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Input-response space-filling designs
Quality and Reliability Engineering International ( IF 2.3 ) Pub Date : 2021-06-08 , DOI: 10.1002/qre.2931
Lu Lu 1 , Christine M. Anderson‐Cook 2
Affiliation  

Traditional space-filling designs are a convenient way to explore throughout an input space of flexible dimension and have design points close to any region where future predictions might be of interest. In some applications, there may be a model connecting the input factors to the response(s), which provides an opportunity to consider the spacing not only in the input space but also in the response space. In this paper, we present an approach for leveraging current understanding of the relationship between inputs and responses to generate designs that allow the experimenter to flexibly balance the spacing in these two regions to find an appropriate design for the experimental goals. Applications where good spacing of the observed response values include calibration problems where the goal is to demonstrate the adequacy of the model across the range of the responses, sensitivity studies where the outputs from a submodel may be used as inputs for subsequent models, and inverse problems where the outputs of a process will be used in the inverse prediction for the unknown inputs. We use the multi-objective optimization method of Pareto fronts to generate multiple non-dominated designs with different emphases on the input and response space-filling criteria from which the experimenter can choose. The methods are illustrated through several examples and a chemical engineering case study.

中文翻译:

输入响应空间填充设计

传统的空间填充设计是一种在灵活维度的输入空间中探索的便捷方式,并且设计点靠近可能对未来预测感兴趣的任何区域。在某些应用中,可能存在将输入因子与响应关联的模型,这提供了一个机会,不仅可以考虑输入空间中的间距,还可以考虑响应空间中的间距。在本文中,我们提出了一种利用当前对输入和响应之间关系的理解来生成设计的方法,该设计允许实验者灵活地平衡这两个区域的间距,以找到适合实验目标的设计。观察响应值之间良好间隔的应用包括校准问题,其目标是证明模型在响应范围内的充分性,敏感性研究,其中子模型的输出可用作后续模型的输入,以及逆问题其中过程的输出将用于未知输入的逆向预测。我们使用帕累托前沿的多目标优化方法来生成多个非支配设计,不同重点是输入和响应空间填充标准,实验者可以从中选择。这些方法通过几个例子和一个化学工程案例研究来说明。和逆问题,其中过程的输出将用于未知输入的逆预测。我们使用帕累托前沿的多目标优化方法来生成多个非支配设计,不同重点是输入和响应空间填充标准,实验者可以从中选择。这些方法通过几个例子和一个化学工程案例研究来说明。和逆问题,其中过程的输出将用于未知输入的逆预测。我们使用帕累托前沿的多目标优化方法来生成多个非支配设计,不同重点是输入和响应空间填充标准,实验者可以从中选择。这些方法通过几个例子和一个化学工程案例研究来说明。
更新日期:2021-06-08
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