Abstract
The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy of the numerical solution of the adjoint differential equation has a great impact on the gradient. Hence, an alternative approach is the discrete adjoint method, where the adjoint differential equations are replaced by algebraic equations. Therefore, a finite difference scheme is constructed for the adjoint system directly from the numerical time integration method. The method provides the exact gradient of the discretized cost function subjected to the discretized equations of motion.
Highlights
In the last few years the complexity of the multibody systems has grown tremendously
The advantage of the presented method is that the cost function may depend on the accelerations if the discrete adjoint method is used
We show a new approach for the computation of the gradient of a cost function associated with a dynamical system for a parameter identification problem
Summary
In the last few years the complexity of the multibody systems has grown tremendously. We consider an optimization problem for the multibody system, which can be described in the general form as follows: Find the vector of unknown parameters u such that the cost function given by. Serban et al [19] realized the parameter identification in multibody systems by minimizing a cost function by the Levenberg–Marquardt method. A recent paper [11] shows how the adjoint method can be applied efficiently to a multibody system described by differential-algebraic equations of index three. It presents the structure of the adjoint equations depending on the Jacobian matrices of the system equations. 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
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