scholarly journals Slow manifolds for a nonlocal fast-slow stochastic system with stable Lévy noise

2019 ◽  
Vol 60 (9) ◽  
pp. 091501
Author(s):  
Hina Zulfiqar ◽  
Shenglan Yuan ◽  
Ziying He ◽  
Jinqiao Duan
Keyword(s):  
Stochastic System ◽  
Lévy Noise ◽  
Slow Manifolds ◽  
Levy Noise

Slow manifolds for dynamical systems with non-Gaussian stable Lévy noise

2019 ◽  
Vol 17 (03) ◽  
pp. 477-511 ◽  
Author(s):  
Shenglan Yuan ◽  
Jianyu Hu ◽  
Xianming Liu ◽  
Jinqiao Duan
Keyword(s):  
Biological Sciences ◽  
Dynamical Systems ◽  
Scale Parameter ◽  
Lévy Noise ◽  
Stochastic Dynamical Systems ◽  
Time Dynamics ◽  
Slow Manifolds ◽  
Long Time ◽  
Non Gaussian ◽  
Levy Noise

This work is concerned with the dynamics of a class of slow–fast stochastic dynamical systems driven by non-Gaussian stable Lévy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, and then we eliminate the fast variables to reduce the dimensions of these stochastic dynamical systems. It is shown that as the scale parameter tends to zero, the slow manifolds converge to critical manifolds in distribution, which helps to investigate long time dynamics. The approximations of slow manifolds with error estimate in distribution are also established. Furthermore, we corroborate these results by three examples from biological sciences.

Data assimilation and parameter estimation for a multiscale stochastic system withα-stable Lévy noise

2017 ◽  
Vol 2017 (11) ◽  
pp. 113401 ◽  
Author(s):  
Yanjie Zhang ◽  
Zhuan Cheng ◽  
Xinyong Zhang ◽  
Xiaoli Chen ◽  
Jinqiao Duan ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Stochastic System ◽  
Lévy Noise ◽  
Levy Noise

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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