SENSITIVITY OF THE IDENTIFIED MODAL PARAMETERS ON IMPRECISE EXPERIMENTAL DATA T. Tison, B. Lallemand, A. Cherki and P. Level Laboratoire d'Automatique et de Mecanique lndustrielles et Humaines URA CNRS 01775 Universite de Valenciennes, BP311 59304 Valenciennes Cedex, France. ABSTRACT. In the field of structural analysis, many factors are sources of errors on finite element modelling. Many sources, identified or not, could create a model more or less erroneous. An important research consists in developing, by inverse analysis, some methods allowing to correct finite element models in relation to the experimental data. In these methods, the hypothesis is the following : the observed reality is the aim to reach, consequently, the complete error is imputable to the model. However, the experimental data contain a part of the error due to the measurement system and the role of the human factor. This type of uncertainty is moreover difficult to quantify. In this paper, we have developed an algorithm allowing us to identify the eigensolutions of a prototype considering imprecise frequency response functions. This algorithm is based on both a classical identification technique and the used of fuzzy number for modelling imprecise experimental data. This methodology have two potentials of interest : - the ability to supply imprecise data to modal updating tools, - the capacity to filter the imprecision on the measured data. NOMENCLATURE X:: a fuzzy number. x L : lower bound of the number or matrix x. xu : upper bound of the number or matrix x. [ x L, xu la : interval of the fuzzy number at the a-level cut. 1. INTRODUCTION The elaboration of a good quality modal model with respect to the experimentation, often necessitates the use of modal updating tools. These tools exploit the hypothesis that observed behavior is correct and that, consequently, all the error is imputable to the initial model. Some updating procedures use directly modal parameters identified from transfer functions measured on the prototype. Applying the basis hypothesis, these modal parameters are the objective to reach during the updating process. Manifestly, this hypothesis does not take possible errors on modal parameters into account. 1615 Many authors [1 ][2] have nevertheless counted a great number of errors being able to come from the experimentation or the identification phase . In the absence of reference, it is often difficult to estimate the error or the imprecision intervening on these data. All the more, the human factor holds an important role during all the experimental phase. To take the error on experimental data into account , we have envisaged two possibilities. In the first one, we introduce the imprecision directly on identified modal parameters. An adapted updating algorithm allows then the processing of these data [3]. Note that here the imprecision is estimated a posteriori "to goods feel the engineer". The second possibility, that makes the object of this paper, consists in taking the experimental error into account, very upstream in the updating process. In this case, we introduce the imprecision directly on frequency response functions (FRF). To modelize the imprecision, we have chosen the fuzzy formalism. We propose then an algorithm of identification in which FRF are fuzzy functions and whose basis is the method of curve-fitting developed at the LMA [4] . 2. DEVELOPMENT 2.1 Basis Relationships The forced response of a structure can be expressed according to the principle of modal superposition by the expression : In a narrow frequency band, the forced response depends essentially on the contribution of the some present modes in this band. The contribution of the external modes (including conjugated modes) to the analyzed frequency band is very weak and the response can be estimated by the expression :