电阻层析成像有限元模型优化

Optimization of Finite Element Model for Electrical Resistance Tomography

为了提高电阻层析成像正问题计算精度,以有限元模型次最外层半径为变量,以敏感场均匀分布时模型均方根值的倒数为适应度函数,利用求解低维多峰值函数优化问题的改进遗传算法,优化模拟敏感场内电流线分布密度与分布形式的新型拓扑结构有限元模型,最后以各峰值点对应的中心流模型均方根值为误差函数,选择新型拓扑结构有限元模型次最外层半径的最优值.仿真实验结果表明,相同实验条件下,相比优化前新型拓扑结构有限元模型、传统按等间隔原理剖分的有限元模型及其改进模型,优化后有限元模型在敏感场均匀分布时模型均方根值分别降低了32.002 5%、83.395 8%和44.760 5%,有效提高了电阻层析成像正问题计算精度与图像重建质量.

Aiming to improve the accuracy of solving the forward problem in electrical resistance tomography （ERT）,the new topological finite element model was optimized in this paper. Using the radius of the second outer-most layer of the model as a variable,and the reciprocal of the root mean square value of a homogeneous sensitive field distribution as a fitness function,the improved genetic algorithm for solving low-dimension multi-peak function optimization problem was adopted to optimize the new topological finite element model which simulated the current line density and distribution of the sensitive field. Finally,the root mean square value of the core flow model corre-sponding to each peak point was used as an error function to determine the optimal value of the radius of the second outermost layer of the model. Simulation results demonstrate that,compared to the unoptimized topological finite element model,the conventional finite element model based on uniformly-spaced dissection and its modified version,the optimized model reduce the root mean square value of a homogeneous sensitive field distribution by 32.002 5%,83.395 8%and 44.760 5%,effectively improves both the accuracy of solving the forward problem and the quality of image reconstruction under the same experimental conditions.