The Application of Univariate Dimension Reduction Method Based on Mean Point Expansion in the Research of Electrical Impedance Tomography Uncertainty Quantification
Zhao Yingge1,2, Li Ying1,2, Wang Lingyue1,2, Cui Yangyang1, Wang Guanxiong1
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300130 China; 2. Tianjin Key Laboratory of Bioelectromagnetic Technology and Intelligent Health Hebei University of Technology Tianjin 300130 China
Abstract：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.
赵营鸽, 李颖, 王灵月, 崔阳阳, 王冠雄. 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[J]. 电工技术学报, 2021, 36(18): 3776-3786.
Zhao Yingge, Li Ying, Wang Lingyue, Cui Yangyang, Wang Guanxiong. The Application of Univariate Dimension Reduction Method Based on Mean Point Expansion in the Research of Electrical Impedance Tomography Uncertainty Quantification. Transactions of China Electrotechnical Society, 2021, 36(18): 3776-3786.
[1] Brodland G W.How computational models can help unlock biological systems[J]. Seminars in Cell & Developmental Biology, 2015, 47(48): 62-73. [2] 颜湘武, 徐韵, 李若瑾, 等. 基于模型预测控制含可再生分布式电源参与调控的配电网多时间尺度无功动态优化[J]. 电工技术学报, 2019, 34(10): 2022-2037. Yan Xiangwu, Xu Yun, Li Ruojin, et al.Multi-time scale reactive power optimization of distribution grid based on model predictive control and including RDG regulation[J]. Transactions of China Electrotechnical Society, 2019, 34(10): 2022-2037. [3] 汤涛, 周涛. 不确定性量化的高精度数值方法和理论献给林群教授80华诞[J]. 中国科学: 数学, 2015, 45(7): 891-928. Tang Tao, Zhou Tao.Recent developments in high order numerical methods for uncertainty quanti-fication[J]. Scientia Sinica: Mathematica, 2015, 45(7): 891-928. [4] Feinberg J, Langtangen H P.Chaospy: an open source tool for designing methods of uncertainty quanti-fication[J]. Journal of Computational Science, 2015, 11(1): 46-57. [5] Tennoe S, Halnes G, Einevoll G T.Uncertainpy: a Python toolbox for uncertainty quantification and sensitivity analysis in computational neuroscience[J]. Frontiers in Neuroinformatics, 2018, 12(1): 49-77. [6] 方斯顿, 程浩忠, 徐国栋, 等. 基于Nataf变换含相关性的扩展准蒙特卡洛随机潮流方法[J]. 电工技术学报, 2017, 32(2): 255-263. Fang Sidun, Cheng Haozhong, Xu Guodong, et al.A Nataf transformation based on extended quasi Monte Carlo simulation method for solving probabilistic load flow problems with correlated random variables[J]. Transactions of China Electrotechnical Society, 2017, 32(2): 255-263. [7] 于全毅, 刘长英, 吴定超, 等. 基于广义混沌多项式法的多导体传输线辐射敏感度分析方法[J]. 电工技术学报, 2020, 35(17): 3591-3600. Yu Quanyi, Liu Changying, Wu Dingchao, et al.Radiation sensitivity analysis of multiconductor trans-mission Lines based on generalized polynomial chaos method[J]. Transactions of China Electrotechnical Society, 2020, 35(17): 3591-3600. [8] 谢仕炜, 胡志坚, 王珏莹, 等. 基于不确定随机网络理论的主动配电网多目标规划模型及其求解方法[J]. 电工技术学报, 2019, 34(5): 1038-1054. Xie Shiwei, Hu Zhijian, Wang Yuying, et al.A multi-objective planning model of active distribution network based on uncertain random network theory and its solution algorithm[J]. Transactions of China Electrotechnical Society, 2019, 34(5): 1038-1054. [9] 李幸芝, 韩蓓, 李国杰, 等. 考虑非高斯耦合不确定性的交直流配电网两阶段概率状态估计[J]. 电工技术学报, 2020, 35(23): 4949-4960. Li Xingzhi, Han Bei, Li Guojie, et al.Two-stage probabilistic state estimation for AC/DC distribution network considering non-Gaussian coupling uncer-tainties[J]. Transactions of China Electrotechnical Society, 2020, 35(23): 4949-4960. [10] Zhang Xinlei, Xiao Heng, Gomez T, et al.Evaluation of ensemble methods for quantifying uncertainties in steady-state CFD applications with small ensemble sizes[J]. Computers and Fluids, 2020, 203(1): 104530. [11] Chen Yangli, Ma Weimin.Uncertainty quantification for trace simulation of fix-II no.5052 test[J]. Annals of Nuclear Energy, 2020, 143(1): 107490. [12] Saturnino G B, Thielscher A, Madsen K H, et al.A principled approach to conductivity uncertainty analysis in electric field calculations[J]. Neuroimage, 2019, 188(1): 821-834. [13] 甘源, 白锐, 张琪. 基于场-路耦合的干式空心电抗器稳态电磁场及电动力分析[J]. 电力系统保护与控制, 2019, 47(21): 144-149. Gan Yuan, Bai Rui, Zhang Qi.Steady-state electro-magnetic field and electrodynamic analysis of dry-type air-core reactor based on field-circuit coupling[J]. Power System Protection and Control, 2019, 47(21): 144-149. [14] Weise K, Rienzo L D, Brauer H, et al.Uncertainty analysis in transcranial magnetic stimulation using nonin-trusive polynomial chaos expansion[J]. IEEE Transactions on Magnetics, 2015, 51(7): 1-8. [15] Codecasa L, Rienzo L D, Weise K, et al.Fast MOR-based approach to uncertainty quantification in transcranial magnetic stimulation[J]. IEEE Transactions on Magnetics, 2016, 52(3): 1-4. [16] Codecasa L, Rienzo L D.MOR-based approach to uncertainty quantification in electrokinetics with correlated random material parameters[J]. IEEE Transactions on Magnetics, 2017, 53(6): 1-4. [17] Codecasa L, Weise K, Rienzo L D, et al.MOR-based uncertainty quantification in transcranial magnetic stimulation[J]. Model Reduction of Parametrized Systems, 2017, 17(1): 421-437. [18] Torchio R, Rienzo L D, Codecasa L.Stochastic PEEC method based on polynomial chaos expansion[J]. IEEE Transactions on Magnetics, 2019, 55(6): 1-4. [19] Rahman S, Xu Heqin.A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics[J]. Probabilistic Engineering Mechanics, 2004, 19(4): 393-408. [20] Xu Heqin, Rahman S.A generalized dimension-reduction method for multidimensional integration in stochastic mechanics[J]. International Journal for Numerical Methods in Engineering, 2004, 61(12): 1992-2019. [21] Xu Heqin, Rahman S.Decomposition methods for structural reliability analysis[J]. Probabilistic Engin-eering Mechanics, 2005, 20(3): 239-250. [22] 徐灿华, 董秀珍. 生物电阻抗断层成像技术及其临床研究进[J]. 高电压技术, 2014, 40(12): 3738-3745. Xu Canhua, Dong Xiuzhen.Advancements in electrical impedance tomography and its clinical applications[J]. High Voltage Engineering, 2014, 40(12): 3738-3745. [23] 周润奭, 隆云, 李尊柱, 等. 重视电阻抗成像技术在重症急性呼吸窘迫综合征患者肺部护理中的应用[J]. 中华急危重症护理杂志, 2020, 1(6): 536-539. Zhou Runshi, Long Yun, Li Zunzhu, et al.Attention to the application of electrical impedance imaging in the pulmonary care of patients with severe acute respiratory distress syndrome[J]. Chinese Journal of Emergency and Critical Care Nursing, 2020, 1(6): 536-539. [24] Gabriel S, Lau R W, Gabriel C.The dielectric properties of biological tissues Ⅱ: measurements in the frequency range 10Hz to 20GHz[J]. Physics in Medicine and Biology, 1996, 41(11): 2251-2269. [25] Gabriel C, Peyman A, Grant E H.Electrical con-ductivity of tissue at frequencies below 1MHz[J]. Physics in Medicine and Biology, 2009, 54(16): 4863-4878. [26] 杨宁, 张杰, 代萌, 等. 具有真实颅骨分层解剖结构与电阻率分布的电阻抗成像头部物理模型构建[J]. 医疗卫生装备, 2018, 39(4): 15-19. Yang Ning, Zhang Jie, Dai Meng, et al.Novel human-head phantom with realistic skull anatomy and resistivity distribution[J]. Chinese Medical Equipment Journal, 2018, 39(4): 15-19. [27] Suksawang S, Niamsri K, Ouypornkochagorn T.Scalp voltage response to conductivity changes in the brain in the application of electrical impedance tomography (EIT)[C]//Proceedings of the 2018 15th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), Chiang Rai, Thailand, 2018: 223-236. [28] 李颖, 崔阳阳, 闫伟, 等. 电导率分布变化影响EIT正问题的不确定性量化方法[J]. 天津大学学报(自然科学与工程技术版), 2021, 54(1): 51-60. Li Ying, Cui Yangyang, Yan Wei, et al.Uncertainty quantization methods of the influence of the change of conductivity distribution on the EIT forward problem[J]. Journal of Tianjin University (Science and Technology), 2021, 54(1): 51-60. [29] 陈志国, 邓忠民, 毕司峰. 基于Monte Carlo法的结构动力学模型确认[J]. 振动与冲击, 2013, 32(16): 76-81. Chen Zhiguo, Deng Zhongmin, Bi Sifeng.Structural dynamics model validation based on Monte Carlo method[J]. Journal of Vibration and Shock, 2013, 32(16): 76-81. [30] Tripathy R K, Bilionis I.Deep U Q: learning deep neural network surrogate models for high dimensional uncertainty quantification[J]. Journal of Computa-tional Physics, 2018, 375(1): 565-588. [31] 李颖. 脑电逆问题求解的数值计算方法研究[D]. 天津: 河北工业大学, 2003. [32] Anusha V, Sudha B.Influence of skewing design for reduction of force ripples in DSL-SynRM using 3D FEA[J]. CES Transactions on Electrical Machines and Systems, 2019, 3(4): 397-402. [33] 徐征, 何为, 何传红, 等. 头部电阻抗成像正问题的解析解研究[J]. 计算物理, 2010, 27(1): 107-114. Xu Zheng, He Wei, He Chuanhong, et al.Analytical solution of forward problem in brain electrical impedance tomography[J]. Chinese Journal of Com-putational Physics, 2010, 27(1): 107-114. [34] 熊芬芬, 杨树兴, 刘宇. 工程概率不确定性分析方法[M]. 北京: 科学出版社, 2015.
2021, Vol. 36 
