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基于稳健参数设计理论提出了一种将主成分分析法与逼近理想点决策方法(TOPSIS)相结合的非线性轮廓图(Non-Linear profile)优化方法。首先利用两步建模法拟合响应模型,计算模型参数的满意度函数值,其次对模型参数的满意度函数值进行主成分分析,消除参数之间的相关性,并构建模型参数变异模式图,确定选定主成分的优化方向。最后利用TOPSIS模型求得选定主成分的最优贴近度(OPI),将其作为最终的优化指标。传统的优化方法都忽略了模型参数之间的相关性及优化过程的稳健性,并且需要复杂的数学计算,而本文所提方法可以有效解决这些问题。最后利用该方法对文献中的实例进行了分析研究,证明本文方法切实可行,优化结果令人满意。
Based on the robust parameter design theory, a non-linear profile optimization method combining principal component analysis and approximation of ideal point decision method (TOPSIS) is proposed. Firstly, the two-step model was used to fit the response model, and the satisfaction function value of the model parameters was calculated. Secondly, the principal component analysis was performed on the satisfaction function values of the model parameters to eliminate the correlation between the parameters and construct the model of variation of the model parameters , Determine the direction of optimization of the selected principal components. Finally, the TOPSIS model is used to determine the optimal closeness (OPI) of the selected principal components as the final optimization index. Traditional optimization methods ignore the correlation between model parameters and the robustness of the optimization process, and require complex mathematical calculations, and the proposed method can effectively solve these problems. Finally, this method is used to analyze and study the examples in the literature, which proves that the method in this paper is feasible and the optimization result is satisfactory.