Parameter estimation for the generalized fractional element network Zener model based on the Bayesian method

Wang, Fan; Jiang, Xiaoyun; Qi, Haitao

doi:10.1016/j.physa.2015.02.037

Cited by 50 publications

(23 citation statements)

References 31 publications

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“…In this paper, we study the derivative order estimation, trough Bayesian approach, for a fractional logistic model. Fan et al, [17,18] give evidence of the effectiveness to solve inverse problems under the Bayesian perspective in fractional models. In [8] we can find in detail the Bayesian approach for inverse problems.…”

Section: Bayesian Estimationmentioning

confidence: 99%

Bayesian Derivative Order Estimation for a Fractional Logistic Model

et al. 2020

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In this paper, we consider the inverse problem of derivative order estimation in a fractional logistic model. In order to solve the direct problem, we use the Grünwald-Letnikov fractional derivative, then the inverse problem is tackled within a Bayesian perspective. To construct the likelihood function, we propose an explicit numerical scheme based on the truncated series of the derivative definition. By MCMC samples of the marginal posterior distributions, we estimate the order of the derivative and the growth rate parameter in the dynamic model, as well as the noise in the observations. To evaluate the methodology, a simulation was performed using synthetic data, where the bias and mean square error are calculated, the results give evidence of the effectiveness for the method and the suitable performance of the proposed model. Moreover, an example with real data is presented as evidence of the relevance of using a fractional model.

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Section: Bayesian Estimationmentioning

confidence: 99%

Bayesian Derivative Order Estimation for a Fractional Logistic Model

et al. 2020

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“…The likelihood function in the Bayesian method is always taken as

p false(boldy false| ρ false) = \frac{1}{{false(2 π v_{σ} false)}^{n false/ 2}} \cdot \exp ((), - \frac{{false(Q false(ρ false) - boldy false)}^{T} false(Q false(ρ false) - boldy false)}{2 v_{σ}}),

where y is the experimental data vector, v σ is the variance of the independent identically distributed Gauss random noise contained in experimental data, and n is the length of y .…”

Section: Parameter Estimationmentioning

confidence: 99%

Efficient and accurate spectral method for the time‐fractional dual‐phase‐lag heat transfer model and its parameter estimation

Zheng

Jiang

Zhang

2019

Math Methods in App Sciences

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In the current paper, a heat transfer model is suggested based on a time‐fractional dual‐phase‐lag (DPL) model. We discuss the model in two parts, the direct problem and the inverse problem. Firstly, for solving it, the finite difference/Legendre spectral method is constructed. In the temporal direction, we employ the weighted and shifted Grünwald approximation, which can achieve second order convergence. In the spatial direction, the Legendre spectral method is used, it can obtain spectral accuracy. The stability and convergence are theoretically analyzed. For the inverse problem, the Bayesian method is used to construct an algorithm to estimate the four parameters for the model, namely, the time‐fractional order α, the time‐fractional order β, the delay time τT, and the relaxation time τq. Next, numerical experiments are provided to demonstrate the effectiveness of our scheme, with the values of τq and τT for processed meat employed. We also make a comparison with another method. The data obtained for the direct problem are used in the parameter estimation. The paper provides an accurate and efficient numerical method for the time‐fractional DPL model.

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“…The inverse problems [4,5] approach involves the estimation of unknown parameters that can be determined by using experimental data and solutions from DEs. A commonly used technique in an inverse problem is the Least Squares method in which the sums of the squares of the residuals of the model solution estimates and the experimental data is minimised.…”

Section: Inverse Problemsmentioning

confidence: 99%

Simultaneous estimation of tracer kinetic model parameters using analytical and inverse approaches with a hybrid method

Kokulan

Hai

George

et al. 2019

International Journal of Computer Mathematics

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The inverse problem approach to Tracer Kinetic Modelling (TKM) using dynamic positron-emission tomography (PET) images is important in identifying the kinetic parameters and then quantifying the tracer concentrations in the region of interest. In parameter estimation, knowledge of good initial approximations to the parameters is essential. The aim of this paper is to extend existing work on an inverse method for tracer kinetics by proposing an improved hybrid method integrated with an analytic solution in a multi-objective formulation of the inverse method. The analytical solution is derived through the use of the Laplace transformation technique. This integrated approach will be compared against other parameter estimation techniques in terms of computational efficiency and accuracy.

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Parameter estimation for the generalized fractional element network Zener model based on the Bayesian method

Cited by 50 publications

References 31 publications

Bayesian Derivative Order Estimation for a Fractional Logistic Model

Bayesian Derivative Order Estimation for a Fractional Logistic Model

Efficient and accurate spectral method for the time‐fractional dual‐phase‐lag heat transfer model and its parameter estimation

Simultaneous estimation of tracer kinetic model parameters using analytical and inverse approaches with a hybrid method

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