Sensitivity evaluation methods of electromagnetic quantities with FE‐analysis

Abstract

The sensitivity analysis determines the influence of geometrical or physical parameters on some global or local quantities, used as objective function. Two different methods for nodal and global sensitivity evaluation are discussed. A very efficient method of direct differentiation is proposed which enables calculation of energy functional perturbation caused by the nodal position movement. Otherwise, the optimal nodal position minimizing the energetic functional can be obtained. The second method, based on stiffness matrix inversion, is well known from circuit theory. It was adapted for computing the sensitivity of nodal potentials in finite elements to perturbations in chosen parameter of analyzed model. After the stiffness matrix has been inverted we obtain the new solution of the FEM problem and the sensitivity values of all nodal potentials of our model. This sensitivity can be easily computed versus many parameters, for example versus electrical conductivity in different elements. Such an approach allows us to identify conductivity variations, e.g. cracks in metals. To identify the crack shape and its conductivity, the iterative process is necessary. The desired data, as magnetic flux density, come from measurement. For the aim of test cases in this work, the measurement was simulated by finite element computation. On the surface of the conducting plate, cracks of different shape and conductivity were inserted. The models with cracks were analyzed with the FEM providing training data for further iterative process. Then the cracks were removed, and the algorithm tried to reconstruct the conductivity distribution based on sensitivity values of the nodes.

Citation

Gawrylczyk, K.M. (1998), "Sensitivity evaluation methods of electromagnetic quantities with FE‐analysis", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 17 No. 1, pp. 78-84. https://doi.org/10.1108/03321649810202991