Construction of response surfaces based on progressive-lattice-sampling experimental designs with application to uncertainty propagation
Construction of response surfaces based on progressive-lattice-sampling experimental designs with application to uncertainty propagation
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DOI：
10.1016/j.strusafe.2003.03.001
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发表时间：
2004-04
影响因子：
5.8
通讯作者：
V. Romero;L. Swiler;A. Giunta
中科院分区：
文献类型：
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作者：
V. Romero;L. Swiler;A. Giunta
响应面函数通常被用作计算昂贵的计算机模型的简单且廉价的替代品，这些计算机模型模拟复杂系统在某些参数空间上的行为。在这里，我们研究了几种数据拟合和插值技术（有限元插值、克里金法和多项式回归），这些技术可用于构建基于渐进格子采样 (PLS) 增量实验设计的逐步升级的响应曲面近似序列。 PLS 是超立方体参数空间结构化采样的范例，通过在设计的每个级别放置并增量添加样本，以有效利用所有先前级别的样本。当与兼容的插值方法相结合时，PLS 可用于构建高效的可升级响应面近似值。升级后，获得收敛启发式，可用于估计响应曲面中所包含的近似误差的大小。此处尝试的三种插值方法在几个测试问题中进行了拟合和收敛行为的检查。
Response surface functions are often used as simple and inexpensive replacements for computationally expensive computer models that simulate the behavior of a complex system over some parameter space. Here we examine several data fitting and interpolation techniques (finite-element interpolation, kriging, and polynomial regression) that can be used to construct a sequence of progressively upgraded response surface approximations based on Progressive Lattice Sampling (PLS) incremental experimental designs. PLS is a paradigm for structured sampling of a hypercube parameter space by placing and incrementally adding samples at each level of the design in a manner intended to efficiently leverage the samples at all previous levels. When combined with compatible interpolation methods, PLS can be used to construct efficiently upgradable response surface approximations. Upon upgrading, convergence heuristics are gained that can be used to estimate the magnitude of the approximation error entailed in the response surface. The three interpolation methods tried here are examined for fitting and convergence behavior in several test problems.