Solution of the nonlinear inverse thermal conductivity problem by the iteration method

Alifanov, O. M.; Mikhailov, V. V.

doi:10.1007/bf01104861

Cited by 87 publications

(28 citation statements)

References 3 publications

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“…Equations (50)- (51)), and according to (53) the heat source function at the final time g(t f ) remains at its initial guess g 0 (t f ). The difficulty encountered at the final time can be alleviated by employing the following modification suggested by Alifanov [15]. We seek a continuously differentiable function g(t) such that…”

Section: The Optimal Step Length (I) Is Obtained By Differentiating Fmentioning

confidence: 99%

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Solution of a multidimensional inverse radiation problem by means of mode reduction

Park

Sung

2004

Numerical Meth Engineering

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SUMMARYThe Karhunen-Loève Galerkin procedure is employed to solve an inverse radiation problem of determining the time-varying strength of a heat source, which mimics flames in a furnace, from temperature measurements in three-dimensional participating media where radiation and conduction occur simultaneously. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, using a conjugate gradient method. Through the Karhunen-Loève Galerkin procedure, one can represent the system dynamics with a minimum degree of freedom, and consequently the amount of computation required in the solution of the inverse problem is reduced drastically when the present technique is adopted.

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Section: The Optimal Step Length (I) Is Obtained By Differentiating Fmentioning

confidence: 99%

“…The inverse algorithm employing the full model may be summarized as The difficulty encountered at the final time is also resolved by employing the modification suggested by Alifanov [15], which is explained in detail in the previous section.…”

mentioning

confidence: 99%

Solution of a multidimensional inverse radiation problem by means of mode reduction

Park

Sung

2004

Numerical Meth Engineering

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“…The equations of the boundary-value problem in the computation of @i(z~, l),i=l, n, for the IHCP formulation under consideration are written analogously to the equation in [2].…”

Section: Q~o)-[:i(t)]e~(l T R~)dtmentioning

confidence: 99%

“…Considering qo(t) as a certain control function minimizing functional (13), by following the methodology elucidated in [2], the equation of this problem can be written as…”

Section: L(t) Ot~(i T)mentioning

confidence: 99%

Solution of the inverse boundary-value problem of heat conduction in an overdefined formulation

Alifanov¹,

Mikhailov²

1983

Journal of Engineering Physics

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An interaction scheme is considered for the solution of a nonlinear inverse heatconduction problem with the results of measuring the temperature at an arbitrary number of points within the body taken into account.In solving inverse heat-conduction problems (IHCP), formulations of the IHCP with the least number of temperature sensors needed from which the information will assure uniqueness of the solution of the problem are distinguished from overdefined formulations when the number of temperature sensors installed is greater than is required from the uniqueness condition.Installation of additional sensors permits more complete information to be obtained about the thermal state of the body and the error in determining the temperatures and thermal fluxes on its surface from the solution of the IHCP to be reduced.It is here expedient to use an extremal form of the problem with an iterative principle for regularization of the solution [i].

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“…It is more difficult than that of the determination of the thermophysical properties of the temporal-dependent type and the spatial-dependent type. In order to calculate this inverse problem, there have appeared certain progress of the methodologies in this issue, including the Laplace transformation method [1], the conjugate gradient method [2][3][4], the least-square method [5], the linear inverse method [6][7][8], the Davidon-Fletcher-Powell method [9], the Kirchhoff and other transformation methods [10][11][12], and the boundary element method [13], as well as the finite difference method [14,15].…”

Section: Introductionmentioning

confidence: 99%

Identification of temperature‐dependent thermophysical properties in a partial differential equation subject to extra final measurement data

Liu

2007

Numerical Methods Partial

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We consider an inverse problem for estimating the two coefficient functions c and k in a parabolic type partial differential equation c(u)u t = ∂[k(u)u x ]/∂x with the aid of the measurements of u at two different times. The first-and second-order one-step group preserving schemes are developed. Solving the resultant algebraic equations with a closed-form, we can estimate the unknown temperature-dependent thermal conductivity and heat capacity. The new methods possess threefold advantages: they do not require any a priori information on the functional forms of thermal conductivity and heat capacity; no initial guesses are required; and no iterations are required. Numerical examples are examined to show that the new approaches have high accuracy and efficiency, even there are rare measured data. When the measured temperatures are polluted by uniform or normal random noise, the estimated results are also good.

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Solution of the nonlinear inverse thermal conductivity problem by the iteration method

Cited by 87 publications

References 3 publications

Solution of a multidimensional inverse radiation problem by means of mode reduction

Solution of a multidimensional inverse radiation problem by means of mode reduction

Solution of the inverse boundary-value problem of heat conduction in an overdefined formulation

Identification of temperature‐dependent thermophysical properties in a partial differential equation subject to extra final measurement data

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