改进的稀疏网格配点法对EIT电导率分布的不确定性量化

针对电阻抗成像（EIT）研究中电导率分布的不确定性问题，提出基于灵敏度分析的改进稀疏网格配点法以量化不确定性.以4层同心圆头模型为算例，采用基于方差的全局灵敏度分析法对其进行分析，发现各层电导率的变化对输出电位的影响程度各不相同.考虑模型中各维输入变量对输出结果不同程度的影响，改进传统稀疏网格配点法.改进方法对各维输入变量配置不同的精度水平，将EIT模型的隐式表达式转化为显式表达式，构造出高精度的替代模型.与蒙特卡洛（MC）法、混沌多项式展开（PCE）法和传统稀疏网格配点法相比，改进方法能够以更少的计算成本获得较高精度的量化结果.仿真结果验证了所提改进方法的高效性.

Improved sparse grid collocation method for uncertainty quantification of EIT conductivity distribution

An improved sparse grid collocation method based on sensitivity analysis was proposed to quantify the uncertainty, aiming at the uncertainty problem of conductivity distribution in electrical impedance tomography (EIT) research. The four-layer concentric circular head model was taken for simulation, and the variance-based global sensitivity analysis method was used to analyze the model. The results of sensitivity analysis show that the conductivity changes of each layer have different effects on the output potential. Furthermore, the influence of the input variables of each dimension in the model on the output results were considered, the traditional sparse grid collocation method was improved. The input variables of each dimension were assigned with different accuracy levels in the improved method, the implicit expression of the EIT model was transformed into an explicit expression and the high-precision substitute model was constructed. Compared with the Monte Carlo (MC) method, polynomial chaos expansion (PCE) method and traditional sparse grid collocation method, the results show that the improved method can obtain the more accurate quantified results with less calculation cost. The simulation results were given to verify the efficiency of the proposed improved method.