Kernel orthogonal manifold angle based dissimilarity for nonlinear dynamic process monitoring

For process with nonlinear and dynamic features, a kernel orthogonal manifold angle based dissimilarity is developed to quantitatively evaluate the statistical relationship between the manifold subspaces of normal benchmark and test data sets. The kernel orthogonal manifold angle based dissimilarity index is derived from the singular values of the inner-product matrix calculated by the orthogonal vectors in the two manifold subspaces. Firstly, the historical process data is mapped into feature space by using the nonlinear function based on multi-manifold. Then, the projection vectors are orthogonalized by using Gram-Schmidt method, and base vectors of the manifold subspace are constructed. Furthermore, the kernel orthogonal manifold angle with singular value decomposition(SVD) of the inner-product of two manifold subspaces, and the dissimilarity monitoring model are got. Angle and distance measures are combined into the monitoring index to trigger fault alarm with better sensitivity. The simulation experiment on the TE process demonstrates the superiority of the proposed method. © 2018, Editorial Office of Control and Decision. All right reserved.