An algorithm with low sensitivity to SNR in thermal-pulse data analysis

Thermal pulse method (TPM) is a powerful tool for probing space charge behavior in thin polymer films, whose data analysis involves the solution of the Fredholm integral equation of the first kind. This is an ill-conditioned problem with multiple solutions. The method based on regularization algorithms have been proved to be an effective way in analyzing thermal-pulse data, but the solution is sensitive to noise superposed on the data. In this paper, a method combined with the method of difference and regularization method is proposed and tested with simulated data containing different levels of white Gaussian noise. Good agreement between the calculated results and the assumed electric field distribution has been found. The results indicate that the presented thermal-pulse data analysis method is less sensitive to data perturbation.

I. Introduction

Polymer films are widely used as the dielectric material for high energy density capacitors, which is of great significance in the modern electronics and electric power system [1, 2]. Increasing electric breakdown field of the polymers is an effective way to improve the energy density for a given polymer. However, this could lead to charge injection and accumulation inside the polymer film and cause serious electric field distortion in the dielectric bulk, which may further lead to dielectric breakdown [3–5]. Hence, Space charge distribution inside dielectric material is a key indicator affecting its electrical life. Therefore, it is necessary to probe the space charge behavior to understand the effect of the discharge of trapped charge in the dielectric material. Thermal pulse method (TPM) has been proved to be an effective method to detect space charge and polarization distributions in thin polymer films [6, 7]. The thermal-pulse data analysis involves the Fredholm integral equation of the 1^st kind with multiple and very different solutions. A number of methods have been put forward to solve this problem, such as scale transformation (ST), regularization method and so on. Among these methods, the method based on regularization algorithms has succeeded in tackling the analysis of thermal-pulse data with a good reconstruction of electric field distribution over the whole sample [8]. However, the solution is very sensitive to the data perturbation which greatly limits its application. In this work, an algorithm based on the method of difference and regularization method is proposed in the analysis of the thermal pulse data. Besides, the sensitivity to noise and data analysis of the new method is tested with numerical examples.