Current distribution reconstruction in switching arcs by means of regularization based on GSVD

Figures & data

Figure 1. The structure of the AMF vacuum interrupter (VI) and the magnetic sampling points.

Figure 2. Discrete mesh of the current flow region.

Figure 3. The calculated x,y,z-component magnetic field data with the noise r = 10⁻² via forward analysis.

Figure 4. Flowchart of the GSVD regularization.

Figure 5. Comparison of TSVD and TGSVD solutions for problem (12), the abscissa represents the dimension of the solution. The noise level r = 10⁻² is applied: (a) the first 4 TSVD solutions; (b) the first 4 TGSVD solutions when L = L₁; (c) the first 4 TGSVD solutions when L = L₂.

Figure 6. Current distribution of arc column section reconstructed by TGSVD with different regularization operators (noise level r = 10⁻²): (a) reference distribution; (b) TSVD; (c) TGSVD (L₁ operator); (d) TGSVD (L₂ operator).

Table 1. SNR and δ_r of reconstruction results of TGSVD and TSVD (noise level r = 10⁻²).

Regularization operator	SNR	δr
In	21.25	8.66%
L1	36.43	1.51%
L2	49.51	0.33%

Figure 7. Current distribution of arc column section reconstructed by Tikhonov regularization (noise level r = 10⁻²): (a) the reference distribution; (b) standard-form Tikhonov (L = I_n); (c) general-form (L = L₁).

Table 2. SNR and δ_r of Tikhonov regularization (noise level r = 10⁻²).

Regularization operator	SNR	δr
In	21.1864	8.72%
L1	39.0355	1.12%
L2	39.1370	1.10%

Table 3. Regularization parameter λ and corresponding relative error δ_r of three parameter-choice methods: GCV, QO and NCP.

Regularization operator	Parameter selection method	λ	SNR	δr
In	GCV	0.1408	21.1864	8.72%
In	QO	5.3663	19.8095	10.22%
In	NCP	2.1118	19.9681	10.04%
L1	GCV	14.4738	39.0355	1.12%
L1	QO	35.7915	34.4192	1.90%
L1	NCP	17.1821	38.8931	1.14%
L2	GCV	2.2391 × 10^3	39.1370	1.10%
L2	QO	3.9290 × 10^4	54.6635	0.18%
L2	NCP	100.5347	26.9391	4.50%

Figure 8. SNR versus noise level with three parameter selection criterions for different regularization operators: (a) standard-form Tikhonov, L = I_n; (b) general-form, L = L₁; (c) general-form, L = L₂.