,
Blacksburg, VA 24061
e-mail: asandu7@vt.edu

Corina Sandu

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

1Address all correspondence to this author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 18, 2013; final manuscript received January 10, 2014; published online September 12, 2014. Assoc. Editor: Parviz Nikravesh.

J. Comput. Nonlinear Dynam 10(1), 011012 (Sep 12, 2014) (7 pages) Paper No: CND-13-1184; doi: 10.1115/1.4026492 History: Received July 18, 2013; Revised January 10, 2014

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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