r7.20.02 Extrapolation of measurements on a numerical model in dynamics

Summary:

An approach for extrapolating the results of experimental measurements in dynamics (displacements, speeds, accelerations, deformations, constraints) on a numerical model is presented. Based on a representation of the structure on a previously chosen projection base, it consists in solving the inverse problem defined by identifying the generalized coordinates relating to the projection base. The proposed resolution uses a minimization, in the sense of least squares, by using the LU decomposition or the decomposition into singular values (SVD), of a functional that is possibly regularized via the addition of a criterion of proximity to a solution that is known a priori. In the case of temporal identification, an explicit formulation of the a priory information is proposed.

Table of Contents

• 1. Problem
• 2. Notations
• 3. Extrapolation approach
• 4. Relationships between physical quantities and generalized quantities
• 5. Generalized coordinate calculation
  • 5.1. Formulation of the problem
  • 5.2. Determination of a virtual solution
  • 5.3. Determination of a regularized inverse solution
• 6. Implemented in Code_Aster
• 7. Bibliography
• 8. Description of document versions