基于自适应Kalman滤波的平面阵列电容成像  

Planar array capacitance imaging based on adaptive Kalman filter

作　　者：张玉燕[1,2] 殷东哲 温银堂[1,2] 罗小元 Zhang Yu-Yan;Yin Dong-Zhe;Wen Yin-Tang;Luo Xiao-Yuan(School of Electrical Engineering,Yanshan University,Qinhuangdao 066004,China;Hebei Province Key Laboratory of Measurement Technology and Instrumentation,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学电气工程学院,秦皇岛066004 [2]燕山大学,测试计量技术及仪器河北省重点实验室,秦皇岛066004

出　　处：《物理学报》2021年第11期299-307,共9页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:61573302);河北省自然科学基金(批准号:E2017203240)资助的课题。

摘　　要：针对平面阵列电极边缘电场和病态特性严重影响电容图像重建质量的问题,提出了一种改进的自适应Kalman滤波图像重建算法来同时减小电容及介电常数矩阵的噪声,在构建引入噪声的平面阵列电容成像状态模型的基础上,利用极大似然准则来对介电常数矩阵噪声方差阵进行在线估计及实时修正,并且通过对系统误差协方差矩阵进行动态加权的方法来对此算法的收敛速度进行优化.通过一种复合材料结构件进行缺陷检测实验,结果表明与LBP, TR正则化及Kalman滤波算法相比,自适应Kalman滤波算法图像误差最高可降低约20%,图像相关系数高达0.79,收敛速度提升约15%,说明自适应Kalman滤波算法对提升重建图像质量的有效性.此研究对提高平面阵列电容成像的量化精度有着重要意义.Planar array capacitance imaging system has the characteristics of uneven distribution of sensitive field,serious ill posed problem and measurement data vulnerable to external interference,and these characteristics will make the image artifacts particularly serious,affect the quality of the reconstructed image,and even determine the number of defects with difficulty.In order to solve the problem that the edge electric field and ill conditioned characteristics of planar array electrode seriously affect the quality of capacitance image reconstruction,an improved image reconstruction algorithm based on adaptive Kalman filter is proposed to reduce the noise of capacitance data and dielectric constant matrix.On the basis of constructing the state model of planar array capacitance imaging with noise,the maximum likelihood criterion is used to estimate and modify the noise variance matrix of dielectric constant matrix on-line,and the noise variance matrix of dielectric constant matrix is modified in real time.In order to restrain the filtering divergence and accelerate the convergence speed,different weighting coefficients are provided for the error covariance matrix with time going by.Through designing four kinds of samples from simple to complex structure,the defect detection experiment of composite structure is carried out.The experimental results show that compared with linear back projection(LBP),Tikhonov regularization(TR)algorithm and Kalman filtering algorithm,the image error of adaptive Kalman filtering algorithm can be reduced by about 20%,the image correlation coefficient is as high as 0.79 and the convergence speed can be improved by about 15%,the image artifacts of the four samples are greatly reduced.The experimental data show that the proposed adaptive Kalman filter image reconstruction algorithm can effectively reduce the noise of capacitance and permittivity matrix,enhance the stability of planar array capacitance imaging,and reduce the image error,so that the quality of the image can be significantly i

关 键 词：平面阵列电极 电容图像重建 自适应Kalman滤波 复合材料 极大似然准则 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] TN713[自动化与计算机技术—计算机科学与技术]