Uniqueness aspects of model-updating procedures

Abstract

Application of model-updatin g techniques to obtain improved finite-element for dynamic behavior computations is often associated with the critical observation that model-update techniques can yield completely different models. In the past, this has been a reason for avoiding the use of such procedures. In order to obtain more insight into this phenomenon, a theoretical study about the uniqueness aspects of model update results is presented. A first problem is treated in which the of stiffness and mass modifications is evaluated. In a second step, the existence of equivalent finite-element is investigated. As a result, practical conclusions about the quality of model-update results will be drawn. Nomenclature = frequency response function matrix [K] = stiffness matrix [AK] = modification of stiffness matrix [M] = mass matrix [AM] = modification of mass matrix mk - kth modal mass \k - k\h complex eigenfrequency Vk = kth damped eigenfrequency i $k } = fcth mode vector uk = kih undamped eigenfrequency * = complex conjugate ters may lose any physical meaning. Difficulties of this type are related to uniqueness aspects of the model-updating approach. Therefore, this study aims at obtaining better insight into this uniqueness quality. Starting from the definition of identical dynamic behavior, two related problems are treated. First, a study of equivalent mass and stiffness modifications is performed. Next, the related problem of equivalence of finite-elemen t models is considered. From this study, interesting conclusions for practical application of model-updating techniques can be drawn related to the necessity of updating mass and/or stiffness parameters simultaneously, and about the importance of the dimensionality of the vector space of updating parameters as a controlling variable of the updating process. I. Introduction A PPLICATION of finite-element for computation of dynamic behavior is becoming more and more common in industry. However, practical use of these techniques has made it clear that a thorough verification of the accuracy of these is still necessary. A realistic method is to compare finite-element results (eigenfrequencies, mode shapes, generalized masses, etc.) with information obtained from high-quality modal survey tests. If unacceptable discrepancies occur, a model-updating step can be considered in which the model parameters are adjusted for optimal improvement of correlation. These updated can then serve as a basis for further analysis of the design under study (coupling, modification prediction, etc.) Several approaches have been suggested to perform the model-updating task. A classification of these based on the algorithm applied is suggested by Heylen. 1 Another classification is based on the type of updating parameters selected: individual mass and/or stiffness matrix elements,2'6 submatrices of the global mass and/or stiffness matrices,7'8 or the finite-element input data.9 One of the essential obstacles to the increased use of these techniques is the observation that, in general, it is very difficult to interpret the update of results or that the updated parame