论文标题
加权最小二乘（WLS）的密度积分，用于背景的Schlieren（BOS）
Weighted Least Squares (WLS) Density Integration for Background Oriented Schlieren (BOS)
论文作者
论文摘要
我们提出了一种针对背景定向的Schlieren（BOS）测量的改进的密度积分方法，该方法克服了常用的泊松求解器的噪声灵敏度。该方法通过求解过度确定的方程系统，采用加权最小二乘（WLS）优化密度梯度场的2D集成。根据密度梯度不确定性，将权重分配给网格点，以确保较不可靠的测量点对集成过程的影响较小。使用高斯密度场的合成图像分析表明，与最高噪声水平相比，WLS限制了随机误差的传播，并将其减少80％。与Poisson相比，使用WLS与火花等离子体放电诱导的流量的实验BOS测量值降低了30％，从而提高了BOS密度测量值的总体精度。
We propose an improved density integration methodology for Background Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. The method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge show a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.
