Subspace-based Methods for Machinery Analysis and Monitoring

The objective of this presentation is to address the problem of structural damage detection or fault diagnosis in mechanical systems using subspace-based methods. Different methods are reviewed starting from Principal Component Analysis (PCA) also known as Proper Orthogonal Decomposition (POD) of time responses. PCA is known as an efficient method for extracting modal features of linear structures from output-only measurements. Those features define a subspace which characterizes the dynamical behavior of the structure. It becomes than possible to detect structural damage by comparing a reference subspace (obtained from the healthy structure) with current subspaces on the basis of the concept of angles between subspaces. Other damage indexes based on statistics may also be used.
One of the drawbacks of PCA is the need of several sensors. If the number of sensors is too small, modal identification and/or damage detection may not be performed in good conditions using PCA. An alternative PCA-based method named Null Subspace Analysis (NSA) may then be used. The NSA method generates data by means of block Hankel matrices and is proven to be efficient when the number of available sensors is small or even reduced to one sensor only.
However, when damage activates nonlinearity, the detection problem may necessitate methods which are more sensitive to nonlinear behaviors. To this purpose, Kernel Principal Component Analysis (KPCA) is a nonlinear extension of PCA built to authorize features with nonlinear dependence between variables. The method is “flexible” in the sense that different kernel functions may be used to better fit the testing data.
Industrial applications are presented to illustrate the proposed methods.