Deep learning-based parameter estimation of stochastic differential equations driven by fractional Brownian motions with measurement noise

Feng, Jing; Wang, Xiaolong; Liu, Qi; Li, Yongge; Xu, Yong

doi:10.1016/j.cnsns.2023.107589

Cited by 11 publications

(1 citation statement)

References 51 publications

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“…Additionally, the Hermite process, denoted by (1) for q = 2, is referred to as the Rosenblatt process. Most of the studies [18][19][20] involved fBm because of its self-similarity, long-range dependence, and more straightforward calculus of the Gaussian. But, fBm fails in the concrete case of having non-Gaussianity smooth-tongued in the models.…”

Section: Introductionmentioning

confidence: 99%

Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process

AlNemer,

Hosny,

Udhayakumar

et al. 2024

Mathematics

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Under the effect of the Rosenblatt process, time-delay systems of nonlinear stochastic delay differential equations are considered. Utilizing the delayed matrix functions and exact solutions for these systems, the existence and Hyers–Ulam stability results are derived. First, depending on the fixed point theory, the existence and uniqueness of solutions are proven. Next, sufficient criteria for the Hyers–Ulam stability are established. Ultimately, to illustrate the importance of the results, an example is provided.

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Section: Introductionmentioning

confidence: 99%

Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process

AlNemer,

Hosny,

Udhayakumar

et al. 2024

Mathematics

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Fusing deep learning features for parameter identification of a stochastic airfoil system

Feng,

Wang,

Liu

et al. 2024

Nonlinear Dyn

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Deep learning architectures for data-driven damage detection in nonlinear dynamic systems under random vibrations

Joseph,

Quaranta,

Carboni

et al. 2024

Nonlinear Dyn

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The primary goal of structural health monitoring is to detect damage at its onset before it reaches a critical level. In the present work an in-depth investigation addresses deep learning applied to data-driven damage detection in nonlinear dynamic systems. In particular, autoencoders and generative adversarial networks are implemented leveraging on 1D convolutional neural networks. The onset of damage is detected in the investigated nonlinear dynamic systems by exciting random vibrations of varying intensity, without prior knowledge of the system or the excitation and in unsupervised manner. The comprehensive numerical study is conducted on dynamic systems exhibiting different types of nonlinear behavior. An experimental application related to a magneto-elastic nonlinear system is also presented to corroborate the conclusions.

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Deep learning-based parameter estimation of stochastic differential equations driven by fractional Brownian motions with measurement noise

Cited by 11 publications

References 51 publications

Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process

Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process

Fusing deep learning features for parameter identification of a stochastic airfoil system

Deep learning architectures for data-driven damage detection in nonlinear dynamic systems under random vibrations

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