scholarly journals On Lp-strong convergence of an averaging principle for non-Lipschitz slow-fast systems with Lévy noise

2021 ◽  
Vol 115 ◽  
pp. 106973
Author(s):  
Yong Xu ◽  
Hongge Yue ◽  
Jiang-Lun Wu
Keyword(s):  
Strong Convergence ◽  
Lévy Noise ◽  
Averaging Principle ◽  
Levy Noise

An averaging principle for neutral stochastic fractional order differential equations with variable delays driven by Lévy noise

2021 ◽  
Author(s):  
Guangjun Shen ◽  
Jiang-Lun Wu ◽  
Ruidong Xiao ◽  
Xiuwei Yin
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lévy Noise ◽  
Averaging Principle ◽  
Fractional Order Differential Equations ◽  
Variable Delays ◽  
Fractional Differential ◽  
Stochastic Fractional Differential Equations ◽  
Levy Noise ◽  
Convergence In Mean

In this paper, we establish an averaging principle for neutral stochastic fractional differential equations with non-Lipschitz coefficients and with variable delays, driven by Lévy noise. Our result shows that the solutions of the equations concerned can be approximated by the solutions of averaged neutral stochastic fractional differential equations in the sense of convergence in mean square. As an application, we present an example with numerical simulations to explore the established averaging principle.

scholarly journals An Enhanced Intrinsic Time-Scale Decomposition Method Based on Adaptive Lévy Noise and Its Application in Bearing Fault Diagnosis

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 617
Author(s):  
Jianpeng Ma ◽  
Shi Zhuo ◽  
Chengwei Li ◽  
Liwei Zhan ◽  
Guangzhu Zhang
Keyword(s):  
Fault Diagnosis ◽  
Time Scale ◽  
Lévy Noise ◽  
Model Parameters ◽  
Rolling Bearings ◽  
Intrinsic Time ◽  
Time Scale Decomposition ◽  
Weak Fault ◽  
Levy Noise ◽  
The Impact

When early failures in rolling bearings occur, we need to be able to extract weak fault characteristic frequencies under the influence of strong noise and then perform fault diagnosis. Therefore, a new method is proposed: complete ensemble intrinsic time-scale decomposition with adaptive Lévy noise (CEITDALN). This method solves the problem of the traditional complete ensemble intrinsic time-scale decomposition with adaptive noise (CEITDAN) method not being able to filter nonwhite noise in measured vibration signal noise. Therefore, in the method proposed in this paper, a noise model in the form of parameter-adjusted noise is used to replace traditional white noise. We used an optimization algorithm to adaptively adjust the model parameters, reducing the impact of nonwhite noise on the feature frequency extraction. The experimental results for the simulation and vibration signals of rolling bearings showed that the CEITDALN method could extract weak fault features more effectively than traditional methods.

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