Manifold subspace distance derived from kernel principal angles and its application to machinery structural damage assessment

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Abstract
Damage assessment of machinery structure is beneficial for identifying structural health states and preventing sudden failures. A novel scheme for damage assessment is presented by using manifold subspace distance in this study. Vibration response signals from the machinery structure are collected by accelerometers first, and feature matrices are extracted to characterize the acceleration response comprehensively. Thereafter, a manifold learning method, namely kernel locality preserving projection (KLPP), is performed to obtain manifold subspace from the feature matrix. KLPP is available to mine nonlinear information hidden in the feature matrix, which makes it different from the linear subspace analysis method. This merit enables KLPP to be more effective in exploring the intrinsic model of the feature matrix. Further, kernel principal angles that represent similarity between the manifold subspaces are calculated. Finally, a manifold subspace distance is derived from the kernel principal angles. This distance is an appropriate metric for measuring closeness or similarity between the subspaces embedded on a manifold. The distance between manifold subspaces from normal state and damage state of a machinery structure is defined as a damage index. Effectiveness of the proposed scheme is validated by two case studies with regard to damage assessment for different machinery structures. The results show that the defined damage index is not only sensitive to the occurrence of structural damage but also increases obviously with the increasing damage level. These positive results illustrate that the proposed scheme has promise for future performance and is a valuable method for damage assessment.

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