Abstract Simulating surfaces with defined surface roughness parameters is a common task in tribology. This task is likely to become more relevant as modelling rough surface contact becomes less costly as it enables parametric studies linking behaviour to roughness parameters independent of a particular surface profile. The linear transform method allows the specification of the autocorrelation function (ACF) and gives some control over the height function, however these methods only fit the linear transformation matrix to half of the ACF. Behaviour outside of this half is unspecified and can lead to large errors. In this work we show that this problem can be overcome by using a symmetrical linear transformation matrix. This ensures that the resulting ACF is symmetrical. The method given by Liao et al. (2018) is extended to include this constraint, including the analytical gradient formula. Additionally, an improvement allowing for the generation of periodic surfaces is given. The use of a symmetric filter reduced errors in the unfitted region of the ACF, to the same levels as within the fitted region, in one example, this was a reduction from 50% to 3% error. The surface realisations produced by this technique show fewer unphysical effects than those produced by nonsymmetric filters. Particularly, high frequency noise in line with the coordinate axes is removed.

中文翻译：

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用于生成具有对称自相关函数的随机粗糙表面的线性变换技术的改进

摘要 用定义的表面粗糙度参数模拟表面是摩擦学中的一项常见任务。随着对粗糙表面接触建模的成本降低，这项任务可能会变得更加重要，因为它使参数化研究能够将行为与与特定表面轮廓无关的粗糙度参数相关联。线性变换方法允许指定自相关函数 (ACF) 并对高度函数进行一些控制，但是这些方法仅将线性变换矩阵拟合到 ACF 的一半。这一半之外的行为是未指定的，可能会导致大错误。在这项工作中，我们表明可以通过使用对称线性变换矩阵来克服这个问题。这确保生成的 ACF 是对称的。Liao 等人 给出的方法。(2018) 扩展到包括这个约束，包括解析梯度公式。此外，还给出了允许生成周期性表面的改进。对称滤波器的使用将 ACF 未拟合区域中的误差降低到与拟合区域内相同的水平，在一个示例中，误差从 50% 减少到 3%。这种技术产生的表面实现比非对称滤波器产生的非物理效应更少。特别是去除了与坐标轴一致的高频噪声。这种技术产生的表面实现比非对称滤波器产生的非物理效应更少。特别是去除了与坐标轴一致的高频噪声。这种技术产生的表面实现比非对称滤波器产生的非物理效应更少。特别是去除了与坐标轴一致的高频噪声。