The adjoint method coupled with the modal identification method for nonlinear model reduction

Abstract

In order to obtain reduced models (RMs) from original detailed ones, the Modal Identification Method (MIM) has been developed for several years for linear and then for nonlinear systems. This identification is performed through the resolution of an inverse problem of parameter estimation. So far, the MIM was used with the Finite Difference Method (FDM) for the computation of the gradient of the functional to be minimized. This leads to important computation times. In order to save it up, the Adjoint Method (AM) has been coupled with the MIM to compute the gradient. All the equations related to the reduced model, the adjoint equations, the gradient and the optimization algorithm are clearly expressed. A test case involving a 3D nonlinear transient heat conduction problem is proposed. The accuracy of the identified RM is shown and the comparison between the proposed AM and the classical FDM shows the drastic reduction of computation time.

Keywords:

• Reduced Model
• Modal Identification Method
• Inverse Heat Conduction Problem
• Adjoint Methods

Notes

§Present address: From October 2004, the author has been staying at the Laboratoire d’Energétique et de Mécanique Théorique et Appliquée, UMR CNRS 7563-2, Avenue de la Forêt de Haye, BP 160, 54504 Vandoeuvre les Nancy – France.

Additional information

Notes on contributors

M. Girault§

§Present address: From October 2004, the author has been staying at the Laboratoire d’Energétique et de Mécanique Théorique et Appliquée, UMR CNRS 7563-2, Avenue de la Forêt de Haye, BP 160, 54504 Vandoeuvre les Nancy – France.