Estimation of Location and Size of Defects in a Solid Body via Inverse Heat Conduction Problem

In the present paper, geometry specification in the inverse heat conduction problems (IHCP) is applied to detect the location and size of defect in a solid body. A crack or cavity is modeled as a supper-elliptic geometry whose parameters are estimated with inverse heat conduction problems. Both inverse analysis and gradient-based optimization method have been applied to an inverse algorithm that iteratively estimates the defect shape parameters. The inverse analysis is based on recording temperatures data on outer surface of solid domain that determines the objective function in the inverse algorithm with estimated and calculated temperatures. The employed gradient-based optimization method is constructed with the adjoint and sensitivity equations that are used to calculate the gradient of the objective function and the search step size, respectively. An unstructured grid is used and the computational domain is discretized with triangular elements. The finite element method (FEM) is employed to discretize the equations in analysis plus sensitivity and adjoint equations. The effects of different Biot numbers and noisy temperature data are investigated on inverse algorithm and the size and location of crack and complex cavity are calculated. Results show that the estimated shape has good agreement with exact shape of defect. The decrease of noisy data has improve the convergence rate and the increase of Biot numbers causes the estimated shape has the best accuracy in all cases.