Fractional frequency domain identification of NaCl–glucose solutions at physiological levels

Olarte, Oscar; Barbé, Kurt; Moer, Wendy Van; Ingelgem, Yves Van

doi:10.1016/j.measurement.2013.12.041

Cited by 7 publications

(4 citation statements)

References 32 publications

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“…Proposition. The estimation of the TF coefficients c l, k are computed by solving the following optimization problem ∥ ∥ ( ) c arg min subject to 15 holds c (16) The proof is found as in appendix. The solution is however very noise sensitive due to the constraint.…”

Section: Digital Computation Of a Taylor-fourier Analysismentioning

confidence: 99%

“…The idea of the proof is that we make an explicit construc tion of the operator F in (13) through solving the optimization problem (16). To compute an analytical solution of this optim ization we introduce the Lagrange multiplicator Λ ∈ × R N where ′ a denotes the trans pose of the vector a.…”

Section: A2 Proof Of the Propositionmentioning

confidence: 99%

“…Although one is not interested in the difusion component, ignoring this effect in classical dynam ical models introduces a bias in the parameters of interest. To circumvent this problem fractional order models may be part icularly helpful as illustrated in [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

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Taylor–Fourier spectra to study fractional order systems

Barbé¹,

Lauwers²,

Fuentes³

2016

Meas. Sci. Technol.

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In measurement science mathematical models are often used as an indirect measurement of physical properties which are mapped to measurands through the mathematical model. Dynamical systems describing a physical process with a dominant diffusion or dispersion phenomenon requires a large dimensional model due to its long memory. Ignoring a dominant difussion or dispersion component acts as a confounder which may introduce a bias in the estimated quantities of interest. For linear systems it has been observed that fractional order models outperform classical rational forms in terms of the number of parameters for the same fitting error. However it is not straightforward to deal with a fractional order system or long memory effects without prior knowledge. Since the parametric modeling of a fractional system is very involved, we put forward the question whether fractional insight can be gathered in a nonparametric way. In this paper we show that classical Fourier basis leading to the frequency response function lacks fractional insight. To circumvent this problem, we introduce a fractional Taylor-Fourier basis to obtain nonparametric insight in the fractional system. This analysis proposes a novel type of spectrum to visualize the spectral content of a fractional system: Taylor-Fourier spectrum. This spectrum is fully measurement driven which can be used as a first to explore the fractional dynamics of a measured diffusion or dispersion system.

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Section: Digital Computation Of a Taylor-fourier Analysismentioning

confidence: 99%

Section: A2 Proof Of the Propositionmentioning

confidence: 99%

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Taylor–Fourier spectra to study fractional order systems

Barbé¹,

Lauwers²,

Fuentes³

2016

Meas. Sci. Technol.

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“…The fractional-order transfer function of a voltammetric electronic tongue system is approximated through identification in [11]. The impedance response of NaClglucose solutions is identified from measurements in [19].…”

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confidence: 99%

Frequency Response and Transfer Functions of Large Self-similar Networks

Ni¹

2020

Preprint

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This paper focuses on computing the frequency response and transfer functions for large self-similar networks under different circumstances. Modeling large scale systems is difficult due, typically, to the dimension of the problem, and self-similarity is the characteristic we exploit to make the problem more tractable. For each circumstance, we propose algorithms to obtain both transfer functions and frequency response, and we show that finite networks' dynamics are integer order, while infinite networks are fractional order or irrational. Based on that result, we also show that the effect of varying a network's operating condition to its dynamics can always be isolated, which is then expressed as a multiplicative disturbance acting upon a nominal plant. In addition, we analyze the non-integer-order nature residing in infinite dimensional systems in the context of selfsimilar networks. Finally, leveraging the main result of this paper, we also illustrate its capability of approximating some irrational expressions by using rational functions.

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Fractional-order identification and synthesis of equivalent circuit for electrochemical system based on pulse voltammetry

Kumar

Ghosh

2022

Fractional-Order Design

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Fractional frequency domain identification of NaCl–glucose solutions at physiological levels

Cited by 7 publications

References 32 publications

Taylor–Fourier spectra to study fractional order systems

Taylor–Fourier spectra to study fractional order systems

Frequency Response and Transfer Functions of Large Self-similar Networks

Fractional-order identification and synthesis of equivalent circuit for electrochemical system based on pulse voltammetry

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