Using Response Surface Methodology in Fuzzy Set Based Design Optimization
Using Response Surface Methodology in Fuzzy Set Based Design Optimization
复制标题
在基于模糊集的设计优化中使用响应面方法
DOI：
10.2514/6.1998-1776
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
R. Haftka
中科院分区：
文献类型：
--
作者：
G. Venter;R. Haftka
本文着重于使用模糊集理论模型的不确定性典型的飞机工业，与未来材料的设计。设计问题涉及在固定重量预算下最大限度地提高结构的安全水平，其中结构将由尚未可用的材料建造。在这种情况下，几乎没有关于不确定性的信息，这些信息是基于专家意见和设计师做出的假设来描述的。因此，模糊集模型是适合这种类型的不确定性。响应面方法是在整个设计过程中所描述的本文件，主要是为了减少与设计的不确定性的计算负担。响应面方法也被用来集成的分析代码与优化算法，并消除数值噪声，这是固有的响应函数。响应函数中噪声的消除允许使用基于导数的优化算法。厚度沿宽度方向变化的各向同性板被认为是一个设计问题。所有的问题参数是不确定的，屈服应力和屈曲载荷的破坏准则被认为是。从模糊集理论获得的最优设计相比，传统的确定性设计，它使用的安全系数来考虑的不确定性。结果表明，对于所考虑的示例问题，基于模糊集的设计是上级等效的确定性设计。此外，在设计过程中使用响应面方法时，实现了大量节省计算成本。
The paper focuses on the use of fuzzy set theory to model uncertainty typical of the aircraft industry, associated with design with future materials. The design problem involves maximizing the safety level of a structure for a fixed weight budget, where the structure will be built from materials not yet available. In this case little information is available regarding the uncertainty, which is described based on expert opinion and assumptions made by the designer. Therefore, fuzzy set models are appropriate for this type of uncertainty. Response surface methodology is used throughout the design process described in the present paper, mainly to reduce the computational burden associated with designing for uncertainty. Response surface methodology is also used to integrate the analysis code with the optimization algorithm and to eliminate numerical noise, which is inherent to the response function. The elimination of noise in the response function, allows the use of a derivative based optimization algorithm. An isotropic plate with a change in thickness across its width is considered as a design problem. All problem parameters are uncertain and both yield stress and buckling load failure criteria are considered. The optimum design obtained from fuzzy set theory is compared to a traditional deterministic design, which uses a safety factor to account for the uncertainty. It is shown that for the example problem considered, the fuzzy set based design is superior to the equivalent deterministic design. Also, substantial savings in computational cost are realized when using response surface methodology during the design process.