A frequency-weighted energy operator and swarm decomposition for bearing fault diagnosis

The weak fault characteristics of rolling bearings are difficult to identify due to strong background noise. To address this issue, a bearing fault detection scheme combining swarm decomposition (SWD) and frequency-weighted energy operator (FWEO) is presented. First, SWD is applied to decompose the bearing fault signal into single mode components. Then, a new evaluation index termed LEP is constructed by combining the advantages of envelope entropy, Pearson correlation coefficient and L-kurtosis, and it is utilized to choose the sensitive component containing the richest bearing fault characteristics. Finally, FWEO is employed for extracting the bearing fault features from the sensitive component. Simulation and experimental analyses indicate that the LEP index has better performance than the L-kurtosis index in determining the sensitive component. The method has the effect of suppressing noise and enhancing impulse characteristics, which is superior to the SWD-based envelope demodulation method.

On asymptotic behavior of solution to a nonlinear wave equation with Space-time speed of propagation and damping terms

In this paper, we consider the asymptotic behavior of solution to the nonlinear damped wave equation utt – div(a(t, x)∇u) + b(t, x)ut = −|u|p−1u t ∈ [0, ∞), x ∈ Rn u(0, x) = u0(x), ut(0, x) = u1(x) x ∈ Rn with space-time speed of propagation and damping potential. We obtained L2 decay estimates via the weighted energy method and under certain suitable assumptions on the functions a(t, x) and b(t, x). The technique follows that of Lin et al.[8] with modification to the region of consideration in Rn. These decay result extends the results in the literature.

General stability and exponential growth of nonlinear variable coefficient wave equation with logarithmic source and memory term

This paper is concerned with the asymptotic stability and instability of solutions to a variable coefficient logarithmic wave equation with nonlinear damping and memory term. This model describes wave travelling through nonhomogeneous viscoelastic materials. By choosing appropriate multiplier and using weighted energy method, we prove the exponential decay of the energy. Besides, we also obtain the instability at the infinity of the solutions in the presence of the nonlinear damping.

Global classical solutions to the elastodynamic equations with damping

In this paper, we show the global existence of classical solutions to the incompressible elastodynamics equations with a damping mechanism on the stress tensor in dimension three for sufficiently small initial data on periodic boxes, that is, with periodic boundary conditions. The approach is based on a time-weighted energy estimate, under the assumptions that the initial deformation tensor is a small perturbation around an equilibrium state and the initial data have some symmetry.

Global stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interaction

<p style='text-indent:20px;'>This paper is concerned with the traveling wave fronts for a lattice dynamical system with global interaction, which arises in a single species in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction by delay. We prove that all non-critical traveling wave fronts are globally exponentially stable in time, and the critical traveling wave fronts are globally algebraically stable by the weighted energy method combined with the comparison principle and the discrete Fourier transform.</p>