Kernel Local Linear Discriminate Method for Dimensionality Reduction and Its Application in Machinery Fault Diagnosis

Dimensionality reduction is a crucial task in machinery fault diagnosis. Recently, as a popular dimensional reduction technology, manifold learning has been successfully used in many fields. However, most of these technologies are not suitable for the task, because they are unsupervised in nature and fail to discover the discriminate structure in the data. To overcome these weaknesses, kernel local linear discriminate (KLLD) algorithm is proposed. KLLD algorithm is a novel algorithm which combines the advantage of neighborhood preserving projections (NPP), Floyd, maximum margin criterion (MMC), and kernel trick. KLLD has four advantages. First of all, KLLD is a supervised dimension reduction method that can overcome the out-of-sample problems. Secondly, short-circuit problem can be avoided. Thirdly, KLLD algorithm can use between-class scatter matrix and inner-class scatter matrix more efficiently. Lastly, kernel trick is included in KLLD algorithm to find more precise solution. The main feature of the proposed method is that it attempts to both preserve the intrinsic neighborhood geometry of the increased data and exact the discriminate information. Experiments have been performed to evaluate the new method. The results show that KLLD has more benefits than traditional methods. 1. Introduction With the information collection technology becoming more and more advanced, a huge number of data have been produced during mechanical equipment running process. The sensitive information which reflects the running status of the equipment has been submerged in a large amount of redundant data. Effective dimensionality reduction can solve this problem. Dimensionality reduction is one of the key technologies for equipment condition monitoring and fault diagnosis. Nonlinear and nonstationary vibration signals generated by the rolling bearing [1, 2] make the original high-dimensional feature space which consists of the statistical characteristics of the signal inseparable. The traditional linear dimensionality reduction methods such as PCA and ICA not only are under the assumption of global linear structure of the data but also use different linear transformation matrix to find the best low-dimensional projection. The classification information plays an important role. In nonlinear conditions such as the original high dimensional feature space possesses a non-linear structure, however, the classification information is difficult to obtain by linear methods. KPCA is a traditional nonlinear dimensionality reduction method, which achieves the task of dimensionality