Multi-level PCA and its application in fault diagnosis

The traditional principal component analysis (PCA) method divides the variable space into two parts: Principal subspace and Residual subspace by orthogonal decomposition. It has been widely used in fault detection process, but it is difficult to interpret the modes of the fault because of model compound effect, and the ability to distinguish the pattern which is no significant is affected. In industrial process, there may exist a larger fault cause deviation from the normal state of system and may exist security risks cause a larger fault, take different responses for different sizes of faults can reduce expenses, thus identify the fault size is extremely important. In this paper, we put forward a multi-level PCA method that the variable space is divided into several principal subspaces and a residual subspace to solve the problem of identify the size of the fault, and apply it to fault diagnosis. For different sizes of fault data, project them onto each subspace step by step, calculate indicators and compare with the control limits of normal subspaces. The method can not only find faults, but also can identify the fault size, according to the subspace in which the fault is detected. Simulation shows the effectiveness of the algorithm.