Study On Numerical Methods Of Structural Defect Identification Based On Level Set

The nondestructive identification of structural defects is defined as identifying the location and shape of the defects in the structure without damaging the structure itself.It is of great significance to the prediction of the safety and life of the structure.Presently,the identification of structural defects is mainly realized by experiment and numerical calculation,or a combination of the two methods.Most of the identification methods are constructed to obtain inversely the parameters of the defects based on the measured experimental data of the structural response.The successful implementation of these methods needs the accurate description of defect parameters,the proper selection and the accurate solution of the forward problem,and the effective construction of the optimization algorithm.Presently,the research and application in this field has been very extensive,but there are still some problems that need to be improved.So this paper presents some new identification methods.An identification method based on explicit parameter description is established.The genetic algorithm and smooth extended finite element method are used to identify the parameters of structural defects.Secondly,considering the description of the defect parameters,an identification method based on level set method and structural static response is proposed.Thirdly,an identification method based on level set method and the time-domain dynamic response of structure is developed.In addition,an identification method based on level set method and structural topological derivative is studied,and this method is applied to numerical examples that based on the static response and time-domain dynamic response,respectively.Finally,an identification method based on binary level set method is proposed for the case of the defects of several different kinds in the structure.The specific work carried out in this paper is as follow:(1)An identification method based on explicit parameter description is established.In this method,the smooth extended finite element method is used as the solver of the forward problem.The error function of displacement response is taken as the objective function and the genetic algorithm is used as the optimization tool to identify the explicit defect parameters.The validity of the method is verified by some numerical examples.(2)An identification method based on level set method and the structural static response is proposed.In this method,the zero level set is used to implicitly express the boundaries of structural defects and the finite element method is used to solve the forward problem to improve the computational efficiency.A gradient-based optimization method is used to solve the identification problem.The error function of the structural static displacement response is taken as the objective of the optimization.The Frechet derivative of the objective function to the structural shape is derived and it is also called the shape derivative.Then the velocity field of the level set function is defined according to the shape derivative,and the value of the level set function is updated in the whole problem domain so that the boundaries of the structural defects can be updated.Finally the defect region to be identified can be obtained.The method is applied to structural defect identification in both two-dimensional and three-dimensional numerical models.The results of the numerical examples verify the validity of the proposed method.(3)An identification method based on the level set method and the structural time-domin dynamic response is developed.Level set method is still used to implicitly express the boundaries of structural defects.The forward problem is solved by the dynamic finite element method,and the error function of the time-domain dynamic displacment response is taken as the objective of the optimization.The shape derivative of the objective function about the time-domain dynamic response is derived,and then the velocity field updating the level set function is determined.This method is firstly applied to the two-dimensional identification problem,and the results are compared with those obtained by the method based on modal response,which verifies the accuracy advantage of the proposed method.On the other hand,the effects of some key model parameters,such as excitation force,number and location of measuring points,initial defect distribution,model error,data noise and defect size on the identification results are also studied.Finally,this method is applied to a simple example of three-dimensional numerical model.(4)An identification method based on level set method and the structural topological derivative is studied.The method is still based on the implicit expression of defect boundary by level set method.The structural topological derivative is introduced into the identification process.The topological derivatives of the objective functions based on the static and dynamic responses are derived,respectively.Moerover,the cases of two-dimensional and three-dimensional numerical models are both involved.Then,according to the calculated topological derivatives,a new defect region is generated at the corresponding location of the structure in some specific iteration steps during the identification process,which gets rid of the dependence on the initial layout of the defect location.The results of numerical examples verify the validity of the proposed method.(5)An identification method based on the binary level set method is proposed.In this method,the discontinuity of the binary level set function is used to implicitly express the boundaries of structural defects.The relationship among the structural material function,the binary level set function and the material constant is established.The derivative of the objective function to the binary level set function is derived.The first-order Euler method is used to search the optimal level set function.In the numerical implementation of the optimization,the original binary level set function is approximately replaced by the signed function with control parameters.This can not only accelerate the convergence rate of the algorithm,but also make the level set function approximately satisfy the constraint by setting the control parameters.Finally,several identification examples with several different kinds of defects are given,and the results verify the validity of the proposed method.