scholarly journals Stochastic generalized porous media equations driven by Lévy noise with increasing Lipschitz nonlinearities

2021 ◽  
Author(s):  
Weina Wu ◽  
Jianliang Zhai
Keyword(s):  
Porous Media ◽  
Lévy Noise ◽  
Porous Media Equations ◽  
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.

scholarly journals Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

2020 ◽  
Vol 42 (1) ◽  
pp. 65-84
Author(s):  
Jinzhong Ma ◽  
Yong Xu ◽  
Yongge Li ◽  
Ruilan Tian ◽  
Shaojuan Ma ◽  
...  
Keyword(s):  
Lévy Noise ◽  
Stable Model ◽  
Efficient Tool ◽  
Escape Probability ◽  
Critical Transitions ◽  
Current State ◽  
Undesirable State ◽  
Parameter Dependent ◽  
Levy Noise ◽  
The Given

AbstractIn real systems, the unpredictable jump changes of the random environment can induce the critical transitions (CTs) between two non-adjacent states, which are more catastrophic. Taking an asymmetric Lévy-noise-induced tri-stable model with desirable, sub-desirable, and undesirable states as a prototype class of real systems, a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out. We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability, which is named as the absorbed region. Then, a new concept of the parameter dependent basin of the unsafe regime (PDBUR) under the asymmetric Lévy noise is introduced. It is an efficient tool for approximately quantifying the ranges of the parameters, where the noise-induced CTs from the desirable state directly to the undesirable one may occur. More importantly, it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.

Adaptive state estimation of Markov switched neural networks driven by Lévy noise

2019 ◽  
Vol 42 (2) ◽  
pp. 330-336
Author(s):  
Dongbing Tong ◽  
Qiaoyu Chen ◽  
Wuneng Zhou ◽  
Yuhua Xu
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Lévy Noise ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Switched Neural Networks ◽  
Inequality Technique ◽  
Levy Noise

This paper proposes the [Formula: see text]-matrix method to achieve state estimation in Markov switched neural networks with Lévy noise, and the method is very distinct from the linear matrix inequality technique. Meanwhile, in light of the Lyapunov stability theory, some sufficient conditions of the exponential stability are derived for delayed neural networks, and the adaptive update law is obtained. An example verifies the condition of state estimation and confirms the effectiveness of results.

scholarly journals L q -Functional Inequalities and Weighted Porous Media Equations

2007 ◽  
Vol 28 (1) ◽  
pp. 35-59 ◽  
Author(s):  
Jean Dolbeault ◽  
Ivan Gentil ◽  
Arnaud Guillin ◽  
Feng-Yu Wang
Keyword(s):  
Porous Media ◽  
Functional Inequalities ◽  
Porous Media Equations

Transport of coupled particles in rough ratchet driven by Lévy noise

2021 ◽  
Vol 31 (3) ◽  
pp. 033104
Author(s):  
Yao Song ◽  
Lijuan Ning
Keyword(s):  
Lévy Noise ◽  
Levy Noise

scholarly journals ORLICZ–POINCARÉ INEQUALITIES

2008 ◽  
Vol 51 (2) ◽  
pp. 529-543 ◽  
Author(s):  
Feng-Yu Wang
Keyword(s):  
Porous Media ◽  
Probability Measure ◽  
Poincaré Inequality ◽  
Dirichlet Forms ◽  
Sobolev Inequalities ◽  
Young Function ◽  
Poincare Inequality ◽  
Poincaré Inequalities ◽  
Poincare Inequalities ◽  
Porous Media Equations

AbstractCorresponding to known results on Orlicz–Sobolev inequalities which are stronger than the Poincaré inequality, this paper studies the weaker Orlicz–Poincaré inequality. More precisely, for any Young function $\varPhi$ whose growth is slower than quadric, the Orlicz–Poincaré inequality$$ \|f\|_\varPhi^2\le C\E(f,f),\qquad\mu(f):=\int f\,\mathrm{d}\mu=0 $$is studied by using the well-developed weak Poincaré inequalities, where $\E$ is a conservative Dirichlet form on $L^2(\mu)$ for some probability measure $\mu$. In particular, criteria and concrete sharp examples of this inequality are presented for $\varPhi(r)=r^p$ $(p\in[1,2))$ and $\varPhi(r)= r^2\log^{-\delta}(\mathrm{e} +r^2)$ $(\delta>0)$. Concentration of measures and analogous results for non-conservative Dirichlet forms are also obtained. As an application, the convergence rate of porous media equations is described.

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