Abstract
The dimension reduction methods have been proved powerful and practical to extract latent features in the signal for process monitoring. A linear dimension reduction method called nonlocal orthogonal preserving embedding (NLOPE) and its nonlinear form named nonlocal kernel orthogonal preserving embedding (NLKOPE) are proposed and applied for condition monitoring and fault detection. Different from kernel orthogonal neighborhood preserving embedding (KONPE) and kernel principal component analysis (KPCA), the NLOPE and NLKOPE models aim at preserving global and local data structures simultaneously by constructing a dual‐objective optimization function. In order to adjust the trade‐off between global and local data structures, a weighted parameter is introduced to balance the objective function. Compared with KONPE and KPCA, NLKOPE combines both the advantages of KONPE and KPCA, and NLKOPE is also more powerful in extracting potential useful features in nonlinear data set than NLOPE. For the purpose of condition monitoring and fault detection, monitoring statistics are constructed in feature space. Finally, three case studies on the gearbox and bearing test rig are carried out to demonstrate the effectiveness of the proposed nonlinear fault detection method.
Highlights
Mechanical equipment is widely used in modern industrial production, but it often suffers from damage during the long time operation, such as the fracture of bearings and the broken tooth of gears; the defect of these parts may cause the performance of the machine to degrade, or even cause security accidents
For the purpose of taking full advantages of global and local data structure and processing the nonlinear monitoring problem efficiently, a kernel global-local preserving projections (KGLPP) method [13] based on KLPP and kernel principal component analysis (KPCA) has been proposed, and the results show that it outperforms the linear global-local preserving projections (GLPP) method [14]
The parameter η describes different roles of global and local data structure preserving in constructing the nonlocal orthogonal preserving embedding (NLOPE) model; it is important to choose an appropriate value of η, which will affect the extraction of latent variables
Summary
Mechanical equipment is widely used in modern industrial production, but it often suffers from damage during the long time operation, such as the fracture of bearings and the broken tooth of gears; the defect of these parts may cause the performance of the machine to degrade, or even cause security accidents. LPP and NPE both are linear projection methods that can process the testing data conveniently; manifold learning based monitoring methods can overcome some limits of the PCA-based monitoring method These manifold learning methods only consider the neighborhood relationships to preserve local properties among samples and may lose crucial information contained in the global data structure. In order to take both global and local data structure characteristics into account, the methods which unify LPP and PCA have been proposed, and the fault detection performances have proven to be better than LPP and PCA [11, 12] These approaches are still linear methods, as they are employed to process the nonlinear process data; these methods have limitations and may obtain a poor monitoring performance.
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