• 대한수학회지
• /
• 제38권4호
• /
• pp.781-791
• /
• 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
• /
• 제28권3_4호
• /
• pp.651-661
• /
• 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.

• 한국추진공학회:학술대회논문집
• /
• 한국추진공학회 2012년도 제38회 춘계학술대회논문집
• /
• pp.397-402
• /
• 2012

본 논문에서는 미지의 두 열물성 값인 열전도율과 열확산율을 구하기 위하여 Levenberg-Marquardt 방법에 의한 역해석 기법을 도입하였다. 일차원 열전도 문제에 대하여 연산식을 유도하였으며, 시편에 대하여 두 지점의 온도 및 입력유동의 열유속 측정값을 적용하였다. 예측된 열전도율 및 열확산율은 알려진 그라파이트 시편에 대한 열물성 값과 비교하였으며 그 결과 본 논문에서 제시된 역해석 예측 기법 실험의 유효성이 파악되었다.

• 대한수학회논문집
• /
• 제24권3호
• /
• pp.467-479
• /
• 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.

• 전자공학회논문지
• /
• 제54권4호
• /
• pp.91-98
• /
• 2017

전기 임피던스 단층촬영 기법은 도메인의 표면에 부착된 전극들을 통해 주입된 전류와 측정된 전압 데이터를 기반으로, 미지의 도전율 분포를 복원하는 비파괴 기술이다. 이 논문에서는 전기 임피던스 단층촬영법에서 일반적 Tikhonov 조정을 갖는 역문제를 풀고 도전율 분포를 복원하기 위해 절단된 특이값 분해 기반의 역문제 해법을 제안하였다. 역문제 계산시간을 줄이기 위해 일반 조정행렬을 역행렬 항목에서 분리시키고 절단된 특이값 분해 방법을 적용하였다. 제안한 방법의 성능을 검증하기 위해 모의실험과 팬텀실험을 수행하고 복원결과를 비교하였다.

• 전기전자학회논문지
• /
• 제25권4호
• /
• pp.650-663
• /
• 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.

• 한국안전학회지
• /
• 제22권4호
• /
• pp.13-19
• /
• 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.

• 에너지공학
• /
• 제9권1호
• /
• pp.37-40
• /
• 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.

• 대한수학회논문집
• /
• 제16권3호
• /
• pp.333-369
• /
• 2001

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

• 한국구조물진단유지관리공학회 논문집
• /
• 제16권4호
• /
• pp.99-106
• /
• 2012

본 연구는 콘크리트의 열전도 역문제의 해를 통해 온도의존적 열전도도를 추정하는 방법을 제안하였다. 온도의존적 열전도도의 추정은 실물모형 화재실험에서 측정된 하이브리드 섬유보강 쉴드터널 라이닝의 시간 및 깊이별 온도분포 데이터를 이용하였다. 추정된 온도의존적 열전도도는 실험시간이 짧은 시점에서는 상온 영역에서 열전도도의 급격한 감소가 나타나는 것으로 추정되었다. 반면 깊이 25mm 위치에서 최대온도가 측정된 실험시간대에서는 온도에 따른 콘크리트의 특성변화 및 강섬유 혼입 효과를 반영하고 있다. 따라서 온도의존적 열전도도 추정 시 가열면 부근에서 최대온도가 측정된 시점을 기준으로 실험시간을 결정해야 한다. 추정된 열전도도는 유사배합을 사용한 기존연구와 유사한 결과를 나타내고 있다.