Local coordinates and global structure preservation for fault detection and diagnosis

Abstract

Fault detection is crucial for the safe and reliable operation of industrial processes. Manifold learning methods have been widely used by the fault detection community. However, traditional manifold learning-based fault detection methods extract either the global structure information of the given data or the local structure information hidden in the data without capturing both global and local representations, which probably deteriorates the detection capabilities of these methods. This paper proposes a new feature extraction method named local coordinates and global structure preservation (LCGSP) for fault detection, where the local tangent space information and global geometric structure of data are captured simultaneously. A distance ratio is proposed and then integrated into principal component analysis to approximate the local tangent space, and this technique can improve the accuracy of the approximated local tangent space even if the data are sparse or non-uniformly distributed. In this context, the proposed method can better preserve the local manifold structure through the use of an accurate local tangent space. Furthermore, the geodesic distances between non-neighbors are introduced to preserve the global intrinsic relationships among data points. In this way, more faithful representations of the original data can be captured, thus enhancing the detection performance of the proposed method. In addition, a Bayesian fault diagnosis strategy is developed to make decisions about fault statuses. Two case studies demonstrate the superiority of the proposed LCGSP-based fault detection and diagnosis approach.