Finite Element Model Updating Using Resonance–Antiresonant Frequencies with Radial Basis Function Neural Network

Abstract

The modal frequencies, model shapes or their derivatives are generally used as the characteristic quantities of the objective function for the finite element model (FEM) updating. However, the measurement accuracy of the model shapes is low due to the few numbers of measurement points for actual structures, which results in a large correction error. The antiresonant frequency reflects the local information of the structure more accurately than the mode shapes, which is a good complement to the resonance frequencies. In this paper, a FEM updating using resonance and antiresonant frequencies with radial basis function (RBF) neural network is proposed. The elastic modulus, added mass, tensile stiffness and torsional stiffness are selected as the updating parameters of FEM for a cantilever beam, which were grouped by the uniform design method. The resonance and antiresonant frequencies identified from the frequency response function (FRF) obtained from corresponding FEM at only one node are taken as the characteristic quantities. The RBF neural network is adopted to construct the mapping relationships between the characteristic quantities and the updating parameters. The updated parameters are substituted into the FEM, and the FRF is obtained to verify the validity of the method. The results show that the relative errors between all the updated parameters and the target values are less than 7%, and the relative errors of the characteristic quantities in the updating frequency band are less than 3%. The proposed method can accurately reproduce the dynamic characteristics of the cantilever beam. It can be applied to the damage detection and safety evaluation of large structures which are difficult to arrange more measuring points.