Nonlinear Process Monitoring Using Data-Dependent Kernel Global–Local Preserving Projections

A new nonlinear dimensionality reduction method called data-dependent kernel global–local preserving projections (DDKGLPP) is proposed and used for process monitoring. To achieve performance improvements, DDKGLPP uses a data-dependent kernel rather than a conventional kernel. A unified kernel optimization framework is developed to optimize the data-dependent kernel by minimizing a data structure preserving index. The optimized kernel can unfold both global and local data structures in the feature space. The data-dependent kernel principal component (DDKPCA) and data-dependent kernel locality preserving projections (DDKLPP) also can be developed under the unified kernel optimization framework. However, unlike DDKPCA and DDKLPP, DDKGLPP is able to preserve both global and local structures of the data set when performing dimensionality reduction. Consequently, DDKGLPP is more powerful in capturing useful data characteristics. A DDKGLPP-based monitoring method is then proposed for nonlinear processes. Its performance is tested in a simple nonlinear system and the Tennessee Eastman (TE) process. The results validate that the DDKGLPP-based method has much higher fault detection rates and better fault sensitivity than those methods based on KPCA, KGLPP, DDKPCA, and DDKLPP.