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A Two-Stage Filter for Smoothing Multivariate Noisy Data on Unstructured Grids

机译:用于平滑非结构化网格上的多变量噪声数据的两阶段滤波器

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Experimental data as well as numerical simulations are very often affected by "noise", random fluctuations that distort the final output or the intermediate products of a numerical process. In this paper, a new method for smoothing data given on nonstructured grids is proposed. It takes advantage of the smoothing properties of kernel-weighted averaging and least-squares techniques. The weighted averaging is performed following a Shepard-like procedure, where Gaussian kernels are employed, while least-squares fitting is reduced to the use of very few basis functions so as to improve smoothness, though at the price of interpolation accuracy. Once we have defined an n-point grid and want to make a smoothed fit at a given grid point, this method reduces to consideration of all m-point stencils (for a given value of in where m < n) that include that point, and to make a least-squares fitting, for that particular point, in each of those stencils; finally, the various results, thus obtained, are weight-averaged, the weights being inversely proportional to the distance of the point to the middle of the stencil. Then this process is repeated for all the grid points so as to obtain the smoothing of the input function. Though this method is generalized for the multivariate case, one-, two-, and five-dimensional test cases are shown as examples of the performance of this method.
机译:实验数据和数值模拟通常会受到“噪声”,随机波动的影响,这些波动会使最终输出或数值过程的中间产物变形。本文提出了一种平滑非结构化网格上给定数据的新方法。它利用了内核加权平均和最小二乘技术的平滑特性。加权平均是按照类似于Shepard的过程进行的,该过程采用了高斯核,而最小二乘拟合减少到使用很少的基函数,从而提高了平滑度,尽管是以内插精度为代价。一旦我们定义了一个n点网格并想要在给定的网格点上进行平滑拟合,此方法就简化为考虑包括该点的所有m点模板(对于其中m≤n的给定值),并针对每个特定点在每个模具中进行最小二乘拟合;最后,将由此获得的各种结果进行加权平均,权重与点到模具中间的距离成反比。然后,对所有网格点重复此过程,以便获得输入函数的平滑度。尽管此方法适用于多变量情况,但仍显示了一维,二维和五维测试用例作为该方法性能的示例。

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