Differential-difference regularization for a 2D inverse heat conduction problem

Qian, Zhi; Zhang, Qiang

doi:10.1088/0266-5611/26/9/095015

Cited by 11 publications

(3 citation statements)

References 23 publications

(63 reference statements)

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“…Several studies have been carried out in order to choose the regularization parameter [17,18]. Qian et al indicate for example how to choose the time step length and the spatial step length in order to obtain a stable numerical solution for a 2D inverse heat conduction problem [19]. In their published work [20], they studied first the regularization through equation modification and through truncation method of high frequency components, proposing a principle for solving an ill-posed 2D inverse heat conduction problem.…”

Section: Introductionmentioning

confidence: 99%

Real-time identification of PMSM losses through a novel past-time averaging method

Zeaiter¹,

Videcoq²,

Fénot³

2022

Inverse Problems

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The aim of this paper is the identification of unknown losses in a Permanent-Magnet Synchronous Motor (PMSM) through the thermal assessment of the motor behavior. These unknown losses can be sometimes hardly determined with analytical calculations. Their influence could be critical to some materials of the electric motor, such as windings and rotor, which are sensitive to hot-spot temperatures. The evaluation of the evolution of these unknown losses during cycles of mission is a crucial step in the motor conception phase. The applied method consists in solving a heat transfer inverse problem in real time. A new approach is used in this study for the regularization of the solution. It is based on a past-time averaging method. The work is numerically carried out based on a Lumped-Parameter Thermal Model (LPTM) developed for a high specific-power motor for the propulsion of hybrid aircrafts. Few reachable temperature nodes with known data are considered for the simulation. A dynamical mission profile is studied herein for a flight scenario of a hybrid aircraft, propelled by motors having around 1 MW of power. Three cases are investigated for the losses identification using the inverse technique. A study on the number of past time steps for the regularization of the ill-posed problem is presented. The results show that the thermal heat dissipated due to losses can be accurately estimated with an acceptable average error. The proposed procedure allows real-time determination of losses and monitoring of critical temperatures.

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Section: Introductionmentioning

confidence: 99%

Real-time identification of PMSM losses through a novel past-time averaging method

Zeaiter¹,

Videcoq²,

Fénot³

2022

Inverse Problems

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“…Most numerical methods for the SPE problem have been restricted to one-dimensional (1D) models, and only a few results are available in the 2D case [15,27,32,36,41,26,33]. To our knowledge, there are no papers presenting numerical algorithms for sideways parabolic Cauchy problems in two dimensions with variable coefficients.…”

Section: Introductionmentioning

confidence: 99%

Solving an Ill-Posed Cauchy Problem for a Two-Dimensional Parabolic PDE with Variable Coefficients Using a Preconditioned GMRES Method

Ranjbar¹,

Eldén²

2014

SIAM J. Sci. Comput.

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Abstract. The sideways parabolic equation (SPE) is a model of the problem of determining the temperature on the surface of a body from the interior measurements. Mathematically it can be formulated as a noncharacteristic Cauchy problem for a parabolic partial differential equation. This problem is severely ill-posed in an L 2 setting. We use a preconditioned generalized minimum residual method (GMRES) to solve a two-dimensional SPE with variable coefficients. The preconditioner is singular and chosen in a way that allows efficient implementation using the FFT. The preconditioner is a stabilized solver for a nearby problem with constant coefficients, and it reduces the number of iterations in the GMRES algorithm significantly. Numerical experiments are performed that demonstrate the performance of the proposed method.

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“…Motivated by the works [15,[19][20][21]24], we propose in this paper a general principle of constructing an e cient regularization method for solving the two-dimensional radially symmetric inverse heat conduction problem. The principle can be considered as a natural extension of the regularization methods proposed in [3][4][5] and serves to explain the e ectiveness of the numerical algorithm devised by Xiong [23].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of two-dimensional radially symmetric inverse heat conduction problem

Qian¹,

Hon²,

Xiong³

2014

Journal of Inverse and Ill-Posed Problems

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We investigate a two-dimensional radially symmetric inverse heat conduction problem, which is ill-posed in the sense that the solution does not depend continuously on input data. By generalizing the idea of kernel approximation, we devise a modi ed kernel in the frequency domain to reconstruct a numerical solution for the inverse heat conduction problem from the given noisy data. For the stability of the numerical approximation, we develop seven regularization techniques with some stability and convergence error estimates to reconstruct the unknown solution. Numerical experiments illustrate that the proposed numerical algorithm with regularization techniques provides a feasible and e ective approximation to the solution of the inverse and ill-posed problem.

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Differential-difference regularization for a 2D inverse heat conduction problem

Cited by 11 publications

References 23 publications

Real-time identification of PMSM losses through a novel past-time averaging method

Real-time identification of PMSM losses through a novel past-time averaging method

Solving an Ill-Posed Cauchy Problem for a Two-Dimensional Parabolic PDE with Variable Coefficients Using a Preconditioned GMRES Method

Numerical solution of two-dimensional radially symmetric inverse heat conduction problem

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