基于均值点展开的单变元降维法在EIT不确定性量化研究中的应用  

The Application of Univariate Dimension Reduction Method Based on Mean Point Expansion in the Research of Electrical Impedance Tomography Uncertainty Quantification

作　　者：赵营鸽 李颖[1,2] 王灵月 崔阳阳 王冠雄 Zhao Yingge;Li Ying;Wang Lingyue;Cui Yangyang;Wang Guanxiong(State Key Laboratory of Reliability and Intelligence of Electrical Equipment,Hebei University of Technology,Tianjin,300130,China;Tianjin Key Laboratory of Bioelectromagnetic Technology and Intelligent Health,Hebei University of Technology,Tianjin,300130,China)

机构地区：[1]省部共建电工装备可靠性与智能化国家重点实验室(河北工业大学),天津300130 [2]河北工业大学天津市生物电工与智能健康重点实验室,天津300130

出　　处：《电工技术学报》2021年第18期3776-3786,共11页Transactions of China Electrotechnical Society

基　　金：河北省自然科学基金资助项目(E2015202050)。

摘　　要：在电阻抗成像(EIT)技术中,介质参数的不确定性会对正问题计算产生影响,进而影响图像重构,因而,对EIT介质参数不确定性量化的研究具有重要的意义。采用四层同心圆模型和二维圆模型作为仿真算例对EIT正问题进行研究,将电导率分布参数作为无相互作用的随机输入变量,使其服从随机均匀分布,基于均值点展开的单变元降维法(UDRM)计算得到边界电极电压的均值、标准差和概率分布等相关统计信息,分析电导率的不确定性对模型输出边界测量电压的影响,并与蒙特卡罗模拟(MCS)法、混沌多项式展开(PCE)法仿真结果进行比较。结果表明,UDRM能够准确高效地处理低维不确定性问题,且在处理高维不确定性问题时能有效缓解“维数灾难”问题。In electrical impedance tomography(EIT),the uncertainty of medium parameters will affect the calculation of the forward problem and then affect the image reconstruction.Therefore,it is of great significance to study the uncertainty quantification of EIT medium parameters.In this paper,the four-layer concentric circle model and the two-dimensional circle model were used as simulation examples to study the EIT forward problem.The conductivity distribution parameters were taken as non-interactive random input variables that subject to random uniform distribution.The univariate dimension reduction method(UDRM)based on the mean-point expansion was used to calculate the mean value,standard deviation,probability distribution and other relevant statistical information of voltage distribution on boundary electrodes,and the influence of the uncertainty of conductivity on the output boundary voltage distribution was analyzed.The results were compared with the results of Monte Carlo simulation(MCS)method and polynomial chaos expansion(PCE)method.It is shown that UDRM can deal with low-dimensional uncertainty problems accurately and efficiently,and can effectively alleviate the“curse of dimensionality”problem when dealing with high-dimensional uncertainty problems.

关 键 词：电阻抗成像 不确定性量化 单变元降维法 蒙特卡罗模拟 混沌多项式展开 

分 类 号：TM470.4011[电气工程—电器]