Nonlinear fault detection based on locally linear embedding

In this paper, a new nonlinear fault detection technique based on locally linear embedding (LLE) is developed. LLE can efficiently compute the low-dimensional embedding of the data with the local neighborhood structure information preserved. In this method, a data-dependent kernel matrix which can reflect the nonlinear data structure is defined. Based on the kernel matrix, the Nystr¨om formula makes the mapping extended to the testing data possible. With the kernel view of the LLE, two monitoring statistics are constructed. Together with the out of sample extensions, LLE is used for nonlinear fault detection. Simulation cases were studied to demonstrate the performance of the proposed method.