Dynamic characteristics for a hydro-turbine governing system with viscoelastic materials described by fractional calculus

Long, Yan; Xu, Beibei; Chen, Diyi; Ye, Wei

doi:10.1016/j.apm.2017.09.052

Cited by 22 publications

(6 citation statements)

References 33 publications

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“…FC is concerned with the calculation of real-order derivatives and integrals 4 . The FC has been successfully used to solve problems in circuit design 5 , artistic paintings 6 , vibration analysis 7 , hydro turbine systems 8 , control engineering 9 , 10 , nanotechnology 11 , and biological processes 12 , 13 . Fractional adaptive algorithms are used to estimate the parameters of power signals.…”

Section: Introductionmentioning

confidence: 99%

RETRACTED ARTICLE: Fractional boundary element solution of three-temperature thermoelectric problems

Fahmy

Almehmadi

Subhi

et al. 2022

Sci Rep

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The primary goal of this article is to propose a new fractional boundary element technique for solving nonlinear three-temperature (3 T) thermoelectric problems. Analytical solution of the current problem is extremely difficult to obtain. To overcome this difficulty, a new numerical technique must be developed to solve such problem. As a result, we propose a novel fractional boundary element method (BEM) to solve the governing equations of our considered problem. Because of the advantages of the BEM solution, such as the ability to treat problems with complicated geometries that were difficult to solve using previous numerical methods, and the fact that the internal domain does not need to be discretized. As a result, the BEM can be used in a wide variety of thermoelectric applications. The numerical results show the effects of the magnetic field and the graded parameter on thermal stresses. The numerical results also validate the validity and accuracy of the proposed technique.

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Section: Introductionmentioning

confidence: 99%

RETRACTED ARTICLE: Fractional boundary element solution of three-temperature thermoelectric problems

Fahmy

Almehmadi

Subhi

et al. 2022

Sci Rep

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“…Minimizing the objective function () by taking first‐order derivative and fractional derivative with respect to

{\hat{w}}_k

, 37,45 and combined with the negative gradient search, the conventional fractional least mean square (FLMS) algorithm is expressed as:

{\hat{w}}_k(n)={\hat{w}}_k\left(n-1\right)-\frac{\mu }{2}\frac{\partial J(n)}{\partial {\hat{w}}_k}-\frac{\mu_{fr}}{2}\frac{\partial^{fr}J(n)}{\partial {\hat{w}}_k^{fr}},

where

\mu

and

{\mu}_{fr}

are the step size parameter of the filter corresponding to first‐order derivative and fractional derivative of objective function,

k=0,1,\dots, M-1

.…”

Section: Proposed Auxiliary Model Based Normalized Fractional Adaptiv...mentioning

confidence: 99%

Design of auxiliary model and hierarchical normalized fractional adaptive algorithms for parameter estimation of bilinear‐in‐parameter systems

Yan-cheng

Chen

et al. 2022

Adaptive Control & Signal

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This study investigates the parameter identification issues of bilinear-in-parameter systems through fractional adaptive algorithms. An auxiliary model based 𝜀-normalized modified fractional least mean square algorithm is proposed for accelerating the parameter estimation accuracy based on the auxiliary model identification idea and the introduced convergence index, a normalized modified hierarchical fractional least mean square algorithm is presented for improving the computational efficiency based on the hierarchical identification principle. The proposed normalized fractional adaptive strategies are effective and could provide more accurate parameter estimates comparing with conventional counterparts for bilinear-in-parameter identification model based on the mean square error metrics and the average predicted output error.The effectiveness and accuracy of the proposed algorithms are further verified and validated through numerical simulations for different noise variances, fractional orders and gain parameters.

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“…The fractional order theory has been developed for more than 100 years and has been widely applied [10][11][12]. Various definitions of fractional order such as Grunwald-Letnikov (GL) definition, Riemann-Liouville (RL) definition and Caputo definition have been given by different scholars.…”

Section: Fractional Order Calculusmentioning

confidence: 99%

Nonlinear modeling of PEMFC based on fractional order subspace identification

Sun

et al. 2019

Asian Journal of Control

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Aiming at the multivariable, nonlinear and fractional‐order characteristics of proton exchange membrane fuel cell (PEMFC), this paper presents a nonlinear state space model based on a novel fractional Hammerstein model subspace identification theory. To reduce the complexity of modeling and choose the suitable input variables, canonical correlation analysis (CCA) method is used to select the most influential factors as the model input variables, and correlation analysis (CA) method is employed to remove the redundant input variables. To guarantee that the input‐output data are derivable at different fractional order, a Poisson moment function (PMF) is employed to construct the fractional order Hammerstein model with a six‐order polynomial as the front static nonlinear unit. To improve computing speed, a fractional differential short memory method (SMM) is proposed to reduce the computation cost of the identification algorithm. Meanwhile, a fuzzy genetic algorithm is adopted to acquire the best fractional order. Simulation results show that the fractional subspace identifying method can avoid fuel cell's internal complexity and PEMFC identification model can describe the working process of PEMFC accurately and quickly, which will provide an ideal control model for some advanced controller.

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Dynamic characteristics for a hydro-turbine governing system with viscoelastic materials described by fractional calculus

Cited by 22 publications

References 33 publications

RETRACTED ARTICLE: Fractional boundary element solution of three-temperature thermoelectric problems

RETRACTED ARTICLE: Fractional boundary element solution of three-temperature thermoelectric problems

Design of auxiliary model and hierarchical normalized fractional adaptive algorithms for parameter estimation of bilinear‐in‐parameter systems

Nonlinear modeling of PEMFC based on fractional order subspace identification

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