Experimental design of measurements for the solution of coefficient-type inverse heat-conduction problems

Artyukhin, E. A.

doi:10.1007/bf00878208

Cited by 9 publications

(10 citation statements)

References 1 publication

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“…However, they differ from the conventional design tests [1,7,13,14,21,23]. The difference is the transition from the implicit to the explicit form of the identification error.…”

Section: Definition 2 R-optimal Observation Design Is a Measurement mentioning

confidence: 93%

“…A very large number of investigations, combing experimental and mathematical activities, have been devoted to the reconstruction of the specific heat and thermal conductivity [2-5, 9-12, 16, 24]. The final trend in the development of heat inverse theory is a design of experiments [1,6,7,13,14,[18][19][20][21]23]. The efforts in this direction are focused on the advance of numerical methods to determine the optimum conditions to conduct the experiment.…”

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confidence: 99%

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Heat experiment design to estimate temperature dependent thermal properties

Romanovskii¹

2008

J. Phys.: Conf. Ser.

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Abstract. Experimental conditions are studied to optimize transient experiments for estimating temperature dependent thermal conductivity and volumetric heat capacity. A mathematical model of a specimen is the one-dimensional heat equation with boundary conditions of the second kind. Thermal properties are assumed to vary nonlinearly with temperature. Experimental conditions refer to the thermal loading scheme, sampling times and sensor location. A numerical model of experimental configurations is studied to elicit the optimal conditions. The numerical solution of the design problem is formulated on a regularization scheme with a stabilizer minimization without a regularization parameter. An explicit design criterion is used to reveal the optimal sensor location, heating duration and flux magnitude. Results obtained indicate that even the strongly nonlinear experimental design problem admits the aggregation of its solution and has a strictly defined optimal measurement scheme. Additional region of temperature measurements with allowable identification error is revealed. IntroductionThe estimation of thermal properties as a solution of an inverse problem is constantly of great interest in the theory of ill-posed problems. A very large number of investigations, combing experimental and mathematical activities, have been devoted to the reconstruction of the specific heat and thermal conductivity [2-5, 9-12, 16, 24]. The final trend in the development of heat inverse theory is a design of experiments [1,6,7,13,14,[18][19][20][21]23]. The efforts in this direction are focused on the advance of numerical methods to determine the optimum conditions to conduct the experiment. The rules on the choice of various optimal experimental variables, including sensor locations, sampling times and heat loading are studied.To design experiment the investigation of the state function sensitivity over the sought quantities is mainly executed. The sensitivity approach gives very important information on mathematical model features. However, in the framework of the sensitivity approach a number of theoretically and practically important questions remain unanswered.The major open question is the existence of the structure of the design problem solution. The requirement of the structure seeking means that the typical classes of the problem solutions should be revealed. The basic feature of the structure is a similar behaviour of a certain set of solutions. By virtue of it, the respective change of the initial data will not vary the nature of the optimal design solution. Therefore, the absence of the structure knowledge limits the received solution only to a narrow particular field. On the other hand, the determination of the design solution structure indicates the typical cases of the identification error behaviour and specifies the ways of the design generalization. In total, the general solution of the design problem is divided into certain classes of the optimal experimental conditions, in the framework of which the best measurement ...

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“…However, they differ from the conventional design tests [1,7,13,14,21,23]. The difference is the transition from the implicit to the explicit form of the identification error.…”

Section: Definition 2 R-optimal Observation Design Is a Measurement mentioning

confidence: 93%

mentioning

confidence: 99%

Heat experiment design to estimate temperature dependent thermal properties

Romanovskii¹

2008

J. Phys.: Conf. Ser.

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“…The minimization of the confidence region given by Eq. (12) can be obtained by maximizing the determinant of V À1 , in the so-called D-optimum design [11][12][13][14][15]. Since the covariance matrix V is given by Eq.…”

Section: Design Of Optimum Experimentsmentioning

confidence: 99%

“…In this article, we extend the analysis of [8,10] to address the choice of the magnitudes of the applied heat fluxes and of the body dimensions, by using the D-optimum experimental design [11][12][13][14][15]. A transformation, that maps the heat conduction equation for an orthotropic material into the heat conduction equation for an isotropic material [16], is utilized to choose such experimental variables, so that parameters with identical relative accuracies can be obtained.…”

Section: Introductionmentioning

confidence: 99%

“…It basically consists in examining a priori some kind of measure of the accuracy of the estimated quantities in order to choose experimental variables, such as the number and location of sensors, experimental duration, etc., so that minimum variance estimates are obtained via the inverse analysis. Different approaches can be found in the literature, taking into account different measures of the accuracy of the estimated parameters, for the optimum experimental design [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Effects of the Heating Process and Body Dimensions on the Estimation of the Thermal Conductivity Components of Orthotropic Solids

Mejias

Orlande

Özişik

2003

Inverse Problems in Engineering

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In this article, we design the experiment for estimating the thermal conductivity components of an orthotropic medium, with respect to the solid dimensions and to the magnitude of the fluxes that are used to heat the solid. The D-optimum approach is used in the experimental design. By using a transformation that maps the heat conduction equation for an orthotropic medium into the heat conduction equation for an isotropic medium, we show that thermal conductivity components with identical relative accuracies can be estimated by appropriately selecting the experimental variables under picture. The Levenberg-Marquardt method is applied for the solution of the present parameter estimation problem by using simulated temperature measurements.

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Optimal sensor placement for structural parameter identification

Chisari

Macorini

Amadio

et al. 2016

Struct Multidisc Optim

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The identification of model material parameters is often required when assessing existing structures, in damage analysis and structural health monitoring. A typical procedure considers a set of experimental data for a given problem and the use of a numerical or analytical model for the problem description, with the aim of finding the material characteristics which give a model response as close as possible to the experimental outcomes. Since experimental results are usually affected by errors and limited in number, it is important to specify sensor position(s) to obtain the most informative data. This work proposes a novel method for optimal sensor placement based on the definition of the representativeness of the data with respect to the global displacement field. The method employs an optimisation procedure based on Genetic Algorithms and allows for the assessment of any sensor layout independently from the actual inverse problem solution. Two numerical applications are presented, which show that the representativeness of the data is connected to the error in the inverse analysis solution. These also confirm that the proposed approach, where different practical constraints can be added to the optimisation procedure, can be effective in decreasing the instability of the parameter identification process

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Experimental design of measurements for the solution of coefficient-type inverse heat-conduction problems

Cited by 9 publications

References 1 publication

Heat experiment design to estimate temperature dependent thermal properties

Heat experiment design to estimate temperature dependent thermal properties

Effects of the Heating Process and Body Dimensions on the Estimation of the Thermal Conductivity Components of Orthotropic Solids

Optimal sensor placement for structural parameter identification

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