The Parametric Level Set Method For Defect And Inclusion Identification In Heat Conduction

The operation safety of facilities is more likely affected by corrosion and thermal fatigue aging under a variety of complex thermal environments,to this effect,it is of great significance to identify the defect of the facilities by the technical of nondestructive evaluation(NDE).The NDE method that is adapted to a variety of defect types and easy to employ automatically can be established based on the theory of inverse problem and numerical optimization.However,this method needs to build the defect mathematical description that is not restricted by connectedness,and that requires forming shapes with varying degrees of complexity.On the other hand,an efficient numerical optimization algorithm is an important prerequisite for fast and stable identification.In this thesis,a novel defect identification method based on the parametric level set method(PLSM)and the method of moving asymptotes(MMA)is proposed to identify defect and inclusion,the related research contents include:A material related high-dimensional level set function is defined in the identification domain to establish the ersatz material model,which is further verified in a numerical example.Based on this model,the mesh reconstruction during the identification can be avoided.After the interpolation of level set function by radial basis function(RBF),the objective function which varied with the expansion coefficients can be minimized by the MMA,so that the identification is achieved.The efficiency and accuracy of the proposed method are further validated in several numerical examples by discussing the RBF,measurement points,knots,initial guess,excitation and measurement error,also the configuration reference in different cases is given.This work also shows the stability of the MMA in solving ill-posed problems and extends the application field of this method.The multiple-material PLSM is employed to identify the defect and inclusion simultaneously,which expands the application of the proposed method.The distribution of three kinds of material is determined by the two level set functions without the overlap constraint,which maintains the shape description property of the PLSM.Then the ersatz material model is established by a defined function combination.Finally,the update of two level set functions is realized simultaneously through the MMA.The stability and efficiency of this method are verified in numerical examples by discussing the measurement points,knot density,excitation,initial guess and measurement error.And the applicable conditions are also explored for the implementation.