A fault detection method

i.e.

multistage multiway kernel entropy component analysis (MsMKECA) was proposed on the basis of nonlinearity and multistage characteristics of batch process. First

in order to divide a batch process into multiple stages

a matrix similarity stage division method was constructed from correlation matrixes of the time-series kernel entropy components. Then

a batch-variable 3-D unfolding technique was introduced to build MKECA model in each stage and to monitor operations in each stage of the batch process

which overcame on-line monitoring impediments of requiring estimation on future values by conventional batch-wise unfolding technique. Simulation study on penicillin fermentation process showed that the proposed method can offer much faster fault detection than traditional MKECA.