Graph-theoretic sensitivity analysis of multi-domain dynamic systems: theory and symbolic computer implementation

Abstract

A graph-theoretic formulation for the sensitivity analysis of multi-domain dynamic systems is presented in this article. In this formulation, a linear graph is used to capture the system topology and a graph-theoretic formulation is used to generate the system equations and the sensitivity equations simultaneously from the linear graph. Symbolic generation ensures automated, accurate, and efficient generation of sensitivity equations. The proposed method of sensitivity analysis avoids differentiation of complicated algebraic expressions, and the corresponding equation swells, by using pre-formed (and stored) expressions that are combined according to the topology captured by the linear graph. To illustrate the application of graph-theoretic sensitivity analysis to multi-domain systems, an electric motor-driven slider-crank mechanism and an automotive torque converter are considered as examples. The generation of the sensitivity equations is demonstrated, and the results are validated using a finite difference formulation. Also, the efficiencies of the generated equations are gauged by measuring the associated computational costs. Finally, some features of multi-domain multibody systems that pose unique challenges to the theory and software implementation are presented, along with a brief description of the symbolic software platform that has been used to implement the algorithm.