Crack size estimation using model reduction and genetic algorithm

In this study we use the material elastic properties as a base. A tow dimensional cracked plate under traction is modelled by finite element method (FEM) then a reduced model is built using the proper orthogonal decomposition method (POD) with help of radial basis functions (RBF) method of interpolation. The crack length is estimated as an inverse identification problem, basing on the deformation obtained from the boundary nodes considered as sensor points. A genetic algorithm (GA) is used for the minimization of the error function which is expressed as the difference between displacement field of the boundaries caused by the crack size value proposed randomly by GA and the field measured at the actual identity. The approach presented accurate results and could guess the real crack size in a precession of 10 of the fitness function, proving its effectiveness even with a very low number of 4 sensors. To test the stability of the method against uncertainty a white noise was introduced later. The use of the reduced model provides tangible benefits mainly the very low computational cost.