• 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 Computing Science and Engineering
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• v.2 no.1
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• pp.98-108
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• 2008

Terrain reconstruction from images is an ill-posed, yet commonly desired Structure from Motion task when compositing visual effects into live-action photography. These surfaces are required for choreography of a scene, casting physically accurate shadows of CG elements, and occlusions. We present a novel framework for generating the geometry of landscapes from extremely noisy point cloud datasets obtained via limited resolution techniques, particularly optical flow based vision algorithms applied to live-action video plates. Our contribution is a new statistical approach to remove erroneous tracks ('outliers') by employing a unique combination of well established techniques-including Gaussian Mixture Models (GMMs) for robust parameter estimation and Radial Basis Functions (REFs) for scattered data interpolation-to exploit the natural constraints of this problem. Our algorithm offsets the tremendously laborious task of modeling these landscapes by hand, automatically generating a visually consistent, camera position dependent, thin-shell surface mesh within seconds for a typical tracking shot.

• Korea-Australia Rheology Journal
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• v.20 no.2
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• pp.51-58
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• 2008

This paper describes a two-step Tikhonov regularization procedure for converting the steady shear data generated by parallel-disk viscometers, in the presence of wall slip, into a shear stress-shear rate function and a wall shear stress-slip velocity functions. If the material under test has a yield stress or a critical wall shear stress below which no slip is observed the method will also provide an estimate of these stresses. Amplification of measurement noise is kept under control by the introduction of two separate regularization parameters and Generalized Cross Validation is used to guide the selection of these parameters. The performance of this procedure is demonstrated by applying it to the parallel disk data of an oil-in-water emulsion, of a foam and of a mayonnaise.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 2004.06a
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• pp.89-94
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• 2004

우리가 일반적으로 다루는 많은 대상들은 대부분 복잡하고 불규칙적인 형태를 지니고 있다. 이로 인해 보통 사용하는 미분연산자와 같은 전통의 수학적 기법들은 경우에 따라 심각한 불량 문제(ill-posed problem)를 야기하여 부정확한 결과를 나타내기도 한다. 이의 해결을 위해 전처리 과정으로 평활화를 위한 여러 가지 mean filter를 사용하기도 한다. 그렇지만 원 자료가 근본적으로 복잡한 경우 위 과정으로 오히려 중요 정보가 소실될 수도 있다. 이에 본 논문에서는 먼저 전처리로서 흔히 사용되는 각종 평균필터 대신 손실을 최소화하면서 곡면의 부드러움(smoothness)을 유도할 수 있는 접평면 접근 방식을 이용하고. 아울러 대상 영상의 복잡도에 연동한 프랙탈 차원을 적용하여 보다 효과적으로 영상의 경계를 추출하고자 했다.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.1-6
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• 2007

Two impedance imaging systems of multi-frequency electrical impedance tomography (MFEIT) and magnetic resonance electrical impedance tomography (MREIT) are described. MFEIT utilizes boundary measurements of current-voltage data at multiple frequencies to reconstruct cross-sectional images of a complex conductivity distribution (${\sigma}+i{\omega}{\varepsilon}$) inside the human body. The inverse problem in MFEIT is ill-posed due to the nonlinearity and low sensitivity between the boundary measurement and the complex conductivity. In MFEIT, we therefore focus on time- and frequency-difference imaging with a low spatial resolution and high temporal resolution. Multi-frequency time- and frequency-difference images in the frequency range of 10 Hz to 500 kHz are presented. In MREIT, we use an MRI scanner to measure an internal distribution of induced magnetic flux density subject to an injection current. This internal information enables us to reconstruct cross-sectional images of an internal conductivity distribution with a high spatial resolution. Conductivity image of a postmortem canine brain is presented and it shows a clear contrast between gray and white matters. Clinical applications for imaging the brain, breast, thorax, abdomen, and others are briefly discussed.

• Journal of Korea Water Resources Association
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• v.55 no.7
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• pp.545-556
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• 2022

It is recommended to use long-term hydrometeorological data for more than the service life of the hydraulic structures and water resource planning. For the purpose of expanding rainfall data, stochastic simulation models, such as Modified Bartlett-Lewis Rectangular Pulse (BLRP) and Neyman-Scott Rectangular Pulse (NSRP) models, have been widely used. The optimal parameters of the model can be estimated by repeatedly comparing the statistical moments defined through a combination of parameters of the probability distribution in the optimization context. However, parameter estimation using relatively small observed rainfall statistics corresponds to an ill-posed problem, leading to an increase in uncertainty in the parameter estimation process. In addition, as shown in previous studies, extreme values are underestimated because objective functions are typically defined by the first and second statistical moments (i.e., mean and variance). In this regard, this study estimated the parameters of the NSRP model using the objective function with the third moment and compared it with the existing approach based on the first and second moments in terms of estimation of extreme rainfall. It was found that the first and second moments did not show a significant difference depending on whether or not the skewness was considered in the objective function. However, the proposed model showed significantly improved performance in terms of estimation of design rainfalls.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.18 no.2
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• pp.23-28
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• 2004

In EIT, various image reconstruction algorithms have been used in order to compute the internal resistivity distribution of the unknown object with its electric potential data at the boundary. Mathematically the EIT image reconstruction algorithm is a nonlinear ill-posed inverse problem. In this paper, a SPSA approach is proposed for the solution of the EIT image reconstruction. Results of numerical experiments of EIT solved by the SPSA approach are presented and compared to that obtained by the modified Newton-Raphson(mNR) method.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.831-852
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• 2014

The obstacle shape reconstruction problem has been known to be difficult to solve since it is highly nonlinear and severely ill-posed. The use of local or locally supported basis functions for the problem has been addressed for many years. However, to the authors' knowledge, any research report on the proper usage of local or locally supported basis functions for the shape reconstruction has not been appeared in the literature due to many difficulties. The aim of this paper is to introduce the general concepts and methodologies for the proper choice and their implementation of locally supported basis functions through the two-dimensional Helmholtz equation. The implementations are based on the complex nonlinear parameter estimation (CNPE) formula and its robust algorithm developed recently by the authors. The basic concepts and ideas are simple. The derivation of the necessary properties needed for the shape reconstructions are elementary. However, the capturing abilities for the local geometry of the obstacle are superior to those by conventional methods, the trial and errors, due to the proper implementation and the CNPE algorithm. Several numerical experiments are performed to show the power of the proposed method. The fundamental ideas and methodologies described in this paper can be applied to many other shape reconstruction problems.

• Structural Engineering and Mechanics
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• v.56 no.5
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• pp.871-897
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• 2015

This paper presents a novel method based on sensitivity of structural response for identifying both the system parameters and input excitation force of a bridge. This method, referred to as "Adjoint Variable Method", is a sensitivity-based finite element model updating method. The computational cost of sensitivity analyses is the main concern associated with damage detection by these methods. The main advantage of proposed method is inclusion of an analytical method to augment the accuracy and speed of the solution. The reliable performance of the method to precisely indentify the location and intensity of all types of predetermined single, multiple and random damages over the whole domain of moving vehicle speed is shown. A comparison study is also carried out to demonstrate the relative effectiveness and upgraded performance of the proposed method in comparison to the similar ordinary sensitivity analysis methods. Moreover, various sources of error including the effects of noise and primary errors on the numerical stability of the proposed method are discussed.

• Structural Engineering and Mechanics
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• v.54 no.6
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• pp.1217-1244
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• 2015

In this research a theoretical and numerical study on a bridge damage detection procedure is presented based on vibration measurements collected from a set of accelerometers. This method, referred to as "Adjoint Variable Method", is a sensitivity-based finite element model updating method. The approach relies on minimizing a penalty function, which usually consists of the errors between the measured quantities and the corresponding predictions attained from the model. Moving mass is an interactive model and includes inertia effects between the model and mass. This interactive model is a time varying system and the proposed method is capable of detecting damage in this variable system. Robustness of the proposed method is illustrated by correct detection of the location and extension of predetermined single, multiple and random damages in all ranges of speed and mass ratio of moving vehicle. A comparative study on common sensitivity and the proposed method confirms its efficiency and performance improvement in sensitivity-based damage detection methods. In addition various possible sources of error, including the effects of measurement noise and initial assumption error in stability of method are also discussed.