Industrial processes are often operating under different modes

while there are nonlinear correlations between data monitored.Aiming at these problems

a fault detection method based on relative isometric mapping (RISOMAP) was proposed.Relative geodesic distance was used to establish distance matrix in the high dimensional space

and multi dimensional scaling (MDS) was used to calculate output in the low dimensional embedded space.Information of sub-manifold and error could be obtained

and then monitoring statistics were built for fault detection.Meanwhile

kernel ridge regression was used to obtain the lower dimensional output of test data.Besides

kernel matrix was updated through integrated similarity.The simulations of visualization case and TE process illustrated that in contrast to fault detection methods based on kernel principal component analysis (KPCA) and ISOMAP

the proposed method could detect process fault more effectively and quickly.It also provided an idea to implement fault detection without prior knowledge in the multimode process.