Farid ASMA

Abstract: A finite element model updating method is proposed for damage detection in mechanical structures using frequency measurements. The cost function is made up of a frequency residual formulated by the gradient of a correlation function in the frequency domain. An optimization algorithm is proposed for the resolution of the numerical problem. The suggested technique is applied to simulated structures considering the effect of noisy measurements. The simulation tests results show the effectiveness of this new damage identification technique. Mathematical and algorithmic analyses highlight very interesting characteristics of the proposed optimization algorithm. The updating method thus obtained has application in structural damage detection and finite elements models validation. It allows also a structural health monitoring of large mechanical structures.

Abstract: Usually, for defects detection in structures, it is necessary to establish a mathematical model for the un-damaged mechanical structure to pose a template from which deviations can be measured. The dynamic behaviours of the analytical model and the real structure consid-ered are compared in order to detect any appearance of defect at its early stage. The presence of defects results in a difference between the measured behaviour and that given by the analytical model. The extent of the damage is obtained after some correction stages of this analytical model. Damage detection methods can be classified into three categories: methods of detection then correction, inverse correction methods, and simultaneous detection – correction methods. The proposed method is of the third type: it rebuilds the stiffness matrix considering proportional damping. A frequency correlation function is used to evaluate the sensitivity of the frequency response to a defect simu-lated successively into each element of the structure. This function which varies in the interval [0, 1] informs us about the influence of a simulated defect on the frequency response of the structure. When this one is close to the unity, the defects then are located and quantified. This function indicates if one approaches or moves away from the solution when a defect is supposed in a given element. The problem then consists in determining the stiffness cor-rections which as close as possible bring the frequency responses of the analytical model and those of the experi-mental structure. The method presented here consists of determin-ing the stiffness corrections by incrementing and/or decrementing of a step ε until as close as possible bringing the analytical model to the structure. The method thus obtained, applied to simulated measures for a lattice structure, shows the effectiveness and the precision of this correction strategy.

Abstract: In the field of structural dynamics, reliable finite element response predictions are becoming increasingly important to industry and there is a genuine interest to improve these in the light of measured frequency response functions. Unlike modal-based model updating formulations, response-based methods have been applied only with limited success due to incomplete measurements and numerical ill-conditioning problems. The least squares approximation method is one of the methods used but often poses a problem of pseudo inverse due to the number of incomplete measurements. The proposed algorithm is a modification and extension of a previously-developed nonlinear least squares method for damage detection and finite element model updating. The paper derives explicit expressions for the first and second order partial derivatives with respect to the correction parameters and for the Jacobian matrix used in the Newton–Raphson solution of the nonlinear set of equations in order to avoid the pseudo inverse and to build a symmetrical system. The proposed method, assigned to a frequency parameterization which considers the minimum distance to be minimized, shows a good numerical stability. The performance of the method in localizing structural damage and updating model is examined using simulated measurements.

Abstract: This study presents a new updating method based on measured frequency response functions. The objective function of the minimization procedure is formed by the difference between the measured and the analytical frequency responses. The updating parameters are the correction coefficients related to each the elementary mass and stiffness matrices. While making use of a number of incomplete measurements for some frequencies, one builds a non-linear system of equations. The linearisation of the numerical system leads to an iterative procedure. An intrinsic frequency parametrization is proposed in order to accelerate the convergence of the iterative system. The obtained results are comparable with those of the known least squares methods.