噪声因子存在下的多响应参数设计的优化

Optimization of Multiresponse Parameter Design Involving Noise Factors

采用多元损失函数法,对噪声因子存在下的多响应稳健性参数设计进行了优化。该方法考虑了噪声因子的影响,结合响应期望值和响应方差,其中响应方差结合了噪声因子产生的方差和拟合模型的预测方差,给出了综合方差的无偏估计,使解决方案对噪声因子和参数估计的不确定性都具有稳健性,避免了方差出现非正定的可能性。采用该方法对实例进行分析,得到较好的优化结果。

In this paper a multivariate loss function methodology involving noise factors is proposed. This method incorporates the mean value and variance with the multivariate loss function, in which the variance combines the variance caused by noise factors with the variance due to predictions, which leads to an unbi-ased estimator of the combined variance. The proposed method can avoid the possible non-definiteness of estimated variance, thus the solutions obtained are robust to both noise factors and parameter estimation. This method is applied to an example, which gives a satisfactory result.