3D crack identification using the Nelder-Mead Simplex algorithm combined with a random generation of crack positions

Abdelouahab Benzerdjeb,Hocine Kebir,Nasreddine Amoura

doi:10.3221/igf-esis.59.18

Abstract

In this paper, we present a scheme for cracks identification in three-dimensional linear elastic mechanical components. The scheme uses a boundary element method for solving the forward problem and the Nelder-Mead simplex numerical optimization algorithm coupled with a low discrepancy sequence in order to identify an embedded crack. The crack detection process is achieved through minimizing an objective function defined as the difference between measured strains and computed ones, at some specific sensors on the domain boundaries. Through the optimization procedure, the crack surface is modelled by geometrical parameters, which serve as identity variables. Numerical simulations are conducted to determine the identity parameters of an embedded elliptical crack, with measures randomly perturbed and the residual norm regularized in order to provide an efficient and numerically stable solution to measurement noise. The accuracy of this method is investigated in the identification of cracks over two examples. Through the treated examples, we showed that the method exhibits good stability with respect to measurement noise and convergent results could be achieved without restrictions on the selected initial values of the crack parameters.

Highlights

The identification of cracks in mechanical components remains as one of the challenges of inverse problems in mechanics
The inverse problem of crack identification has been defined as a minimization of a least squares functional given as an objective function
The direct problem was solved by the Dual boundary Element Method to compute strains at selected sensor points on the boundaries, since strains allow to better capture the effect of crack opening on the domain boundaries, by a judicious fixture of elastic strain gauges

Summary

INTRODUCTION

The identification of cracks in mechanical components remains as one of the challenges of inverse problems in mechanics. Engineers process the response of the component to an applied field (static or dynamic), and give an approximate evaluation of the crack’s identity (size and position) These experimental methods have their specific advantages and limitations depending on the application and the setup of the measurement system employed [1,2,3]. Amoura et al [10] developed a crack identification algorithm for 2-D and axisymmetric structures using a coupled DBEM and NelderMead function minimization method (The simplex method) [17] to set a stable procedure In their work, they used a lowdiscrepancy sequence (LDS) to produce the initial crack’s identity for the simplex launch, which considerably reduced the computing time. An extension of the procedure to 3D problems is done with application to the identification of elliptical embedded cracks

CRACK IDENTIFICATION PROCEDURE

CONCLUSIONS