Robust damage assessment of multiple cracks based on the frequency response function and the Constitutive Relation Error updating method

Abstract

To cite this version:Béatrice Faverjon, Jean-Jacques Sinou. Robust damage assessment of multiple cracks based on the frequency response function and the Constitutive Relation Error updating method. Journal of Sound and Vibration, Elsevier, 2008, 312, pp.821-837 AbstractThe aim of this paper is to present a damage assessment technique for the non destructive detection and sizing of multiple open cracks in beams. The Constitutive Relation Error updating method is used for the identification of the location and the size of multi-cracks in a simply supported beam. The present identification method is illustrated through numerical examples including double and triples cracks. Moreover, the efficiency and robustness of the proposed method is demonstrated through various numerical simulations in regard to the non-dimensional crack depth and the crack location. It is demonstrated that the Constitutive Relation Error updating method can detect the number of cracks on the beam and can estimate both the crack positions and sizes with satisfactory precision, even if 10% or 20% noise levels has been added to the simulations, and only few degrees of freedom are used for the identification procedure.

A Kriging Model Based Finite Element Model Updating Method for Damage Detection

“…A total of 90 samples are obtained by LHS as the initial sample population and the Kriging model based model updating is carried out with the stopping criterion of ε 1 = 10 −10 in Equation (15) and criterion of ε 2 = 10 −4 in Equation (16). At the same time, the model updating based on GA directly is also implemented as a benchmark to compare the results of the two methods.…”

A Model Updating Technique Based on the Constitutive Relation Error for In Situ Identification of Admittance Coefficient of Sound Absorbing Materials

“…Although these relations do not allow describing the exact acoustic behavior of all the porous materials in the frequency range defined by (32), they are widely used and can provide reasonable order of magnitude of Z c and k. Miki suggests slightly different empirical expressions of Z c and k for multilayer fibrous materials, especially at low frequency. The coefficients c i (i = 1, ..., 8) of the Delany-Bazley-Miki model are given in the second row of Tab.…”

“…This error is an indicator based on an energy-norm and can consequently be locally evaluated [31]. It allows to define a two-steps method [31][32][33][34]. First, a step of localization consists in determining the regions in which the less-reliable equations are the most erroneous by checking the local estimators.…”

Definition and updating of simplified models of joint stiffness

“…Updating based on the constitutive relation error was developed for free and forced vibration analysis (Ladevèze and Chouaki, 1999) and, by introducing the dissipation error into the updating technique, for material or contact nonlinearities (Chouaki et al, 2000). Recently, work has also been done on the localization and sizing of multiple cracks (Faverjon and Sinou, 2008) and on updating based on uncertain measurements (Faverjon et al, 2009). Here, this method is applied to the static problem of a structure with multiple fastened joints loaded in tension.…”