Identification à temps continu sur structure continue
Résumé
The purpose of this study is to show that it is possible to use continuous time identification method with a signal discretized either in space and in time domains. The partial differential equations, and particularly those governing continuous mechanical system behaviour, can be transformed into algebraic equations by using the well known properties of orthogonal functions. Before any identification, it is crucial to calculate data that are not directly available by the measurement. This calculation will be performed thanks to an expansion of the signals into an orthogonal basis. After this calculation, all the data calculated and recorded are expanded into a unique orthogonal basis. After this expansion step, the identification is performed through a very classical Least Square process. To validate the formalism, two different tests will be carried out: one for a bar in longitudinal motion and a second one with a bending beam. This study shows that it is possible to reconstruct quantities not available by a direct measurement and that identification is robust to noise. The proposed methodologies and formulations can be easily extended to other orthogonal functions in association with partial differential transformations.