Optimal Selection of Measurement Locations in a Conductor for Approximate Determination of Temperature Distributions

Cannon, John R.; Klein, Richard E.

doi:10.1115/1.3426496

Cited by 23 publications

(7 citation statements)

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“…They have been done under the same setting involving reduced modeling that is presented in this work. More generally, the problem of optimal sensor placement has been extensively studied since the 1970's in control and systems theory (see, e.g., 35‐37 ). One common feature with References 22,34 is that the criterion to be minimized by the optimal location is nonconvex, which leads to potential difficulties when the number of sensors is large.…”

Section: Reconstruction Methodsmentioning

confidence: 99%

Reconstructing haemodynamics quantities of interest from Doppler ultrasound imaging

Galarce

Lombardi

Mula

2020

Numer Methods Biomed Eng

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The present contribution deals with the estimation of haemodynamics Quantities of Interest by exploiting Ultrasound Doppler measurements. A fast method is proposed, based on the Parameterized Background Data‐Weak (PBDW) method. Several methodological contributions are described: a sub‐manifold partitioning is introduced to improve the reduced‐order approximation, two different ways to estimate the pressure drop are compared, and an error estimation is derived. A fully synthetic test‐case on a realistic common carotid geometry is presented, showing that the proposed approach is promising in view of realistic applications.

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Section: Reconstruction Methodsmentioning

confidence: 99%

Reconstructing haemodynamics quantities of interest from Doppler ultrasound imaging

Galarce

Lombardi

Mula

2020

Numer Methods Biomed Eng

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“…Continuous optimization algorithms have been proposed for computing the optimal sensor location, see e.g. [1,6,16]. One common feature with our approach is that the criterion to be minimized by the optimal location is non-convex, which leads to potential difficulties when the number of sensors is large.…”

Section: Remark 12mentioning

confidence: 99%

Greedy Algorithms for Optimal Measurements Selection in State Estimation Using Reduced Models

Binev¹,

Cohen²,

Mula³

et al. 2018

SIAM/ASA J. Uncertainty Quantification

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We consider the problem of optimal recovery of an unknown function u in a Hilbert space V from measurements of the form j (u), j = 1, . . . , m, where the j are known linear functionals on V . We are motivated by the setting where u is a solution to a PDE with some unknown parameters, therefore lying on a certain manifold contained in V . Following the approach adopted in [12,5], the prior on the unknown function can be described in terms of its approximability by finite-dimensional reduced model spaces (V n ) n≥1 where dim(V n ) = n. Examples of such spaces include classical approximation spaces, e.g. finite elements or trigonometric polynomials, as well as reduced basis spaces which are designed to match the solution manifold more closely. The error bounds for optimal recovery under such priors are of the form µ(V n , W m )ε n , where ε n is the accuracy of the reduced model V n and µ(V n , W m ) is the inverse of an inf-sup constant that describe the angle between V n and the space W m spanned by the Riesz representers of ( 1 , . . . , m ). This paper addresses the problem of properly selecting the measurement functionals, in order to control at best the stability constant µ(V n , W m ), for a given reduced model space V n . Assuming that the j can be picked from a given dictionary D we introduce and analyze greedy algorithms that perform a sub-optimal selection in reasonable computational time. We study the particular case of dictionaries that consist either of point value evaluations or local averages, as idealized models for sensors in physical systems. Our theoretical analysis and greedy algorithms may therefore be used in order to optimize the position of such sensors.

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“…We must mention that the problem we are dealing with was discussed by Tihonov and Glasko [9], who especially stressed its numerical aspects. Stability estimates have been obtained, by methods quite different from ours and in a different functional setting, by Cannon [2], [3], [4], [5]. Similar problems have been discussed by Anderssen and Saull [1], Glasko, Zaharov and Kolp [6] and P. Manselli and K. Miller [7].…”

Section: Introductionmentioning

confidence: 69%

“…As 0(A)/X increases with X, (2.12) and (1.6) give (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) In view of the expansion of (/>"' (see lemma below) the estimates (i), (ii) have been established.…”

Section: H« X (O-)hmentioning

confidence: 98%

A note on an ill-posed problem for the heat equation

Talenti¹,

Vessella²

1982

J Aust Math Soc A

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In this paper an ill-posed problem for the heat equation is investigated. Solutions u to the equation u, -u xx = 0, which are approximately known on the positive half-axis t = 0 and on some vertical lines x -xj,... ,x = x n , are considered and stability estimates of these solutions are presented. We assume an a priori bound, governing the heat flow across the boundary x = 0. 1980 Mathematics subject classification (Amer. Math. Soc): 35 K 05.

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Optimal Selection of Measurement Locations in a Conductor for Approximate Determination of Temperature Distributions

Cited by 23 publications

References 0 publications

Reconstructing haemodynamics quantities of interest from Doppler ultrasound imaging

Reconstructing haemodynamics quantities of interest from Doppler ultrasound imaging

Greedy Algorithms for Optimal Measurements Selection in State Estimation Using Reduced Models

A note on an ill-posed problem for the heat equation

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