Identification of Structural Parameters Based on Inverse Modification Theory

摘要

During the service life of a structure its stiffness, mass and damping parameters may be changed due to design modifications or due to a damage event. The effects of such modifications are usually analysed by either supplementing the initial Finite Element model with a model of the modification or, more directly, by calculating the modified structure response using structural modification theory. In practice the parameters of the modification are often unknown, for example when the modification was caused by a crack or by bolting a stiffener to the structure. In such cases a model updating approach can be applied where the parameters of the modified structure model are fitted to the test data of the modified structure. The drawback of this approach comes from the necessity to include not only the additional parameters related to the modification but also parameters related to the unmodified part of the structure since the model of the unmodified structure might include not only parametric errors but also physical modelling errors (e.g. due to oversimplification). Therefore, the model of the unmodified structure is usually fitted to test data of the unmodified structure in advance. In any case the success of the model updating approach is based on the ability of the initial model to represent the physics, i.e. the model should not contain physical model errors but only errors in the parameters of the model [1]. In the present paper an approach based on inverse modification theory is presented which allows the identification of the modification parameters. This approach includes the more classical model updating approach where the parameters of an initial analytical are fitted to measured frequency responses. However, the procedure also allows to use only measured frequency responses of the initial unmodified structure instead of analytical responses, i.e. in this case there is no need for a model of the whole structure, only a model of the modification is necessary. Structural modification theory is used as a tool to calculate the frequency response of a modified structure given the frequency response of the unmodified structure and the location, the type and the magnitude of the modification [4]-[7]. This theory is used here to solve the inverse problem: identify the magnitude of the modification with the frequency responses of the modified and unmodified structure taken either from analysis or test.