Enhancement of the Adjoint Method by Error Control of Accelerations for Parameter Identification in Multibody Dynamics

Abstract

The present paper shows the embedding of the adjoint method in multibody dynamics and its broad applicability for examples for both, parameter identification and optimal control. Especially, in case of parameter identifications in engineering multibody applications, a theoretical enhancement of the proposed adjoint method by an error control of accelerations is inevitable in order to meet the circumstances of experimental studies using acceleration sensors in general.

The discrete adjoint method for parameter identification in multibody system dynamics

“…Hence, the Jacobian matrices that are necessary for the discrete adjoint computations remain similar to the Jacobian matrices that are required for the HHT-solver. Otherwise, in the continuous case, the accelerations are not included in the state vector, but have to be expressed by the motion equations in the cost function, which lead to complex Jacobian matrices [ 12 ]. The straightforward and efficient considerations of the acceleration in the cost function have the advantage that the measured signals from acceleration sensors can be used directly for parameter identification in practice.…”

“…The reason is that the accelerations are included in the state vector of the HHT-solver. In contrast to the discrete adjoint method, in the continuous approach, the accelerations have to be expressed by the equations of motion, leading to a complex Jacobian matrix [ 12 ]. Practically speaking, the new approach allows us to use measured data from acceleration sensors in a straightforward manner as a reference trajectory in the cost function for the parameter identification.…”

Optimal input design for multibody systems by using an extended adjoint approach

“…( 4 ), optimal input design can be seen as the standard problem of optimal control for the extended system. In previous publications of the authors [ 14 , 15 ], the adjoint method is presented to be the most efficient way to solve such problems. Since the cost functional in Eq.…”