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首页> 外文会议>4th International Conference on Integrated Design and Manufacturing in Mechanical Engineering - IDMME 2002 May 14-16, 2002 Clermont-Ferrand, France >A MODEL-BASED FRAMEWORK FOR ROBUST DESIGN
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A MODEL-BASED FRAMEWORK FOR ROBUST DESIGN

机译：基于模型的鲁棒设计框架

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摘要

In this paper we develop an as-yet-missing theoretical framework as well as a general methodology for model-based robust design. At the outset, a distinction is made between three sets: the set of design variables, grouped in the n-dimensional vector x, which are to be assigned values as an outcome of the design job; the set of design-environment parameters (DEP), grouped in the v-dimensional vector p, over which the designer has no control; and the set of performance functions, arrayed in the m-dimensional vector f, representing the functional relations among performance, design variables and DEP. Resorting to the mathematical model available for the object under design, an m x v design performance matrix F, mapping the space of relative variations of p into that of relative variations of f, is derived. Moreover, two pertinent concepts are introduced: the design sensitivity matrix, which plays a major role in the transmission of the variations of p into variations of f, and its associated bandwidth, defined as the logarithm of the square root of the ratio between the maximum to the minimum singular values of the design performance matrix, measured in decades. A result stating the relation between the bandwidth of a matrix and its inverse is shown. Consequently, the aforementioned bandwidth represents an index for evaluating the robustness of a design. To demonstrate our approach, case studies are included.
机译：在本文中，我们为基于模型的鲁棒性设计开发了一个尚欠缺的理论框架和通用方法。首先，要在三组之间进行区分：一组设计变量，它们被分组在n维向量x中，这些变量将被分配作为设计工作结果的值；设计环境参数（DEP）的集合，分组在v维向量p中，设计者无法控制。在m维向量f中排列的性能函数集代表性能，设计变量和DEP之间的函数关系。借助于可用于设计对象的数学模型，得出了一个m x v设计性能矩阵F，将p的相对变化的空间映射到f的相对变化的空间。此外，还引入了两个相关概念：设计灵敏度矩阵，它在将p的变化转换为f的变化中起主要作用；其关联的带宽定义为最大值之间的比率的平方根的对数设计性能矩阵的最小奇异值，以数十年为单位。结果表明了矩阵带宽与其逆之间的关系。因此，上述带宽代表用于评估设计的鲁棒性的指标。为了演示我们的方法，包括案例研究。

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