A new computational scheme on quantitative inner pipe boundary identification based on the estimation of effective thermal conductivity

Fan, Chenglei; Sun, Fengrui; Li, Yahui

doi:10.1088/0022-3727/41/20/205501

Cited by 8 publications

(3 citation statements)

References 16 publications

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“…There is a considerable amount of literature available, dealing with both theoretical and computational aspects of both the individual problems, i.e. estimation of the Robin coefficient or estimation of the domain shape, see e.g [1][2][3][5][6][7][8][9][10][11][12][13][14][15], as well as of the problem of joint estimation [16][17][18][19][20][21][22][23][24][25][26]. We also mention the works [27,28], in which a similar problem is considered using a generalized impedance boundary condition.…”

Section: Introductionmentioning

confidence: 99%

Joint estimation of Robin coefficient and domain boundary for the Poisson problem

Nicholson¹,

Niskanen²

2021

Inverse Problems

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We consider the problem of simultaneously inferring the heterogeneous coeﬃcient ﬁeld for a Robin boundary condition on an inaccessible part of the boundary along with the shape of the boundary for the Poisson problem. Such a problem arises in, for example, corrosion detection, and thermal parameter estimation. We carry out both linearised uncertainty quantiﬁcation, based on a local Gaussian approximation, and full exploration of the joint posterior using Markov chain Monte Carlo (MCMC) sampling. By exploiting a known invariance property of the Poisson problem, we are able to circumvent the need to re-mesh as the shape of the boundary changes. The linearised uncertainty analysis presented here relies on a local linearisation of the parameter-to-observable map, with respect to both the Robin coeﬃcient and the boundary shape, evaluated at the maximum a posteriori (MAP) estimates. Computation of the MAP estimate is carried out using the Gauss-Newton method. On the other hand, to explore the full joint posterior we use the Metropolis-adjusted Langevin algorithm (MALA), which requires the gradient of the log-posterior. We thus derive both the Fréchet derivative of the solution to the Poisson problem with respect to the Robin coeﬃcient and the boundary shape, and the gradient of the log-posterior, which is eﬃciently computed using the so-called adjoint approach. The performance of the approach is demonstrated via several numerical experiments with simulated data.

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Section: Introductionmentioning

confidence: 99%

Joint estimation of Robin coefficient and domain boundary for the Poisson problem

Nicholson¹,

Niskanen²

2021

Inverse Problems

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“…In the inverse progress, a virtual surface is defined, and the unknown boundary shape is obtained by the temperature on the virtual surface. Fan et al (2008, 2009) proposed an indirect method to identify the unknown geometry shape. The boundary shape is transformed into a standard model by a transform method and the inverse problem is solved by identifying the effective thermal conductivities.…”

Section: Introductionmentioning

confidence: 99%

Identification of pipe inner surface in heat conduction problems by deep learning and effective thermal conductivity transform

Chen¹,

et al. 2020

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Purpose The purpose of this paper is to develop a transform method and a deep learning model to identify the inner surface shape based on the measurement temperature at the outer boundary of the pipe. Design/methodology/approach The training process is assisted by the finite element method (FEM) simulation which solves the direct problem for the data preparation. To avoid re-meshing the domain when the inner surface shape varies, a new transform method is proposed to transform the shape identification problem into the effective thermal conductivity identification problem. The deep learning model is established to set up the relationship between the measurement temperature and the effective thermal conductivity. Then the unknown geometry shape is acquired by the mapping between the inner shape and the effective thermal conductivity through the inverse transform method. Findings The new method is successfully applied to identify the internal boundary of a pipe with eccentric circle, ellipse and nephroid inner geometries. The results show that as the measurement points increased and the measurement error decreased, the results became more accurate. The position of the measurement point and mesh density of the FEM model have less effect on the results. Originality/value The deep learning model and the transform method are developed to identify the pipe inner surface shape. There is no need to re-mesh the domain during the computation progress. The results show that the proposed method is a fast and an accurate tool for identifying the pipe inner surface.

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mentioning

confidence: 99%

Joint Estimation of Robin Coefficient and Domain Boundary for the Poisson Problem

Nicholson,

Niskanen

2021

Preprint

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We consider the problem of simultaneously inferring the heterogeneous coefficient field for a Robin boundary condition on an inaccessible part of the boundary along with the shape of the boundary for the Poisson problem. Such a problem arises in, for example, corrosion detection, and thermal parameter estimation. We carry out both linearised uncertainty quantification, based on a local Gaussian approximation, and full exploration of the joint posterior using Markov chain Monte Carlo (MCMC) sampling. By exploiting a known invariance property of the Poisson problem, we are able to circumvent the need to re-mesh as the shape of the boundary changes. The linearised uncertainty analysis presented here relies on a local linearisation of the parameter-to-observable map, with respect to both the Robin coefficient and the boundary shape, evaluated at the maximum a posteriori (MAP) estimates. Computation of the MAP estimate is carried out using the Gauss-Newton method. On the other hand, to explore the full joint posterior we use the Metropolis-adjusted Langevin algorithm (MALA), which requires the gradient of the log-posterior. We thus derive both the Fréchet derivative of the solution to the Poisson problem with respect to the Robin coefficient and the boundary shape, and the gradient of the log-posterior, which is efficiently computed using the so-called adjoint approach. The performance of the approach is demonstrated via several numerical experiments with simulated data.

show abstract

A new computational scheme on quantitative inner pipe boundary identification based on the estimation of effective thermal conductivity

Cited by 8 publications

References 16 publications

Joint estimation of Robin coefficient and domain boundary for the Poisson problem

Joint estimation of Robin coefficient and domain boundary for the Poisson problem

Identification of pipe inner surface in heat conduction problems by deep learning and effective thermal conductivity transform

Joint Estimation of Robin Coefficient and Domain Boundary for the Poisson Problem

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