Fractional Brownian Fields for Response Surface Metamodeling
Fractional Brownian Fields for Response Surface Metamodeling
复制标题
用于响应曲面元建模的分数布朗场
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
D. Apley
中科院分区：
文献类型：
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作者：
Ning Zhang;D. Apley
克里格法是一种广泛使用的计算机模拟数据的元建模方法，它将响应面建模为随机场的实现。平稳协方差函数（如高斯、幂指数或Matérn类）是基础随机场模型最常见的选择。这些相同的协方差函数的尺度参数在空间上变化的非平稳版本有时也被使用。分数布朗场（Fractional Brownian fields，FBFs）是一种不同形式的具有平稳增量的非平稳随机场模型，是更一般的内在平稳过程的一个例子。虽然在空间统计学文献中，FBF被认为是内在克里金法，但它们在计算机模拟响应面元建模中很少受到关注。对于后者的情况下使用，我们认为，他们有一些有吸引力的（以及一些没有吸引力的）属性，以减轻某些固有的问题，许多平稳的协方差模型，如回归均值，数值问题，由于协方差矩阵的近奇异性，并在处理突然的响应面功能的困难。
Kriging, a widely used metamodeling method for computer-simulation data, models the response surface as a realization of a random field. Stationary covariance functions such as the Gaussian, power exponential, or Matérn class are the most common choice for the underlying random field model. Nonstationary versions of these same covariance functions with scale parameters that vary spatially are also sometimes used. Fractional Brownian fields (FBFs) are a different form of nonstationary random field model having stationary increments, an example of more general intrinsic stationary processes. Although FBFs have been considered for intrinsic kriging in the spatial statistics literature, they have received little attention for computer-simulation response surface metamodeling. For use in the latter context, we argue that they have some attractive (as well as some unattractive) properties that mitigate certain problems inherent to many stationary covariance models, such as reversion to the mean, numerical issues due to near-singularity of covariance matrices, and difficulties in handling abrupt response surface features.