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Response surface optimization techniques for multiple objective and randomly valued independent variable problems.

机译：用于多目标和随机值自变量问题的响应面优化技术。

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Automotive research problems can be a challenging area for DOE methods. The number of responses, controllable factors, uncontrollable factors, constraints, qualitative factors, and interactions can be enormous. The primary challenge is combining the quantitative, qualitative, and “intuitive knowledge” into a structured optimization method. The key is to mathematically formulate all of the information into an equation—that is consistent with the goals of the study.; The proposed methods will provide the analyst with new formulation methods for optimizing automotive and industrial processes. The proposed methods are RaVIV, Hyperplane, Combined Response with Distance Constraints, and Minimized Distance with Response Constraints.; The RaVIV method is based on accommodating variables that are uncontrollable or randomly valued. The method combines the random variable process distribution with the fitted regression model. The resulting model is a type of “weighted average” over the range of the (randomly valued & independent) variable. This new approach differs from traditional methods that minimize the mean – process variance.; The MRSM (Multiple Response Surface Method) Hyperplane Method uses the eigenvalue, eigenvector, and stationary point information to construct a series of constraint planes. Depending upon the number of independent variables and eigenvalue information, the intersection of the constraint planes will establish a linear solution vector. This information will identify the starting point and direction of an improvement vector.; The MRSM Combined Response Function with Distance Constraint Method is a multiple response method of optimizing a primary combined response that is subject to a secondary distance constraint. The secondary constraint is the normal (Euclidean) distance from the design region center.; The MRSM Minimized Distance with Response Constraint method minimizes a normal (euclidean) distance objective function that is subject to a set of response constraints. With each set of response constraints, a search is performed to determine the solution that is closest to the region of experimentation.; The proposed methods are applicable to a variety of automotive and industrial optimization problems. They will help the experimenter investigate, study, improve, and optimize one or more responses.
机译：汽车研究问题对于DOE方法可能是一个充满挑战的领域。响应，可控因素，不可控因素，约束，定性因素和相互作用的数量可能很大。主要挑战是将定量，定性和“直觉性知识”组合成结构化的优化方法。关键是用数学方法将所有信息公式化为一个方程，这与研究的目标是一致的。提出的方法将为分析师提供优化汽车和工业过程的新配方方法。提出的方法是RaVIV，超平面，带距离约束的组合响应和带响应约束的最小距离。 RaVIV方法基于容纳不可控制或随机值的变量。该方法将随机变量过程分布与拟合回归模型结合在一起。结果模型是变量（随机值和独立值）范围内的一种“加权平均值”。这种新方法不同于传统方法，该方法使均值–过程差异最小化。 MRSM（多响应面方法）超平面方法使用特征值，特征向量和固定点信息来构造一系列约束平面。根据自变量的数量和特征值信息，约束平面的交点将建立线性解矢量。该信息将确定改进向量的起点和方向。具有距离约束的MRSM组合响应函数方法是一种用于优化受次级距离约束的主组合响应的多响应方法。次要约束是距设计区域中心的法线（欧几里得）距离。带有响应约束的MRSM最小化距离方法可以最小化受一组响应约束的正常（欧几里得）距离目标函数。对于每组响应约束，都执行搜索以确定最接近实验区域的解。所提出的方法适用于各种汽车和工业优化问题。它们将帮助实验者研究，研究，改善和优化一种或多种反应。

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