迭代正则化方法求解电介质中空间电荷分布

首先介绍了迭代正则化方法的理论基础,建立了含有空间电荷密度分布的Fredholm第一类积分方程的反卷积算法,利用数值实验研究了加性高斯白噪声对迭代反卷积算法的影响,以及迭代停止标准对非适定问题的数值解的影响,最后使用该方法求解电介质样品中的空间电荷分布.结果表明,在无噪或者低噪环境下,反卷积算法能够非常好地计算出非适定问题的解.当噪声影响增大,信噪比降低时,反卷积的计算结果受到明显的影响.迭代停止标准对数值解的计算精度起着明显的作用.对实际测量数据进行处理表明,迭代正则化反卷积算法能够计算出固体电介质中的空间电荷分布.

An Iterative Regularization Method for the Space Charge Distribution in Dielectrics

The application of iterative regularization deconvolution to solve an ill-posed problem is discussed. Firstly,the theoretical foundation of iterative regularization is introduced, and a new Fredholm integral equation of the first kind including space charge distribution is derived.The effect of additive Gaussian white noise for iterative deconvolution algorithm, and the effect of iterative convergence criterion for the numerical solution are studied, respectively. It is shown that the solution of ill-posed problems could be obtained with iterative deconvolution algorithm under lower level noise circumstance. It also indicates that the precision of numerical solution is influenced by the iterative convergence criterion. Finally,the original experimental data are dealt with and the real space charge distribution in dielectrics is obtained.