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The quality of information extracted from the vibration signals, and the accuracy of the bearing status detection depend on the methods used to process the signal and select the informative features. In this paper, a new hybrid approach is introduced in which the relatively new swarm decomposition (SWD) method and the optimized compensation distance evaluation technique (OCDET) are used to enhance the signal processing stage and to improve the optimal features selection process, respectively. Firstly, the vibration signals are decomposed into their Oscillatory Components (OCs) using the SWD. The feature matrix is constructed by computing the time-domain features for the OCs. The CDET method is consequently utilized to select the most sensitive features corresponding to the bearing status. On the other hand, The CDET approach contains a parameter called threshold which affects the number of the selected features. In this way, the hybrid optimization algorithm, which is a combination of the Particle Swarm Optimization (PSO) algorithm with the Sine–Cosine Algorithm (SCA) and the Levy flight distribution, has been used to select the optimal CDET threshold and improve the support vector machine (SVM) classifier. The proposed technique ability is evaluated by vibration signals corresponding to different bearing defects and various speeds. The results indicate the capability of the proposed fault diagnosis method in identifying the very small-size defects under various bearing conditions. Finally, the presented method shows better performance in comparison with other well-known methods in the most of the case studies. [ABSTRACT FROM AUTHOR]

Geometrical imperfections and residual stresses are two inevitable aspects in studying of graphene sheets (GSs) which despite of their vital influence on the forced nonlinear vibrational behavior they have not been considered in previous research works. Hence, this work is an attempt to fill this important gap for the first time. Utilizing Eringen's nonlocal plate theory, assuming von Karman nonlinear terms in strain-displacement relations and employing calculus of variations, we have derived partial differential equations (PDEs) of the displacement field. The function of initial curvature was assumed as the first mode-shape of the simply-supported rectangular plates with a variable mode-coefficient. Next, Galerkin decomposition method has been used to achieve the equation of motion and for nonlinear vibration analysis time multiple scales method (TMS) was applied. The nonlinear frequency response relation has been analytically achieved. Afterwards, comparing to molecular dynamic (MD) results presented in previous researches we validated natural frequencies of single layer graphene sheets (SLGSs) in different sizes. Furthermore, nonlinear frequency response curves and time histories based on TMS, were in an excellent agreement with numerical method results. Therefore, the influences of external pressure, nonlocal parameter, geometric imperfection and residual stress have been presented comprehensively. It was observed that both imperfection and stress intensify the softening behavior in the system. Interestingly, for a certain controllable magnitude of the imperfection, it has been illustrated that the generated softening term counteracts with the hardening due to geometrical nonlinearity and consequently the nonlinear system behaves as a linear one. [ABSTRACT FROM AUTHOR]