Nonlinear Subspace Learning

In practice, collected vibration signals usually contain a large collection of responses from several sources in the rotating machine, including some background noise. Various nonlinear subspace learning techniques have been proposed to learn subspace features from a large amount of vibration signals in rotating machines fault diagnosis. This chapter describes various nonlinear subspace learning techniques and their application in machine fault diagnosis. These include kernel principal component analysis (KPCA), kernel linear discriminant analysis, kernel independent component analysis, isometric feature mapping (ISOMAP), diffusion maps (DMs), Laplacian eigenmaps (LE), local linear embedding (LLE), Hessian-based local linear embedding (HLLE), local tangent space alignment analysis (LTSA), maximum variance unfolding (MVU), and stochastic proximity embedding (SPE). Dimensionality reduction is performed using a linear dimensionality-reduction technique and nonlinear dimensionality-reduction techniques (KPCA, ISOMAP, MVU, DM, LLE, LE, HLLE, and LTSA).