Things you wanted to know about the Latin hypercube design and were afraid to ask
Things you wanted to know about the Latin hypercube design and were afraid to ask
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发表时间：
2013
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通讯作者：
F. Viana
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作者：
F. Viana
计算机模型经常用于灵敏度分析、可靠性评估、设计优化和许多其他研究，这些研究往往需要进行大量的功能评估。通常，以前的知识有限(特别是在概念设计这样的情况下)，工程师、设计师和分析人员往往会探索大量的输入变量(在相对较大的域中定义)。计算机日益增长的能力使为设计和分析模拟而创造的技术能够应用于大范围的问题，并在从业者中达到很高的接受度。计算机实验的统计建模包含了一套生成替代模型(也称为元模型或响应面近似)的方法，用于取代昂贵的模拟代码[1]。其目标是在有限数量的昂贵模拟的基础上构建感兴趣的响应的近似值。尽管如此，仔细规划计算机代码的输入是成功进行模拟统计建模的最关键步骤之一。关于计算机实验的实验设计的大量文献清楚地阐明了这一点。通常，关于计算机模型的输入/输出关系的统计假设很少。这可能就是为什么最初的样本计划涵盖所考虑的大部分领域(导致空间填充的实验设计)的原因。在为计算机实验创造的策略中，拉丁超立方体设计[2]、[3]特别受欢迎(其他策略包括最大和最小最大距离设计[4]和正交表[5])。本文旨在对拉丁超立方体设计实验的研究做一个简要的概述，强调它被广泛使用的原因。首先，简要讨论了物理实验和计算机实验之间的差异，为人们对专门为计算机实验创造的策略的兴趣提供了一种可能的解释。接下来，考虑到拉丁超立方体设计可以创建覆盖输入领域不佳的样本，讨论了拉丁超立方体的优化。然后，给出了拉丁超立方体和计算机实验的替代设计的快速比较。在经历了这两个主题后，新从业者应该很好地理解了为什么同行推荐他们使用拉丁超立方体设计。然后，强调了总是使用拉丁超立方体设计来选择实验设计的陷阱。最后，对拉丁超立方体设计的研究现状进行了展望，并对未来的工作提出了展望。
Computer models are often used in sensitivity analysis, reliability assessment, design optimization and a number of other studies which tend to require a large number of function evaluations. Very often, there is limited previous knowledge (particularly in situations like conceptual design) and engineers, designers, and analysts tend explore a large number of input variables (defined over relatively large domains). The growing power of computers enabled techniques coined for design and analysis of simulations to be applied to a large spectrum of problems and reach high level of acceptance among practitioners. Statistical modeling of computer experiments embraces the set of methodologies for generating a surrogate model (also known as metamodel or response surface approximation) used to replace an expensive simulation code [1]. The goal is constructing an approximation of the response of interest based on a limited number of expensive simulations. With that said, careful planning of the inputs for the computer codes is one of the most crucial steps for successful statistical modeling of the simulations. This is clearly elucidated in the vast literature about experimental designs for computer experiments. Often, few statistical assumptions are made about the input/output relationship of computer models. That might be of the reasons why the initial sample is planned to cover most of the considered domain (leading to space-filling experimental designs). Among strategies coined for computer experiments, Latin hypercube designs [2], [3] are particularly popular (other strategies include maximin and minimax distance designs [4] and orthogonal arrays [5]). This paper aims at providing a short overview of the research in Latin hypercube design of experiments highlighting the reasons of its widespread use. First, a brief discussion on the differences between physical and computer experiments is presented offering one possible explanation for the interest in strategies coined specifically for computer experiments. Next, given that Latin hypercube designs can create samples that poorly cover the input domain, optimization of the Latin hypercube is discussed. Then, a quick comparison of Latin hypercube and alternative designs for computer experiments is presented. After going through these two topics, the new practitioners should have a good understanding of why peers recommend them to use Latin hypercube designs. Then, the pitfalls of using always Latin hypercube designs for selecting experimental designs are highlighted. Finally, the research in Latin hypercube designs is situated in the current state of the art and opportunities for future work are also presented.