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首页> 外文学位 >Development of the D-Optimality-Based Coordinate-Exchange Algorithm for an Irregular Design Space and the Mixed-Integer Nonlinear Robust Parameter Design Optimization
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Development of the D-Optimality-Based Coordinate-Exchange Algorithm for an Irregular Design Space and the Mixed-Integer Nonlinear Robust Parameter Design Optimization

机译：不规则设计空间基于D最优性的坐标交换算法的开发及混合整数非线性鲁棒参数设计优化

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摘要

Robust parameter design (RPD), originally conceptualized by Taguchi, is an effective statistical design method for continuous quality improvement by incorporating product quality into the design of processes. The primary goal of RPD is to identify optimal input variable level settings with minimum process bias and variation. Because of its practicality in reducing inherent uncertainties associated with system performance across key product and process dimensions, the widespread application of RPD techniques to many engineering and science fields has resulted in significant improvements in product quality and process enhancement. There is little disagreement among researchers about Taguchi's basic philosophy. In response to apparent mathematical flaws surrounding his original version of RPD, researchers have closely examined alternative approaches by incorporating well-established statistical methods, particularly the response surface methodology (RSM), while accepting the main philosophy of his RPD concepts. This particular RSM-based RPD method predominantly employs the central composite design technique with the assumption that input variables are quantitative on a continuous scale.;There is a large number of practical situations in which a combination of input variables is of real-valued quantitative variables on a continuous scale and qualitative variables such as integer- and binary-valued variables. Despite the practicality of such cases in real-world engineering problems, there has been little research attempt, if any, perhaps due to mathematical hurdles in terms of inconsistencies between a design space in the experimental phase and a solution space in the optimization phase. For instance, the design space associated with the central composite design, which is perhaps known as the most effective response surface design for a second-order prediction model, is typically a bounded convex feasible set involving real numbers due to its inherent real-valued axial design points; however, its solution space may consist of integer and real values.;Along the lines, this dissertation proposes RPD optimization models under three different scenarios. Given integer-valued constraints, this dissertation discusses why the Box-Behnken design is preferred over the central composite design and other three-level designs, while maintaining constant or nearly constant prediction variance, called the design rotatability, associated with a second-order model. Box-Behnken design embedded mixed integer nonlinear programming models are then proposed. As a solution method, the Karush-Kuhn-Tucker conditions are developed and the sequential quadratic integer programming technique is also used. Further, given binary-valued constraints, this dissertation investigates why neither the central composite design nor the Box-Behnken design is effective. To remedy this potential problem, several 0-1 mixed integer nonlinear programming models are proposed by laying out the foundation of a three-level factorial design with pseudo center points. For these particular models, we use standard optimization methods such as the branch-and-bound technique, the outer approximation method, and the hybrid nonlinear based branch-and-cut algorithm.;Finally, there exist some special situations during the experimental phase where the situation may call for reducing the number of experimental runs or using a reduced regression model in fitting the data. Furthermore, there are special situations where the experimental design space is constrained, and therefore optimal design points should be generated. In these particular situations, traditional experimental designs may not be appropriate. D-optimal experimental designs are investigated and incorporated into nonlinear programming models, as the design region is typically irregular which may end up being a convex problem. It is believed that the research work contained in this dissertation is the initial examination in the related literature and makes a considerable contribution to an existing body of knowledge by filling research gaps.
机译：Taguchi最初将稳健的参数设计（RPD）概念化，它是一种有效的统计设计方法，可以通过将产品质量纳入流程设计中来进行持续质量改进。 RPD的主要目标是确定具有最小过程偏差和变化的最佳输入变量级别设置。由于RPD技术在减少与关键产品和过程维度上的系统性能相关的内在不确定性方面具有实用性，因此RPD技术在许多工程和科学领域的广泛应用已导致产品质量和过程增强方面的显着改善。在研究人员之间，田口的基本哲学几乎没有分歧。针对围绕他的RPD原始版本存在的明显数学缺陷，研究人员通过接受公认的RPD概念的主要原理，通过采用公认的统计方法，特别是响应面方法（RSM），仔细研究了替代方法。这种基于RSM的特殊RPD方法主要采用中心组合设计技术，并假设输入变量是连续规模的量化;在许多实际情况下，输入变量的组合是实数值量化变量连续尺度和定性变量，例如整数和二进制值变量。尽管这种情况在现实世界的工程问题中是实用的，但几乎没有进行任何研究尝试（如果有的话），这可能是由于实验阶段的设计空间与优化阶段的解决方案空间之间的数学障碍所致。例如，与中央复合设计相关的设计空间（可能被称为二阶预测模型的最有效响应面设计）通常是有界凸可行集，因为其固有的实值轴向值涉及实数设计要点；沿线，本文提出了三种不同场景下的RPD优化模型。给定整数值约束，本文讨论为何Box-Behnken设计优于中央复合设计和其他三层设计，同时保持与第二阶模型相关的恒定或几乎恒定的预测方差，即设计可旋转性。然后提出Box-Behnken设计嵌入式混合整数非线性规划模型。作为一种求解方法，开发了Karush-Kuhn-Tucker条件，并使用了顺序二次整数编程技术。此外，在给定二元值约束的情况下，本文研究了为什么中央复合设计或Box-Behnken设计都不有效的原因。为了解决这个潜在的问题，通过奠定带有伪中心点的三级因子设计的基础，提出了几种0-1混合整数非线性规划模型。对于这些特定模型，我们使用标准优化方法，例如分支定界技术，外部逼近方法和基于混合非线性的分支定界算法。最后，在实验阶段存在一些特殊情况，其中这种情况可能需要减少实验次数或使用减少的回归模型来拟合数据。此外，在某些特殊情况下，实验设计空间受到限制，因此应生成最佳设计点。在这些特定情况下，传统的实验设计可能不合适。研究D最优实验设计并将其纳入非线性编程模型，因为设计区域通常是不规则的，最终可能会成为凸问题。可以认为，本文所包含的研究工作是相关文献的初步检查，通过填补研究空白​​对现有知识体系做出了相当大的贡献。

著录项

  • 作者

    Ozdemir, Akin.;

  • 作者单位

    Clemson University.;

  • 授予单位 Clemson University.;
  • 学科 Industrial engineering.
  • 学位 Ph.D.
  • 年度 2017
  • 页码 145 p.
  • 总页数 145
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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