工业过程核概率主元模型建立及监控指标

Kernel Probabilistic Principal Component Model and Monitoring Indices in Industrial Process

概率主元分析(PPCA)能够根据过程变量的预测误差及其主元的白化值实现对过程的监控。但是PPCA只适合线性过程,而对非线性过程的监控效果不理想。为克服上述缺点,提出一种基于核PPCA(KPPCA)的过程监控方法,定性讨论了KPPCA模型的参数和主元个数选择问题,构造了高维空间的SPE和T2监控指标。该方法利用核函数将非线性数据映射到高维空间,去除了过程的非线性,然后利用PPCA对满足线性关系的过程变量映射值进行监控。仿真结果验证了该方法对非线性过程监控的优越性。

Probabilistic principal component analysis （PPCA） can realize the process monitoring according to the whiten values of process variables＇ prediction error and their scores. However, PPCA is only suitable to linear process and performs badly in nonlinear process monitoring. To overcome the above disadvantages in PPCA, this paper introduces kernel PPCA （KPPCA） into process monitoring and gives a qualitative analysis on the problems determining the parameters in KPPCA and the number of principal components. In addition, the paper proposes two monitoring indices, SPE and T2 in high-dimensional space. By mapping nonlinear data into high-dimensional space by kernel function, the method elimites process nonlinear features, then PPCA can be used to monitor the linear mapped value of process variables. Simulation results show the superiority of the method in nonlinear process monitoring.