Reconstruction of Current Density Distribution in Low-Voltage Switching Devices Through TSVD and TGSVD Regularization

This article examined two regularization methods for reconstructing the arc current density distribution of a switching device in an arc-quenching chamber. The finite-element method (FEM) was used to discretize the current-flow region of the arc-quenching chamber. Both truncated generalized singular value decomposition (TGSVD) and truncated singular value decomposition (TSVD) regularization were used to reconstruct the current density distribution. TGSVD addressed the poor reconstruction accuracy caused by the ill-posedness of the Biot–Savart operator. Simulation results showed that the reconstruction of current density distribution was more accurate with higher signal-to-noise ratios (SNRs) and lower mean-square errors (MSEs). Both regularization methods were accurate with low noise levels, although the reconstruction accuracy of TGSVD was more sensitive to noise than that of TSVD regularization.