• Journal of the Korean Mathematical Society
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• v.38 no.4
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• pp.781-791
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• 2001

We consider the inverse conductivity problem to identify the unknown conductivity $textsc{k}$ as well as the domain D. We show hat, unlike the case when $textsc{k}$ is known, even a two or three dimensional ball may not be identified uniquely if the conductivity constant $textsc{k}$ is not known. We find a necessary and sufficient condition on the Cauchy data (u│∂Ω, g) for the uniqueness in identification of $textsc{k}$ and D. We also discuss on failure of stability.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.651-661
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• 2010

We consider the inverse problem of the identification of a piecewise-constant conductivity in a bar given the extra information of the heat flux through one end of the bar. Our theoretical results show that such an identification is unique. This approach utilizes a "layer peeling" argument. A computational algorithm based on this method is proposed and implemented. The advantage of this algorithm is that it requires only 3D minimizations irrespective of the number of the unknown discontinuities. Its numerical effectiveness is investigated for several conductivities.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2012.05a
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• pp.397-402
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• 2012

The objective of this study is the estimation of the two unknown thermal conductivity and thermal diffusivity by an inverse heat conduction analysis using the Levenberg-Marguardt method. One dimensional formulation of heat conduction problem in the model was applied. Two point transient temperature of test pieces and heat flux of inflow were measured under the high enthalpy flow environment. Estimated thermal conductivity and thermal diffusivity by an inverse analysis were compared with the known values of graphite test piece. It showed the effectiveness of proposed experimental inverse analysis.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.467-479
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• 2009

This paper ultimately aims to develop noninvasive techniques to identify the inside of a given electrical network. Based on the theory of the partial differentiation equations and mathematical modeling, this paper devises the algorithms to find the locations of possible abnormalities. To ensure the certainty of the algorithms, this study restricted the forms of the network and the number of abnormalities, rendering it easy to prove the uniqueness of the position of the abnormalities.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.4
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• pp.91-98
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• 2017

Electrical impedance tomography is a nondestructive imaging technique to reconstruct unknown conductivity distribution based on applied current data and measured voltage data through an array of electrodes attached on the periphery of a domain. In this paper, an inverse method based on truncated singular value decomposition is proposed to solve the inverse problem with the generalized Tikhonov regularization and to reconstruct the conductivity distribution. In order to reduce the inverse computational time, truncated singular value decomposition is applied to the inverse term after the generalized regularization matrix is taken out from the inverse matrix term. Numerical experiments and phantom experiments have been performed to verify the performance of the proposed method.

• Journal of IKEEE
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• v.25 no.4
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• pp.650-663
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• 2021

Subsurface topology estimation is an important factor in the geophysical survey. Electrical impedance tomography is one of the popular methods used for subsurface imaging. The EIT inverse problem is highly nonlinear and ill-posed; therefore, reconstructed conductivity distribution suffers from low spatial resolution. The subsurface region can be approximated as piece-wise separate regions with constant conductivity in each region; therefore, the conductivity estimation problem is transformed to estimate the shape and location of the layer boundary interface. Each layer interface boundary is treated as an open boundary that is described using front points. The subsurface domain contains multi-layers with very complex configurations, and, in such situations, conventional methods such as the modified Newton Raphson method fail to provide the desired solution. Therefore, in this work, we have implemented a 7-layer artificial neural network (ANN) as an inverse problem algorithm to estimate the front points that describe the multi-layer interface boundaries. An ANN model consisting of input, output, and five fully connected hidden layers are trained for interlayer boundary reconstruction using training data that consists of pairs of voltage measurements of the subsurface domain with three-layer configuration and the corresponding front points of interface boundaries. The results from the proposed ANN model are compared with the gravitational search algorithm (GSA) for interlayer boundary estimation, and the results show that ANN is successful in estimating the layer boundaries with good accuracy.

• Journal of the Korean Society of Safety
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• v.22 no.4
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• pp.13-19
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• 2007

An numerical method to estimate thermal diffusivity has been developed for one-dimensional unsteady heat conduction problem, when the temperatures are know at two positions in a semi-infinite body. Using the closed form solution which has already derived an explicit solution for the inverse problem for one-dimensional transient heat conduction using Laplace transform technique, we first estimate the surface temperature. The thermal diffusivity can be estimated by using the estimated surface temperature and measured temperatures, which include some uncertainties. The estimated surface heat flux and thermal diffusivity are found to be in good agreement with those of the experimented conditions. This method will be extended to the simultaneous measurement of thermal diffusivity and thermal conductivity.

• Journal of Energy Engineering
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• v.9 no.1
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• pp.37-40
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• 2000

An inverse problem is solved to determine the space-dependent thermal conductivity in one-dimensinoal time-dependent heat conduction medium with the data imposed and measured at the two end-points. The thermal conductivity is approximated as a linear combination of known functions with unknown coefficients and the unknowns are obtained by the governing and sensitivity equations using modified Newton-Raphson method. The estimated results are compared with exact thermal conductivities and it shows good agreements. This approach is expected to be used to estimate spatial composition of heat conduction medium.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.333-369
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• 2001

칼데론 문제와 유한번 측정 역전도체 문제에 대한 중요한 결과들을 설명하고, 그 응용으로서 전기임피던스 영상기법에 대하여 설명한다.

• Journal of the Korea institute for structural maintenance and inspection
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• v.16 no.4
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• pp.99-106
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• 2012

This study presents estimation method of temperature-dependent thermal conductivity by using solution of inverse heat conduction problem. Time and depth temperature distribution data from full-scale fire test were used for estimating temperature-dependent thermal conductivity on hybrid-fiber reinforced shield tunnel lining. At short heating time, estimated thermal conductivity sharply decreased within $100^{\circ}C$. On the other hand, it reflected thermal properties of concrete and effect of steel fiber at heating time of measured maximum heating temperature. Thus arbitrary time should be determined to estimate temperature-dependent thermal conductivity in time zone of measured maximum heating temperature. Estimated temperature-dependent thermal conductivity is similar to results of other study.