Ways of allowing fora priori information in regularizing gradient algorithms

Rumyantsev, S. A.

doi:10.1007/bf00871290

Cited by 4 publications

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“…To define thermophysical parameters of electric devices based on the solution of an inverse heat transfer problem we shall use a conjugate gradient method (Alifanov et al, 1995), (Dinh and Reinhardt, 1998), (Rumyantsev, 1985). It is an iterative process of minimizing the objective function…”

Section: Computational Algorithmmentioning

confidence: 99%

Defining Thermophysical Parameters of Electric Devices Based on Solution of Inverse Heat Transfer Problem

Bachvalov¹,

Gorbatenko²,

Grechikhin³

2015

MAS

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This paper describes application of the study methods based on the solution of inverse problems of mathematical physics to define thermophysical parameters of electric devices. The mathematical model of the device is developed based on equations of non-stationary heat conductivity. The algorithm to define thermohysical parameters is developed; this algorithm uses the finite element method to solve a direct heat transfer problem and the gradient method to minimize the objective function. Examples of the algorithm application are given. The problem to define an equivalent heat transfer coefficient of the solenoid area covered with heavy winding and a heat emission from its inside surface is considered. In the second example thermophysical parameters of electromagnetic valve actuator of an ICE (internal combustion engine) gas distribution mechanism are defined. The obtained results show that thermophysical parameters and temperature distribution in non-stationary and steady-state operating conditions of electrical devices may be evaluated with adequate efficiency based on the solution of inverse heat transfer problems.

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Section: Computational Algorithmmentioning

confidence: 99%

Defining Thermophysical Parameters of Electric Devices Based on Solution of Inverse Heat Transfer Problem

Bachvalov¹,

Gorbatenko²,

Grechikhin³

2015

MAS

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“…Two advantages of these methods are that they have had rigorous mathematical investigation and that they can be applied very generally. They are clearly very important methods that have been used to solve a great variety of inverse problems [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], including IHCP, as well as problems of parameters determination and shape identification. However, the generality comes at the expense of greater computational and programming burdens.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional inverse heat conduction problems solution via lagrange theory and model size reduction techniques

Barrio

2003

Inverse Problems in Engineering

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This article is concerned with inverse heat conduction problems (IHCP) involving large-scale linear systems (i.e. multidimensional systems) with unknown sources or boundary conditions. The inverse problem is stated as an optimisation problem with a regularised quadratic objective functional, and it is solved using Lagrange theory. We demonstrate that the IHCP solution is obtained by simple time integration of a state-variable model: the inverse model, which is analytically derived from the so called direct and adjoint problems. In addition, we show that the number of differential equations in the inverse model can be strongly reduced without a significant loss of precision. The inversion is then carried out in three main steps: calculation of the full-order inverse model, size reduction, and time integration of the resulting reduced-order inverse model. A numerical example of heat sources identification in a 2D diffusion problem shows the performances and the accuracy of the proposed approach.

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“…Gradient methods of numerical solution of inverse heat-conduction problems have been developed in many works, mainly in [1][2][3]. In particular, the problem of identification of the nonlinear thermal-conductivity coefficient λ(T) has been considered in [3][4][5][6]. In [1-3, 7, 8], gradient methods have been used for restoration and evaluation of the power of heat sources.…”

mentioning

confidence: 99%

“…As far as the operators K ni * (i = 0, 1 ___ ) are concerned, in [3][4][5], consideration is given to the method of computation of K n0 * , which is associated with the replacement of variables in a double integral. Since this method involves certain difficulties in numerical realization of the algorithm, in [3] and in other works, use is made of the finite-dimensional approximation…”

mentioning

confidence: 99%

“…At the same time, this reduction has drawbacks due to the uncertainty in selection of both basis functions and the number of these functions, i.e., of the parameter m characterizing the degree of approximation of the sought function λ(T). This problem may be solved to some extent with the use of qualitative a priori information on the solution sought [3,5]. We propose another approach to construction of the conjugate operator K n0 * , which enables us to obtain quite an acceptable numerical scheme of calculation of K n0 * values.…”

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confidence: 99%

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Functional Identification of the Nonlinear Thermal-Conductivity Coefficient by Gradient Methods. I. Conjugate Operators

Borukhov

Тимошпольский

2005

J Eng Phys Thermophys

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UDC 536.2Consideration is given to the gradient methods of solution of the inverse heat-conduction problem on determination of the nonlinear coefficient λ(T) without its preliminary finite-dimensional approximation.Introduction. Gradient methods of numerical solution of inverse heat-conduction problems have been developed in many works, mainly in [1][2][3]. In particular, the problem of identification of the nonlinear thermal-conductivity coefficient λ(T) has been considered in [3][4][5][6]. In [1-3, 7, 8], gradient methods have been used for restoration and evaluation of the power of heat sources.One problem frequently arising when gradient methods are used is numerical realization of the values of conjugate (adjoint) operators. For example, in the case of identification of λ(T), the operator conjugate to the internal-superposition operator (other names [9]: the substitution operator, the weighted-shift operator, the operator of replacement of a variable, and the composite operator) is present in the scheme of the method of conjugate gradients. The wellknown approach presented in [3] leads to a complex and difficult-to-control procedure of computation of the values of the operator conjugate to the internal-superposition operator. Therefore, a finite-dimensional approximation of the sought nonlinear coefficients by any system of basis functions has been used in [3] and in subsequent works, thus reducing inverse heat-conduction problems to a problem of restoration of a finite number of parameters. In this connection, such approaches to solution of inverse heat-conduction problems are frequently called parametric ones.In the present work, we consider heat-conduction problems without preliminary approximation of the functions sought. Such an approach is conventionally called functional (or finite-dimensional) identification. Functional identification of the nonlinear thermal-conductivity coefficient by gradient methods is based on new representations of the operator conjugate to the internal-superposition operator; these representations enable one to obtain formulas of the values of a conjugate operator, which are convenient for numerical calculations. We note that similar representations were used earlier in the theory of controlled integro-differential and functional-differential systems [10][11][12].The results of the work are presented in two papers. In the first paper, we describe the algorithm of functional identification of the coefficient λ(T); the emphasis is on finding the gradient of the square of the residual functional for λ(T) in the space L 2 [T (1) , T (2) ] of functions summable with the square and in the Sobolev space W 2 [T

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Ways of allowing fora priori information in regularizing gradient algorithms

Cited by 4 publications

References 0 publications

Defining Thermophysical Parameters of Electric Devices Based on Solution of Inverse Heat Transfer Problem

Defining Thermophysical Parameters of Electric Devices Based on Solution of Inverse Heat Transfer Problem

Multidimensional inverse heat conduction problems solution via lagrange theory and model size reduction techniques

Functional Identification of the Nonlinear Thermal-Conductivity Coefficient by Gradient Methods. I. Conjugate Operators

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