• Communications for Statistical Applications and Methods
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• 제21권5호
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• pp.395-409
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• 2014

Data limited, partial, or incomplete are known as an ill-posed problem. If the data with ill-posed problems are analyzed by traditional statistical methods, the results obviously are not reliable and lead to erroneous interpretations. To overcome these problems, we propose a dual generalized maximum entropy (dual GME) estimator for panel data regression models based on an unconstrained dual Lagrange multiplier method. Monte Carlo simulations for panel data regression models with exogeneity, endogeneity, or/and collinearity show that the dual GME estimator outperforms several other estimators such as using least squares and instruments even in small samples. We believe that our dual GME procedure developed for the panel data regression framework will be useful to analyze ill-posed and endogenous data sets.

• Structural Monitoring and Maintenance
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• 제3권3호
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• pp.195-214
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• 2016

Monitoring of impact loads is a very important technique in the field of structural health monitoring (SHM). However, in most cases it is not possible to measure impact events directly, so they need to be reconstructed. Impact load reconstruction refers to the problem of estimating an input to a dynamic system when the system output and the impulse response function are usually known. Generally this leads to a so called ill-posed inverse problem. It is reasonable to use prior knowledge of the force in order to develop more suitable reconstruction strategies and to increase accuracy. An impact event is characterized by a short time duration and a spatial concentration. Moreover the force time history of an impact has a specific shape, which also can be taken into account. In this contribution these properties of the external force are employed to create a sample-force-dictionary and thus to transform the ill-posed problem into a sparse recovery task. The sparse solution is acquired by solving a minimization problem known as basis pursuit denoising (BPDN). The reconstruction approach shown here is capable to estimate simultaneously the magnitude of the impact and the impact location, with a minimum number of accelerometers. The possibility of reconstructing the impact based on a noisy output signal is first demonstrated with simulated measurements of a simple beam structure. Then an experimental investigation of a real beam is performed.

• International Journal of Air-Conditioning and Refrigeration
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• 제8권2호
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• pp.11-22
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• 2000

Holographic interferometric tomography can provide reconstruction of instantaneous three-dimensional gross flow fields. The technique however confronts ill-posed reconstruction problems in practical applications. Experimental data are usually limited in projection and angular scanning when a field is captured instantaneously or under the obstruction of test models and test section enclosures. An algorithm, based on a series expansion method, has been developed to improve the reconstruction under the ill-posed conditions. A three-dimensional natural convection flow around two interacting isothermal cubes is experimentally investigated. The flow can provide a challenging reconstruction problem and lend itself to accurate numerical solution for comparison. The refractive index fields at two horizontal sections of the thermal plume with and without an opaque object are reconstructed at a limited view angle of 80$\circ$. The experimental reconstructions are then compared with those from numerical calculation and thermocouple thermometry. It confirms that the technique is applicable to reconstruction of reasonably complex, three-dimensional flow fields.

• 대한수학회지
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• 제44권6호
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• pp.1397-1415
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• 2007

We consider an inverse heat conduction problem(IHCP) in a quarter plane which appears in some applied subjects. We want to determine the heat flux on the surface of a body from a measured temperature history at a fixed location inside the body. This is a severely ill-posed problem in the sense that arbitrarily "small" differences in the input temperature data may lead to arbitrarily "large" differences in the surface flux. A semi-discrete central difference scheme in time is employed to deal with the ill posed problem. We obtain some error estimates which also give the information about how to choose the step length in time. Some numerical examples illustrate the effects of the proposed method.

• 대한수학회논문집
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• 제16권3호
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• pp.487-508
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• 2001

We consider the Cauchy problem for Laplacian. Using the single layer representation, we obtain an equivalent system of boundary integral equations. We show the singular values of the ill-posed Cauchy operator decay exponentially, which means that a small error is exponentially amplified in the solution of the Cauchy problem. We show the decaying rate is dependent on the geometry of he domain, which provides the information on the choice of numerically meaningful modes. We suggest a pseudo-inverse regularization method based on singular value decomposition and present various numerical simulations.

• 대한전자공학회논문지SP
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• 제46권5호
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• pp.15-24
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• 2009

Compressed sensing은 소수의 선형 관측으로부터 sparse 신호를 복원하는 문제를 언급하고 있다. 최근 벡터 경우에서의 성공적인 연구 결과가 행렬의 경우로 확장되었다. Low-rank 행렬의 compressed sensing은 ill-posed inverse problem을 low-rank 정보를 이용하여 해결한다. 본 문제는 rank 최소화 혹은 low-rank 근사의 형태로 나타내질 수 있다. 본 논문에서는 최근 제안된 여러 가지 효율적인 알고리즘에 대한 survey를 제공한다.

• 대한수학회지
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• 제55권4호
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• pp.849-875
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• 2018

The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and N inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.

• Communications for Statistical Applications and Methods
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• 제23권1호
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• pp.71-83
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• 2016

In this paper we discuss a deconvolution density estimator obtained using the support vector machines (SVM) and Tikhonov's regularization method solving ill-posed problems in reproducing kernel Hilbert space (RKHS). A remarkable property of SVM is that the SVM leads to sparse solutions, but the support vector deconvolution density estimator does not preserve sparsity as well as we expected. Thus, in section 3, we propose another support vector deconvolution estimator (method II) which leads to a very sparse solution. The performance of the deconvolution density estimators based on the support vector method is compared with the classical kernel deconvolution density estimator for important cases of Gaussian and Laplacian measurement error by means of a simulation study. In the case of Gaussian error, the proposed support vector deconvolution estimator shows the same performance as the classical kernel deconvolution density estimator.

• 설비공학논문집
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• 제11권6호
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• pp.749-757
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• 1999

Holographic interferornetric tomography can provide reconstruction of instantaneous three dimensional gross flow fields. The technique however confronts ill-posed reconstruction problems in practical applications. Experimental data are usually limited in projection and angular scanning when a field is captured instantaneously or under the obstruction of test models and test section enclosures. An algorithm, based on a series expansion method, has been developed to improve the reconstruction under the ill-posed conditions. A three-dimensional natural convection flow around two interacting isothermal cubes is experimentally investigated. The flow can provide a challenging reconstruction problem and lend itself to accurate numerical solution for comparison. The refractive index fields at two horizontal sections of the thermal plume with and without an opaque object are reconstructed at a limited view angle of 80" The experimental reconstructions are then compared with those from numerical calculation and thermocouple thermometry. It confirms that the technique is applicable to reconstruction of reasonably complex, three-dimensional flow fields.elds.

• Journal of Electrical Engineering and Technology
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• 제4권3호
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• pp.365-369
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• 2009

Identification is considered to be among the main applications of inverse theory and its objective for a given physical system is to use data which is easily observable, to infer some of the geometric parameters which are not directly observable. In this paper, a parameter identification method using inverse problem methodology is proposed. The minimisation of the objective function with respect to the desired vector of design parameters is the most important procedure in solving the inverse problem. The conjugate gradient method is used to determine the unknown parameters, and Tikhonov's regularization method is then used to replace the original ill-posed problem with a well-posed problem. The simulation and experimental results are presented and compared.