通过枚举和组合称重设计构建大型正交最小混杂响应面设计
Constructing Large Orthogonal Minimally Aliased Response Surface Designs Through Enumeration and Combination of Weighing Designs
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中文总结 AI 辅助
本研究提出算法框架，通过枚举和组合称重设计构建大型正交最小混杂响应面（OMARS）设计，可扩展至更大规模，适用于复杂实验的高维筛选与响应面建模。
中文摘要 AI 辅助
自动化和高通量实验的进展已能开展涉及众多因子和测试的更大规模、更复杂研究，这催生了对计算有效的设计构建方法日益增长的需求。在这种背景下，高效实验设计仍是关键挑战，需要能生成大型实验同时保持正交性和最小混杂性的框架。与现有可扩展性不足的方法不同，本研究提出一种算法框架，用于通过枚举和组合称重设计（具有正交列且每列非零项数量固定的三水平矩阵）来构建大型正交最小混杂响应面（OMARS）设计。对最多含24次测试的设计完成了称重设计的完整枚举，涵盖了多种因子数量和对应每个因子含2个或3个零的权重。此外，经过验证的部分枚举程序和组合方法将该目录扩展到更大规模的设计。该组合方法可构建测试量为选定基础量倍数的OMARS设计。因此，本文提供了生成大量高质量OMARS设计的方法，非常适合复杂工业和科学实验中的高维筛选及响应面建模。
英文摘要
Advances in automation and high-throughput experimentation have enabled larger and more complex studies involving many factors and tests, creating a growing demand for computationally effective design construction methods. Efficient experimental design remains a key challenge in this context, creating a need for frameworks that can generate large experiments while preserving orthogonality and minimal aliasing. Unlike existing approaches which struggle with scalability, this work introduces an algorithmic framework for constructing large Orthogonal Minimally Aliased Response Surface (OMARS) designs by enumerating and combining weighing designs, three-level matrices with orthogonal columns and a fixed number of non-zero entries per column. Complete enumerations of weighing designs are achieved for designs with up to 24 tests, covering multiple numbers of factors and weights corresponding to two or three zeros per factor. In addition, a validated partial enumeration procedure and a combination method extend the catalog to substantially larger designs. The combination method enables the construction of OMARS designs for any test size that is a multiple of selected base sizes. This paper thus provides the methodology for generating large catalogs of high-quality OMARS designs, well-suited for high-dimensional screening and response-surface modelling in complex industrial and scientific experiments.
