时滞多变量系统PCA优化建模

主元分析（PCA）在工业生产过程的产品质量控制与故障诊断等方面已得到广泛应用，然而当过程的变量间存在着未知时滞性时，必须确定数据间的对应关系，否则PCA模型将会不准．基于此，提出了PCA优化建模方法．该方法以过程变量间的时滞常数为优化变量，在分析PCA模型特点基础上，确定主成分个数和SPE统计量为综合目标函数，并建立模型约束条件，采用遗传算法求解．最后给出了仿真实例，证明了所提出方法的有效性．

PCA optimal modeling for time delay multivariable system

As an effective method to extract correlations among variables,principal component analysis(PCA) is widely applied to multivariate statistical process monitoring,fault diagnosis and quality control.For process modeling with unknown time delay,time delay parameters are determined by using the conventional PCA method.Otherwise,the model will be so inaccurate that influences the monitoring capability.Therefore the PCA optimal modeling method is proposed,in which process variable time delay parameter is used as optimal variable.Based on the analysis characteristic of PCA model,the integration target function of PCs and SPE statistics is designed,and the restriction condition is constructed.The genetic algorithm is adopted for obtaining the solution of optimal model.A simulation result shows that effectiveness of the proposed method.