A recent study investigated the propagation of error in a velocimetry-based pressure (V-pressure) field reconstruction problem by directly analyzing the properties of the pressure Poisson equation (Pan et al 2016 Meas. Sci. Technol. 27 084012). In the present work, we extend these results by quantifying the effect of the error profile in the data field (shape/structure of the error in space) on the resultant error in the reconstructed pressure field. We first calculate the mode of the error in the data that maximizes error in the pressure field, which is the most dangerous error (called the worst error in the present work). This calculation of the worst error is equivalent to finding the principle mode of, for example, an Euler–Bernoulli beam problem in one-dimension and the Kirchhoff–Love plate in two-dimensions, thus connecting the V-pressure problem from experimental fluid mechanics to buckling elastic bodies from elastic mechanics. Taking advantage of this analogy, we then analyze how the error profile (e.g. spatial frequency of the error and the location of the most concentrated error) in the data field coupled with fundamental features of the flow domain (i.e. size, shape, and dimension of the domain, and the configuration of boundary conditions) significantly affects the error propagation from data to the reconstructed pressure. Our analytical results lend to practical applications in two ways. First, minimization of error propagation can be achieved by avoiding low frequency error profiles in data similar to the worst case scenarios and error concentrated at sensitive locations. Second, small amounts of the error in the data, if the error profile is similar to the worst error case, can cause significant error in the reconstructed pressure field; such a synthetic error can be used to benchmark V-pressure algorithms.

最近的一项研究通过直接分析压力泊松方程的性质，调查了基于测速法的压力（V 压力）场重建问题中的误差传播（Pan等人2016 Meas. Sci. Technol. 27084012）。在目前的工作中，我们通过量化数据场中的误差分布（空间误差的形状/结构）对重建压力场中合成误差的影响来扩展这些结果。我们首先计算压力场中误差最大的数据中误差的众数，这是最危险的误差（在目前的工作中称为最坏的误差）。这种最坏误差的计算等效于找到例如一维 Euler-Bernoulli 梁问题和二维 Kirchhoff-Love 板的主模态，从而将实验流体力学中的 V 压力问题联系起来从弹性力学到屈曲弹性体。利用这个类比，我们然后分析错误分布（例如 误差的空间频率和最集中误差的位置）与流域的基本特征（即域的大小、形状和维度，以及边界条件的配置）相结合，显着影响误差传播从数据到重建压力。我们的分析结果以两种方式应用于实际应用。首先，可以通过避免数据中类似于最坏情况的低频错误分布和集中在敏感位置的错误来实现错误传播的最小化。其次，数据中的少量误差，如果误差曲线与最坏的误差情况相似，就会在重建的压力场中造成重大误差；这种综合误差可用于对 V-pressure 算法进行基准测试。