Multichannel Vibration Fault Diagnosis for Rolling Bearings Based on QPCA and SVM

A new method had been proposed in this paper of fault diagnosis for rolling bearings based on multichannel vibration signals and QPCA-SVM-based method. The vibration signals were obtained by some multi-sensors with three channels X, Y, Z, that were orthogonal axes. The three orthogonal axes signals were constructed a pure quaternion sequences as samples for processing. The pure quaternion sequences data set was processed by quaternion principle components analysis (QPCA) for feature extraction, and then combined with pattern recognition tools support vector machine (SVM) for classifying some faults patterns. The experimental results indicated its efficiency, and it provided a method for fault diagnosis on multichannel vibration signals.

ON HERMITIAN PFISTER FORMS

Let K be a field of characteristic different from 2. It is known that a quadratic Pfister form over K is hyperbolic once it is isotropic. It is also known that the dimension of an anisotropic quadratic form over K belonging to a given power of the fundamental ideal of the Witt ring of K is lower bounded. In this paper, weak analogues of these two statements are proved for hermitian forms over a multiquaternion algebra with involution. Consequences for Pfister involutions are also drawn. An invariant uα of K with respect to a nonzero pure quaternion of a quaternion division algebra over K is defined. Upper bounds for this invariant are provided. In particular an analogue is obtained of a result of Elman and Lam concerning the u-invariant of a field of level at most 2.