Parameter Estimation In Discontinuous Descriptor Models

Abstract

Parameter estimation is an important tool for deriving models for multibody systems, which not only describe the dynamical system in a qualitatively correct way, but are also quantitatively correct. A number of efficient methods for treating such problems for general ordinary differential equations and differential-algebraic equations (DAE) have been developed [3, 6, 7]. The problem class of multibody systems (MBS) in descriptor form is especially challenging due to the high index of the DAE and the typical presence of discontinuities. The focus of the present paper is on the reliable computation of derivatives of integration schemes for MBS descriptor models withdiscontinuous effects which is a key task within the parameter estimation process. ¹ It is based on the theoretical background about the exploitation of invariants presented in [7] and has been implemented extending the Runge-Kutta integrator MBSD85 from the integrator library MBSSIM [8]. The paper is organized in three sections. First some basic facts about MBS and parameter identification as well as the efficient solution of initial value problems for MBS descriptor models are recalled. The second section provides the basic methods for the efficient and accurate computation of derivatives of IVP solutions of MBS. Finally numerical results illustrate the practical applicability of the methods developed.