Fault detection based on Kernel Principal Component Analysis

In the field of structural health monitoring or machine condition monitoring, the activation of nonlinear dynamic behavior may render the procedure of damage or fault detection more difficult. Principal Component Analysis (PCA) is known as a popular method for diagnosis but as it is basically a linear method, it may pass over some useful nonlinear features of the system behavior. One possible extension of PCA is Kernel PCA (KPCA), owing to the use of nonlinear kernel functions that allow introduction of nonlinear dependences between variables. The objective of this paper is to address the problem of fault detection (in terms of nonlinear activation) in mechanical systems using a KPCA-based method. The detection is achieved by comparing the subspaces between the reference and a current state of the system through the concept of subspace angle. It is shown in this work that the exploitation of the measurements in the form of block Hankel matrices can effectively improve the detection results. The method is illustrated on an experimental example consisting of a beam with a geometric nonlinearity.