热脉冲法数据处理的反问题求解研究

应用热脉冲法测量聚合物薄膜电介质内空间电荷分布的数据分析过程涉及第一类Fredholm积分方程,过往先求解电场分布后微分的传统做法,会使反问题求解的不适定性带来的误差进一步放大。该文提出一种用于热脉冲法数据分析中反问题求解的直接计算空间电荷分布方法。结合一维热传导方程,推导得到了能够直接求解获取空间电荷分布的热响应电流方程。以Tikhonov正则化与尺度变换法2种数值求解算法为例,研究了不同信噪比对热脉冲法测量方法中直接计算电荷分布结果的影响,并讨论了2种数值算法直接进行空间电荷分布计算的优缺点。仿真结果表明,应用2种数值方法对含有一定噪声的数据处理时,直接计算空间电荷分布的方式相较于传统对电场分布微分的方式而言,能够很好地克服第一类Fredholm积分方程的不适定性,使解分布曲线中的振荡减少,且对仿真电流信号的噪声敏感程度更低,能更好地契合预设分布曲线,提高了空间电荷计算结果的准确性。

Research on Inverse Problem Solution for Thermal Pulse Method Data Analysis

Data analysis for thermal pulse method(TPM) applied to space charge distribution measurement of polymer dielectric film involves the Fredholm integral equation of the first kind. Complying with traditional way to extract space charge distribution by differentiating electric field may aggravate the calculation error arisen from the ill condition of inverse problem solution. A novel way to directly calculate space charge distribution by TPM was proposed in this paper. Combined with the one-dimension heat conduction equation, thermal response current integral equation with the direct solution target of space charge distribution was deduced. Based on the two numerical algorithms, Tikhonov regularization and scale transformation method(ST), several numerical examples were utilized to analyze the impact of the thermal response current with various signal-to-noise ratios(SNR) on retrieved space charge distribution results. The merits and demerits of the two applied numerical algorithms for calculating space charge profiles were also discussed. The results demonstrate that the proposed way, according to several examples of the two algorithms, can overcome the ill condition of the Fredholm integral equation of the first kind and improve the calculation accuracy of space charge distribution with very few unexpected oscillations and low sensitive to SNR of the original current.