Abstract A novel pressure reconstruction method is proposed to use the uncertainty information to improve the instantaneous pressure fields from velocity fields measured using particle image velocimetry (PIV) or particle tracking velocimetry (PTV). First, the pressure gradient fields are calculated from velocity fields, while the local and instantaneous pressure gradient uncertainty is estimated from the velocity uncertainty using a linear-transformation-based algorithm. The pressure field is then reconstructed by solving an overdetermined linear system which involves the pressure gradients and boundary conditions. This linear system is solved with generalized least squares (GLS) which incorporates the previously estimated variances and covariances of the pressure gradient errors as inverse weights to optimize the reconstructed pressure field. The method was validated with synthetic velocity fields of a 2D pulsatile flow, and the results show significantly improved pressure accuracy. The pressure error reduction by GLS was 50% with 9.6% velocity errors and 250% with 32.1% velocity errors compared to the existing baseline method of solving the pressure Poisson equation (PPE). The GLS was more robust to the velocity errors and provides greater improvement with spatially correlated velocity errors. For experimental validation, the volumetric pressure fields were evaluated from the velocity fields measured using 3D PTV of a laminar pipe flow with a Reynolds number of 630 and a transitional pipe flow with a Reynolds number of 3447. The GLS reduced the median absolute pressure errors by as much as 96% for the laminar pipe flow compared to PPE. The mean pressure drop along the pipe predicted by GLS was in good agreement with the empirical estimation using Darcy–Weisbach equation for the transitional pipe flow. Graphic abstract

中文翻译：

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使用不确定性改善 PIV/PTV 流量测量的压力场重建

摘要 提出了一种新的压力重建方法，利用不确定性信息来改善使用粒子图像测速仪 (PIV) 或粒子跟踪测速仪 (PTV) 测量的速度场的瞬时压力场。首先，压力梯度场是从速度场计算出来的，而局部和瞬时压力梯度的不确定性是使用基于线性变换的算法从速度不确定性中估计出来的。然后通过求解涉及压力梯度和边界条件的超定线性系统来重建压力场。该线性系统使用广义最小二乘法 (GLS) 求解，GLS 将先前估计的压力梯度误差的方差和协方差合并为逆权重，以优化重建的压力场。该方法通过二维脉动流的合成速度场进行了验证，结果表明压力精度显着提高。与求解压力泊松方程 (PPE) 的现有基线方法相比，GLS 的压力误差减少了 50%，速度误差为 9.6%，速度误差为 250%，速度误差为 32.1%。GLS 对速度误差更稳健，并在空间相关速度误差方面提供更大的改进。为了进行实验验证，体积压力场是根据使用 3D PTV 测量的速度场评估的，该速度场是雷诺数为 630 的层流管流和雷诺数为 3447 的过渡管流。 GLS 将中值绝对压力误差降低了与 PPE 相比，层流管流量高达 96%。GLS 预测的沿管道的平均压降与使用 Darcy-Weisbach 方程对过渡管道流动进行的经验估计非常一致。图形摘要