基于改进半阈值算法的电容层析成像滑油监测方法研究

Monitoring Method of Lubricating Oil Based on Improvement Semi-Threshold Algorithm of Electrical Capacitance Tomography

关键词:  滑油监测  电容层析成像（ECT）  稀疏正则化  L_1/2正则化  L₂范数  半阈值迭代算法

Key words:  Oil monitoring  Electrical capacitance tomography  Sparse regularization  L_1/2 regularization  L₂ norm  Semi-threshold iterative algorithm

摘要:

针对航空滑油检测过程中电容层析成像（Electrical Capacitance Tomography，ECT）存在的病态性和欠定性问题，将稀疏正则化中基于L_1/2正则化的半阈值迭代算法应用到ECT图像重建，加入L₂范数的惩罚项，构造新的泛函模型，并在迭代过程中设计一种新的约束项以优化解向量。仿真实验采用Comsol 5.3搭建系统模型，Matlab 2014a处理采集数据。实验结果表明，与Landweber迭代算法相比，改进算法成像误差降低37.33%，相关系数提升33.67%；与半阈值迭代算法相比，改进算法成像误差和相关系数分别降低12.31%和提升11.86%，图像误差降低至0.24，相关系数提升至0.92，且成像时间依然保持在0.06s。实际滑油监测的实验系统采用现场可编程门阵列（Field Programmable Gate Array，FPGA）直接数字频率生成模块生成数字量的正弦激励信号，通过D/A转化为正负交流信号对测量电极进行激励。实验结果表明，基于ECT系统的改进半阈值迭代算法可以满足航空发动机滑油监测的实时性和准确性的要求。

Abstract:

Aiming at the ill-conditioned and under deterministic problems of capacitance tomography in the process of aviation oil monitoring， the semi-threshold iterative algorithm based on L_1/2 regularization of sparse regularization is applied to the electrical capacitance tomography（ECT） image reconstruction， and add L₂ norm as punishment item to construct a new functional model， and design a new kind of constraints in the iterative process to optimize the solution vector. In the simulation experiment， Comsol 5.3 is used to build the system model， and Matlab 2014a is used to process and collect data. Experimental results show that compared with the iterative algorithm of Landweber， the imaging error of the improved algorithm is reduced by 37.33% and the correlation coefficient increased by 33.67%. Compared with the semi-threshold iterative algorithm， the imaging error and correlation coefficient of the improved algorithm are reduced by 12.31% and increased by 11.86%， respectively. The image error is reduced to 0.24 and the correlation coefficient increased to 0.92， and the imaging time is still maintained at 0.06s. The actual experimental system for lubricating oil detection uses the Field Programmable Gate Array （FPGA） direct digital frequency generation module to generate sinusoidal excitation signals， which are converted into a positive and negative AC signal through the D/A converter to excite the measuring electrode. The experimental results show that the improved half-threshold iterative algorithm based on the ECT system can meet the real-time and accurate requirements of aero-engine lubricating oil monitoring.