scholarly journals Stochastic hydrodynamic-type evolution equations driven by Lévy noise in 3D unbounded domains—Abstract framework and applications

2014 ◽  
Vol 124 (6) ◽  
pp. 2052-2097 ◽  
Author(s):  
Elżbieta Motyl
Keyword(s):  
Evolution Equations ◽  
Unbounded Domains ◽  
Hydrodynamic Type ◽  
Lévy Noise ◽  
Levy Noise ◽  
Abstract Framework

Optimal relaxed control of stochastic hereditary evolution equations with Lévy noise

2019 ◽  
Vol 25 ◽  
pp. 61
Author(s):  
Utpal Manna ◽  
Debopriya Mukherjee
Keyword(s):  
Evolution Equations ◽  
Galerkin Approximation ◽  
Existence Theory ◽  
Lévy Noise ◽  
Young Measures ◽  
Optimal Controls ◽  
Relaxed Control ◽  
Abstract Theory ◽  
Control Sets ◽  
Levy Noise

Existence theory of optimal relaxed control problem for a class of stochastic hereditary evolution equations driven by Lévy noise has been studied. We formulate the problem in the martingale sense of Stroock and Varadhan to establish existence of optimal controls. The construction of the solution is based on the classical Faedo–Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod theorem for nonmetric spaces, and certain compactness properties of the class of Young measures on Suslin metrizable control sets. As application of the abstract theory, Oldroyd and Jeffreys fluids have been studied and existence of optimal relaxed control is established. Existence and uniqueness of a strong solution and uniqueness in law for the two-dimensional Oldroyd and Jeffreys fluids are also shown.

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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