Conventional methods for generating Gaussian random surfaces, including the moving average (MA) time series model with nonlinear conjugate gradient method (NCGM), two-dimensional (2-D) digital filter method, and spectral representation method (SRM), are implemented with a wide range of autocorrelation length and truncation length values of the autocorrelation function (ACF). The ACF, power spectral density function (PSDF), and essential roughness parameters of the simulated surfaces are calculated and compared. Based on the simulation results, the mechanism of the truncation length of ACF affecting the simulated surfaces can be summarized as that the step formed by truncating ACF is not sufficiently small, thus resulting in non-negligible errors in the corresponding PSDF. Such errors will be propagated to the simulated surfaces. A conservative criterion is proposed to avoid the adverse effects of truncating ACF: make the autocorrelation length less than 8% of the surface dimensions and the truncation length at least seven times autocorrelation length. The results show that the MA model with NCGM overestimates the PSDF values of simulated surfaces in the high-frequency region, meaning significant high-frequency noise in the simulated surfaces. The 2-D digital filter method and the SRM have almost the same performance, and both methods are better than the MA model with NCGM when the criterion of truncating ACF is fulfilled. The SRM generates rough surfaces with the smallest standard deviation in terms of the roughness parameters, ACF, and PSDF in most cases, meaning that it can generate accurate surfaces at every single simulation and is more stable and efficient. Therefore, the SRM is the most recommended method among the three methods studied.

生成高斯随机表面的常规方法，包括使用非线性共轭梯度法 (NCGM)、二维 (2-D) 数字滤波器法和谱表示法 (SRM) 的移动平均 (MA) 时间序列模型，均使用自相关函数 (ACF) 的各种自相关长度和截断长度值。计算并比较了模拟表面的 ACF、功率谱密度函数 (PSDF) 和基本粗糙度参数。基于模拟结果，ACF截断长度影响模拟表面的机制可以概括为ACF截断形成的台阶不够小，从而导致相应PSDF中的误差不可忽略。此类错误将传播到模拟表面。为了避免截断ACF的不利影响，提出了一个保守的标准：使自相关长度小于表面尺寸的8%，截断长度至少为自相关长度的7倍。结果表明，带有NCGM的MA模型高估了高频区域模拟表面的PSDF值，这意味着模拟表面中存在显着的高频噪声。二维数字滤波方法和 SRM 的性能几乎相同，当满足截断 ACF 的准则时，这两种方法都优于带有 NCGM 的 MA 模型。在大多数情况下，SRM 生成粗糙度参数、ACF 和 PSDF 标准偏差最小的粗糙表面，这意味着它可以在每次模拟时生成准确的表面，并且更加稳定和高效。