基于正向投影面积法的层析粒子图像测速权重系数计算方法

Calculation Method of Weight Coefficient for Tomographic PIV Based on FPA

三维重建是层析粒子图像测速(PIV)中重要的一步,重建过程中的权重系数计算通常较为繁琐。基于此,提出一种层析PIV快速权重计算方法——正向投影面积(FPA)法,即将离散体素投影在相应像元上的面积作为权重系数计算的方法。首先,基于针孔相机模型构建三维空间内粒子多视角投影成像仿真程序,生成仿真图片用于方法分析与验证;其次,将FPA方法结合目前主流重建算法开展三维重建精度和耗时分析。结果表明,当用于本研究所述测量区域重建时,相比于传统后向方法与亚网格法权重系数计算方法,FPA法的权重矩阵元素个数分别降低了大约3个和1个数量级,计算时间分别减少了97%与85%,相应地降低了计算机的内存占用,且FPA法与传统后向方法所计算的权重矩阵的平均相似度高于0.9974。在常用实验粒子数分数(pppp=0.05)下,该方法结合目前主流重建算法的重建精度可达0.8以上。同时基于仿真图片分析了相机最佳采集角度以及实验相机噪声对重建结果的影响,结果表明,在实验噪声条件下重建结果仍然满足三维流场重建的要求。

Objective Recently,tomographic particle image velocimetry(TPIV)has been widely employed in the measurement of the flow field around a cylinder,turbulent boundary layer,flame field,and other flow fields since it is highly accurate,multipoint,threedimensional,and instantaneous.The principle of TPIV is to reconstruct the threedimensional scattering intensity distribution of particles in the flow field at the adjacent time and combine the threedimensional crosscorrelation algorithm to obtain its instantaneous flow field.3D particle field reconstruction is the basis of TPIV and the premise of obtaining an accurate 3D flow field.Therefore,it is necessary to develop fast and highprecision 3D particle field reconstruction algorithms.The improvement of the reconstruction algorithm includes two aspects.The first is to improve the reconstruction accuracy,which is the similarity between the reconstructed particle field and the actual particle field,thus affecting the accuracy of the flow field.The second is to shorten the reconstruction time,since the reconstruction process needs to calculate the weight coefficient that is the intensity contribution value of spatial voxels to pixels,and iteration is adopted to update the intensity value of voxels.Thus,the reconstruction process often takes a lot of time,which is the biggest bottleneck in the TPIV application.Therefore,the calculation method of the weight coefficient plays an important role in reconstruction accuracy and reconstruction time.Methods According to the imaging principle,the line of sight received by a pixel is a spatial volume,so only some of the voxels that contribute to the intensity of a certain pixel can be fully projected into the pixel.The partially projected voxels involve the weight coefficient calculation,which is related to the setting of the camera's internal and external parameters and the spatial volume.The traditional method often employs back projection to calculate the weight coefficient.However,due to a large number of divided spatial voxels and pixels,the order of the weight coefficient is usually large.Additionally,the back projection method not only needs to calculate each line of sight equation but also needs to calculate the number and volume of voxels intersected with the line of sight,thereby resulting in a huge amount of the weight matrix calculation.Therefore,reducing the calculation time of the weight matrix is the key to improving the reconstruction speed.In this paper,the area of voxels projected on the corresponding pixel is calculated as the weight coefficient,and a forward projection method(FPA)is proposed.Results and Discussions Firstly,a multiview projection imaging simulation program based on the pinhole camera model for particles in 3D space is constructed,and artificial images are generated for analysis and verification.Secondly,FPA is combined with the current mainstream reconstruction algorithms(such as MART,MLOS+MART,and MLOS+SMART)to analyze reconstruction accuracy and time consumption.The results show that when FPA is employed for the reconstruction volume described in this paper,compared with the traditional backward method and the subgrid method,the number of FPA weight matrix elements is reduced by about three and one orders of magnitude respectively,thus reducing calculation time and computer memory occupation.When the commonly experimental particle concentration pppp(particle per pixel)is 0.05,the reconstruction accuracy of this method combined with the current mainstream reconstruction algorithm will be higher than 0.8.In addition,based on the artificial images,the influence of the best camera acquisition angle and the experimental camera noise on the reconstruction results is analyzed,which proves that the reconstruction accuracy still meets the requirements of threedimensional flow field reconstruction under the experimental noise conditions.Conclusions A forward projection weight calculation method(FPA)based on single voxel is proposed in this paper.A particle projection imaging program in 3D space is constructed to verify the correctness of the proposed method.Taking the simulated imaging image as the reconstruction input,it is shown that the matrix elements of FPA combined with the MLOS algorithm can be reduced by about three and one orders of magnitude respectively compared with the traditional backward method and TSM,and the computing time can be reduced by 97%and 85%respectively,greatly reducing the computer memory consumption.Through similarity analysis,the average similarity of the weight matrix calculated by FPA and the traditional backward method is higher than 0.9974,which proves the reliability of FPA.Comparison between the reconstruction results of FPA and those of predecessors in the simplified twodimensional plane shows that the reconstruction results of the FPA method combined with MART and MLOS+SMART only lose 0.02 reconstruction accuracy.Additionally,FPA together with MART and MLOS+SMART algorithms has good reconstruction results,and the reconstruction accuracy can reach more than 0.8 under the common experimental particle concentration(pppp=0.05).By comparison,MLOS+FPA+MART has higher reconstruction accuracy and faster reconstruction speed,which is suitable for 3D flow field reconstruction.After the experimental noise is added to the imaging process,MLOS+FPA+MART is employed for reconstruction.The results show that the reconstruction accuracy after adding noise is still higher than 0.75,indicating that FPA has good robustness against noise.The analysis of the crosssymmetry camera layout in 3D space shows that the best acquisition angle of CCD2 in the crosssymmetry type is 15°–45°and 10°–40°respectively.