Solving the inverse problem of crack identification using fuzzy genetic algorithms

Abstract

Failure due to low-cycle fatigue initiated cracks in rotating equipment may result in catastrophic scenarios. It is, therefore, important to identify fault parameters, such as crack size and crack location, to avoid such failures, and also to provide an estimate about the remaining safe life of the machine in operation. In this paper, a crack identification system based on vibration measurements and nodal crack force finite element modeling (FEM) approach is presented. The 3-D nodal crack force approach transforms the nonlinear problem of the breathing crack into a series of linear analyses around the static equilibrium. Solving such an identification system represents an inverse problem in which the applied loads and the vibration response are known, whereas fault parameters such as crack size and location are unknowns. The FEM is used to obtain the forward solution of the inverse problem where the applied loads and the crack parameters are input into the FE model. A scaled-down slow-rotating washer drum is constructed and 6 different anticipated crack locations are investigated. The measured vibration signals identifying signatures of certain cracks are experimentally obtained using the bolt removal method (BRM) for simulating the crack. The inverse problem is then formulated as a minimization problem for a scalar error function, and solved using classical as well as genetic optimization algorithms in conjunction with the fuzzy logic approach. The fuzzy logic approach is used to identify the weighting functions within the objective function based on the relative importance of the vibration levels of the 1/rev., 2/rev. and 3/rev. During solving the optimization problem, it is assumed that only one crack exists at a time for a predefined crack location. Several crack sizes at the 6 different discrete locations are identified. A comparison between classical techniques and the genetic algorithms is presented.