李颖^1,2，崔阳阳²，闫伟²，赵营鸽²
AuthorsHTML:李颖^1,2，崔阳阳²，闫伟²，赵营鸽²
AuthorsListE:Li Ying^{1, 2}，Cui Yangyang²，Yan Wei²，Zhao Yingge²
AuthorsHTMLE:Li Ying^{1, 2}，Cui Yangyang²，Yan Wei²，Zhao Yingge²
Unit:1. 天津市生物电工与智能健康重点实验室(河北工业大学)，天津 300130；
2. 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
Unit_EngLish:1. Tianjin Key Laboratory of Bioelectromagnetic Technology and Intelligent Health，Hebei University of Technology，Tianjin 300130，China；
2. State Key Laboratory of Reliability and Intelligence of Electrical Equipment，Hebei University of Technology，Tianjin 300130，China
Abstract_Chinese:在电阻抗成像技术(EIT)中，介质电导率分布的不确定性会对正问题的计算结果产生影响，进而影响图像重构的准确性，因而，研究电导率变化对电阻抗成像不确定性的影响具有重要的意义．本文以4层同心圆头模型作为研究对象，假定4层的电导率分布不是固定数值，分别利用蒙特卡洛法(MCS)和非干涉混沌多项式展开(NIPCE)法对电阻抗成像正问题结果进行不确定性分析，以获得边界电压的概率分布，并对两种方法计算结果的精度和效率进行了比较．当采用MCS方法时，假定电导率分布服从均匀分布或正态分布，当样本数达到1×次时达到收敛，获得了足够的精度，边界电压的概率分布曲线趋于正态分布．采用NIPCE方法，假定电导率分布服从均匀分布，获得的概率分布函数曲线随着多项式展开阶数的增大而逐渐接近MCS方法获得概率分布曲线，边界电压的均值和标准差也逐渐接近MCS方法获得的均值与标准差，精度明显改善．当展开阶数为4阶时，计算结果与MCS方法非常接近．由研究结果可以看出，MCS方法和NIPCE方法均可得到精度较高的边界电压概率分布，MCS方法具有更高的精确性，但计算量过大，而NIPCE方法不仅具有较高的计算精度，同时具有很高的计算效率．
Abstract_English:In electrical impedance tomography(EIT)，the uncertainty of the dielectric conductivity distribution will affect the calculation results of the EIT forward problem and the accuracy of image reconstruction. Therefore，it is of significance to analyze the influence of conductivity change on the uncertainty of EIT. In this study，the four-layer concentric circular head model is selected as the research object. Given that the conductivity variables of the four layers are not fixed，Monte Carlo simulation(MCS)and nonintrusive polynomial chaos expansion(NIPCE)are used to analyze the uncertainty of the EIT forward problem to obtain the probability distribution of the boundary voltage，and the accuracy and efficiency of the two methods are compared. When the MCS method is used，the conductivity distribution is assumed to follow a uniform or normal distribution. When the sample number reaches 10000，convergence is achieved and sufficient accuracy is obtained. The probability distribution curve of the boundary voltage tends to follow a normal distribution. When the NIPCE method is used，the conductivity distribution is assumed to follow a uniform distribution. With the increase in polynomial expansion order，the curve of the probability distribution function obtained by the NIPCE method is relatively close to that obtained by the MCS method，the mean and standard deviation of the boundary voltage obtained by the NIPCE method are also relatively close to that obtained by the MCS method，and the accuracy is considerably improved. When the expansion order is 4，the results of the NIPCE method are relatively close to that of the MCS method. The research results show that both MCS and NIPCE methods can determine the probability distribution of the boundary voltage with high accuracy. The MCS method has a higher accuracy but a large calculation amount，whereas the NIPCE method has a high calculation accuracy as well as a high calculation efficiency.
Keyword_Chinese:电阻抗成像；不确定性量化；蒙特卡洛法；多项式展开；随机响应面法；随机Galerkin投影法
Keywords_English:electrical impedance tomography；uncertainty quantification；Monte Carlo simulation；polynomial chaos method；stochastic response surface method；stochastic Galerkin projection

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