Targeting the characteristics that periodic impulses usually occur whilst the rotating machinery exhibits local faults and the limitations of singular value decomposition (SVD) techniques, the SVD technique based on empirical mode decomposition (EMD) is applied to the fault feature extraction of the rotating machinery vibration signals. The EMD method is used to decompose the vibration signal into a number of intrinsic mode functions (IMFs) by which the initial feature vector matrices could be formed automatically. By applying the SVD technique to the initial feature vector matrices, the singular values of matrices could be obtained, which could be used as the fault feature vectors of support vector machines (SVMs) classifier. The analysis results from the gear and roller bearing vibration signals show that the fault diagnosis method based on EMD, SVD and SVM can extract fault features effectively and classify working conditions and fault patterns of gears and roller bearings accurately even when the number of samples is small.

By using the Fischer-Burmeister function to reformulate the nonlinear complementarity problem (NCP) as a system of semismooth equations and using Kanzow's smooth approximation function to construct the smooth operator, we propose a smoothing trust region algorithm for solving the NCP with P 0 functions. We prove that every accumulation point of the sequence generated by the algorithm is a solution of the NCP. Under a nonsingularity condition, local Q-superlinear/Q-quadratic convergence of the algorithm is established without the strict complementarity condition.

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