基于主成分分析的函数型产品质量特性的优化方法研究

针对质量特性为轮廓（Profile）的输出响应的优化问题展开研究，提出一种基于主成分分析的双响应曲面法和满意度函数相结合的函数响应优化方法。将Profile的每个观测点看成一个独立响应，将Profile问题转化为多响应问题。求得多个观测点的均值和方差的满意度函数值，通过主成分分析法，将多个观测点的均值和方差的满意度函数值转化为主成分综合得分，并将这两者的加权和作为最终的优化指标。本文所提方法可以有效解决观测点之间存在的相关性的问题，并且优化过程同时考虑到每个观测点响应的均值和方差影响。实例证明，该方法简单易行，优化结果满意。

A Study of Optimizing Functional Response Problems Based on Principal Component Analysis

A method is presented to optimize the profile based on functional response optimization method combining the dual response surface method with the satisfaction function based on principal component analysis. The response value of each observation point is treated as an independent response. The Profile has been as multi response optimization problem of nominal the best type. First, desirability function is used to measure the mean and variance for each observed point. Finally, the principal component analysis (PCA) is adopted to derive the overall performance index (OPI) for multiple response which is the weighted sum of principal values of both the desirability values of mean and variance for each observed point. A methodology is utilized for optimizing the problem of correlated observed points while involving the simultaneous optimization of the process mean and variance. Examples show that the method is simple, with satisfactory optimization results.