Frequency Domain Estimation of Spatially Varying Parameters in Heat and Mass Transport

Das, Amritam; Weiland, S.; Berkel, M. van

doi:10.23919/acc.2019.8814465

Cited by 5 publications

(13 citation statements)

References 22 publications

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“…Problem 1 is infinite dimensional with no known analytic solution for z(x, t). Therefore, this section approximates the infinite dimensional problem by creating a finite dimensional model following the methodology from [17].…”

Section: Finite Dimensional Frequency Domain Problemmentioning

confidence: 99%

“…Here, A(θ) and B(θ) contain the boundary conditions, are linear affine in θ, and defined in [17]. The -observation-matrix C maps states to output.…”

Section: Semi-discretizationmentioning

confidence: 99%

“…In the literature for distributed parameter systems, different error criteria are proposed to calculate the parameters. The commonly used criterion is the output error criterion [6]- [8], [11], [17] and the rarely used equation error criterion [7] which we will use in the frequency domain to derive a closed-form solution for the unknown parameters.…”

Section: Semi-discretizationmentioning

confidence: 99%

“…The commonly used cost function is the output error criterion which is the sum of the squared error between solution z(x, t; γ) for a given γ and measurements y(t), i.e., with observation map C that maps state to output. This criterion is transformed into the frequency domain such that the output error criterion for Problem 2 and [17] is given by…”

Section: A Output Error Criterionmentioning

confidence: 99%

“…Hence, we can uniquely and directly -without iteration-determine the diffusivity, convectivity, reactivity, and the source -as function of space-, simultaneously. Combining this with advances in 1) modern frequency domain signal processing to reduce noise and removing the initial condition [14], [15]; 2) recent innovations in dealing with experimentally unknown boundary conditions [16]; 3) a wide variety of functions to spatially parameterize transport [17]. This results in a highly versatile and fast method to acquire reliable estimates of the spatially varying parameters.…”

Section: Introductionmentioning

confidence: 99%

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A Closed-Form Solution to Estimate Spatially Varying Parameters in Heat and Mass Transport

Kampen

Das

Weiland

et al. 2021

IEEE Control Syst. Lett.

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This paper presents a closed-form solution to estimate space-dependent transport parameters of a linear one dimensional diffusion-transport-reaction equation. The infinite dimensional problem is approximated by a finite dimensional model by 1) taking a frequency domain approach, 2) linear parameterization of the unknown parameters, and 3) using a semidiscretization. Assuming full state knowledge, the commonly used output error criterion is rewritten as the equation error criterion such that the problem results in linear least squares. The optimum is then given by a closed-form solution, avoiding computational expensive optimization methods. Functioning of the proposed method is illustrated by means of simulation.

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Section: Finite Dimensional Frequency Domain Problemmentioning

confidence: 99%

“…Here, A(θ) and B(θ) contain the boundary conditions, are linear affine in θ, and defined in [17]. The -observation-matrix C maps states to output.…”

Section: Semi-discretizationmentioning

confidence: 99%

Section: Semi-discretizationmentioning

confidence: 99%

Section: A Output Error Criterionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Closed-Form Solution to Estimate Spatially Varying Parameters in Heat and Mass Transport

Kampen

Das

Weiland

et al. 2021

IEEE Control Syst. Lett.

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LPMLEn–A Frequency Domain Method to Estimate Vertical Streambed Fluxes and Sediment Thermal Properties in Semi‐Infinite and Bounded Domains

Kampen

Schneidewind

Anibas

et al. 2022

Water Resources Research

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This paper presents the LPMLEn, a new method to estimate vertical flux and thermal diffusivity from streambed temperature time series using the frequency domain. The main advantages of this new method are: (a) the use of multiple frequencies and multiple sensors for the parameter estimation; (b) noise/uncertainty handling in an optimal way; (c) the possibility to estimate the parameters with both semi‐infinite and bounded domain models; and (d) the compensation for temperature drifts in the data known as transients. The capabilities of the LPMLEn are demonstrated using both synthetic and field data, highlighting the advantages of the bounded domain model over the semi‐infinite domain model in the parameter estimation process.

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A novel frequency domain maximum likelihood approach for estimating transport coefficients in cylindrical geometry for nuclear fusion devices

Berkel

Oosterwegel

Anthonissen

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper introduces a novel maximum likelihood approach to determine the local thermal transport coefficients belonging to diffusion and convection from excitation (perturbative) transport experiments. It extends previous work developed for linear (slab) geometry to cylindrical (toroidal) geometry for fusion reactors. The previous linear geometry approach is based on analytic solutions of the partial differential equation. However, for cylindrical geometries with convection the analytic solutions are confluent hypergeometric functions (CHFs) with complex valued arguments. Most numerical libraries do not support CHFs evaluation with complex valued arguments. Hence, this paper proposes the use of an ultra-fast transfer function evaluation based on sparse numerical solutions for the discretized partial differential equation. This solution is implemented in MATLAB © and incorporated in the frequency domain Maximum Likelihood Estimation framework. Consequently, transport coefficients can be estimated consistently when measurements are perturbed by coloured and spatially correlated noise.

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Frequency Domain Estimation of Spatially Varying Parameters in Heat and Mass Transport

Cited by 5 publications

References 22 publications

A Closed-Form Solution to Estimate Spatially Varying Parameters in Heat and Mass Transport

A Closed-Form Solution to Estimate Spatially Varying Parameters in Heat and Mass Transport

LPMLEn–A Frequency Domain Method to Estimate Vertical Streambed Fluxes and Sediment Thermal Properties in Semi‐Infinite and Bounded Domains

A novel frequency domain maximum likelihood approach for estimating transport coefficients in cylindrical geometry for nuclear fusion devices

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