Abstract:

Precision measurement of flow field parameters in a supersonic separator is essential for optimizing its structure and performance. Electrical capacitance tomography (ECT) offers a non-invasive approach to accurately measure these parameters. The mathematical model for solving the inverse problem of ECT is mainly obtained by linearization approximation, which ignores the influence of nonlinearity and "soft field" effect on the image reconstruction. As a result, the image reconstruction is of poor quality when the dielectric constants of the media in the field differ significantly. Aiming at the problem, the mathematical model of the ECT inverse problem was modified by introducing the model derivation error. Then, based on the separable property of the objective function, a solution algorithm combining regularization and Split Bregman (RASB) was designed to solve the model error and the media to be reconstructed by cross iteration. The image reconstruction results of the RASB algorithm, Tikhonov regularization algorithm, L1 regularization algorithm and Landweber algorithm for several models using simulation and experimental data showed that the proposed method could reduce the error generated by the linearization approximation, and weaken the effect of noise on the image reconstruction. The RASB algorithm could reconstruct more accurate media distribution with fewer artifacts in the image, and the average correlation coefficient of the reconstructed images was 0.8964, which was higher than that of the Tikhonov regularization algorithm (0.8353), the L1 regularization algorithm (0.8496), and the Landweber algorithm (0.8681).

Key words: supersonic separator, electrical capacitance tomography, model derivation errors, regularization and Split Bregman, cross iteration

摘要：

超音速分离器内流场参数的准确测量对其结构与性能优化至关重要，电容层析成像（electrical capacitance tomography，ECT）能够实现非侵入式参数测量，其逆问题求解的数学模型主要通过线性化近似得到，忽略了非线性、“软场”效应等对结果的影响，使得当场域内介质分布的介电常数差异较大时，图像重建质量不高。针对上述问题，本文通过引入模型推导误差对ECT逆问题数学模型修正，在此基础上，根据目标函数的可分离特性，设计结合正则化与Split Bregman（RASB）的求解算法，分别对模型误差和待重构介质进行交叉迭代求解。最后通过仿真和实验手段对比分析了RASB算法、Tikhonov正则化算法、L1正则化算法和Landweber算法重建图像效果，结果表明所提算法RASB可以减小线性化近似产生的误差，削弱噪声对图像重建结果的影响，重构的介质分布更加准确，图像中伪影更少。RASB算法对几种模型重建图像的平均相关系数为0.8964，高于Tikhonov正则化算法的0.8353、L1正则化算法的0.8496和Landweber算法的0.8681。

关键词: 超音速分离器, 电容层析成像, 模型推导误差, 正则化与Split Bregman, 交叉迭代