基于分数阶Tikhonov正则化方法的电弧反演研究

doi:10.19595/j.cnki.1000-6753.tces.180015

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Abstract The switching apparatus with contact will inevitably produce arc when breaking the circuit. In this paper, a three-dimensional arc model of a straight contact system is constructed, that the arc is assumed to be a cluster of broken lines. Based on the Biot-Savart law, the magnetic distribution is measured in-plane around the arc through the forward analysis, thus the arc current density distribution is inversed according to the magnetic field. In order to improve the accuracy of current reconstruction, the Tikhonov regularization method is used to solve the ill-posed equations based on the electromagnetic inverse problem. Considering the approximate solution of the standard Tikhonov regularization method is too smooth because of the loss of the details of the reconstructed data due to the function of the filter operator, the fractional Tikhonov regularization method is adopted to improve the accuracy of the solution, and the Morozov discrepancy criterion is used to obtain the regularization parameter. The inversion result shows that by reducing the order of α can slow down the convergence speed of the filtering operator, which will increase the norm of the solution vector to approximate to the exact solution. Under the magnetic interference with a standard deviation of 0.001, the maximum relative error of arc inversion is 21.26% and the mean relative error is 8.99% compared with the preset values, which shows more accuracy than the standard Tikhonov method and truncated singular value decomposition, thus the inversion results can indicate the trend of arc distribution.

Key words： Arc inversion electromagnetic inverse problem fractional Tikhonov regularization Morozov discrepancy criterion

Received: 01 January 2018 Published: 10 January 2019

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TM561.1

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	Zhao Hongchen
	Liu Xiaoming
	Yang Yingxuan
	Chen Hai
	Yang Luyu

Cite this article:

Zhao Hongchen,Liu Xiaoming,Yang Yingxuan等. Research on Arc Inversion Based on Fractional Tikhonov Regularization Method[J]. Transactions of China Electrotechnical Society, 2019, 34(1): 84-91.

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https://dgjsxb.ces-transaction.com/EN/10.19595/j.cnki.1000-6753.tces.180015 OR https://dgjsxb.ces-transaction.com/EN/Y2019/V34/I1/84

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