Low-frequency dynamics of systems with modulated high-frequency stochastic excitation

Kremer, Eugen

doi:10.1016/j.jsv.2018.08.053

Cited by 16 publications

(12 citation statements)

References 9 publications

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“…In this paper, we focus on the use of stochastic differential equations (SDEs), which are ordinary differential equations driven by certain noise, for formulating an optimal control problem of a stand‐alone PV system. So far, both mechanistic and conceptual system dynamics have been efficiently described with SDEs of supporting rigorous mathematical analysis results. SDEs have been utilized for describing key elements in renewable energy systems, such as wind speed, solar irradiance forecasting, and water balance in a hydropower reservoir .…”

Section: Introductionmentioning

confidence: 99%

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

Yoshioka

Yano

2019

Appl Stoch Models Bus & Ind

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The operation of a stand‐alone photovoltaic (PV) system ultimately aims for the optimization of its energy storage. We present a mathematical model for cost‐effective control of a stand‐alone system based on a PV panel equipped with an angle adjustment device. The model is based on viscosity solutions to partial differential equations, which serve as a new and mathematically rigorous tool for modeling, analyzing, and controlling PV systems. We formulate a stochastic optimal switching problem of the panel angle, which is here a binary variable to be dynamically controlled under stochastic weather condition. The stochasticity comes from cloud cover dynamics, which is modeled with a nonlinear stochastic differential equation. In finding the optimal control policy of the panel angle, switching the angle is subject to impulsive cost and reduces to solving a system of Hamilton‐Jacobi‐Bellman quasi‐variational inequalities (HJBQVIs). We show that the stochastic differential equation is well posed and that the HJBQVIs admit a unique viscosity solution. In addition, a finite‐difference scheme is proposed for the numerical discretization of HJBQVIs. A demonstrative computational example of the HJBQVIs, with emphasis on a stand‐alone experimental system, is finally presented with practical implications for its cost‐effective operation.

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Section: Introductionmentioning

confidence: 99%

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

Yoshioka

Yano

2019

Appl Stoch Models Bus & Ind

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“…Cf. also papers [11–13], e.g. in [11,13] effects of high-frequency stochastic excitation on low-frequency dynamics of systems are analysed.…”

Section: On the Vibrational Resonance Phenomenon And Replacing Noise With High-frequency Excitations For Bi-stable Systemsmentioning

confidence: 99%

On representing noise by deterministic excitations for interpreting the stochastic resonance phenomenon

Sorokin

Demidov²

2021

Phil. Trans. R. Soc. A.

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Adding noise to a system can ‘improve’ its dynamic behaviour, for example, it can increase its response or signal-to-noise ratio. The corresponding phenomenon, called stochastic resonance, has found numerous applications in physics, neuroscience, biology, medicine and mechanics. Replacing stochastic excitations with high-frequency ones was shown to be a viable approach to analysing several linear and nonlinear dynamic systems. For these systems, the influence of the stochastic and high-frequency excitations appears to be qualitatively similar. The present paper concerns the discussion of the applicability of this ‘deterministic’ approach to stochastic systems. First, the conventional nonlinear bi-stable system is briefly revisited. Then dynamical systems with multiplicative noise are considered and the validity of replacing stochastic excitations with deterministic ones for such systems is discussed. Finally, we study oscillatory systems with nonlinear damping and analyse the effects of stochastic and deterministic excitations on such systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

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“…There is a multitude of articles considering the dynamic behaviour of stochastic systems under combined deterministic and noise excitations, cf., e.g. Berdichevsky and Gitterman (1999), Blekhman and Kremer (2019), Blekhman and Sorokin (2018), Gammaitoni et al (1998), Kremer (2018), Lingala et al (2017a, 2017b), Namachchivaya and Sowers (2001), Sorokin and Blekhman (2019), Wedig (1990), Wiesenfeld and Moss (1995), Ying and Ni (2017) and Yurchenko et al (2013). A major research effort is concerned with the analysis and application of the stochastic resonance phenomenon, which exhibits itself, for example, in nonlinear systems with additive noise (Gammaitoni et al, 1998; Wiesenfeld and Moss, 1995) and linear systems with multiplicative noise (Berdichevsky and Gitterman, 1999).…”

Section: Introductionmentioning

confidence: 99%

Vibrations of a nonlinear stochastic system with a varying mass under near resonant excitation

Sorokin

2019

Journal of Vibration and Control

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Dynamics of a nonlinear second order system with a stochastically varying mass is considered in the article. The system is under an external time-harmonic loading, which is assumed to be near resonant. Damping, excitation strength, nonlinearity, and mass variations are considered to be of the same order of smallness. Under these assumptions, an explicit approximate solution of the problem is obtained using the multiple scales perturbation method. The leading (zero) order component of the solution is not affected by noise, whereas the first order component is stochastic and is energetically unstable because of mass variations. This implies that the considered oscillator will not vibrate in the near resonant regime because of mass variations. Instead, its vibrations will feature a considerable, but limited in amplitude, stochastic component. These vibrations will be stable, which illustrates a qualitative difference of the phenomenon from the motion instability described previously for linear stochastic oscillators for lower values of damping. The presence of the nonlinearity does not considerably affect the stability. To avoid the phenomenon, damping in the system should be increased so as to be much larger than mass variations. The obtained results were validated by a series of numerical experiments. The oscillator can be considered as a simplified model of machines used for processing of granular materials, such as vibrating screens, and the results are relevant for various applications, including mining industry.

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Low-frequency dynamics of systems with modulated high-frequency stochastic excitation

Cited by 16 publications

References 9 publications

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

An optimal switching approach toward cost‐effective control of a stand‐alone photovoltaic panel system under stochastic environment

On representing noise by deterministic excitations for interpreting the stochastic resonance phenomenon

Vibrations of a nonlinear stochastic system with a varying mass under near resonant excitation

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