• Proceedings of the KSME Conference
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• 2000.04b
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• pp.144-147
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• 2000

A numerical method for the solution of one-dimensional inverse heat conduction problem is established and its performance is demonstrated with computational results. The present work introduces the maximum entropy method in order to build a robust formulation of the inverse problem. The maximum entropy method finds the solution that maximizes the entropy functional under given temperature measurement. The philosophy of the method is to seek the most likely inverse solution. The maximum entropy method converts the inverse problem to a non-linear constrained optimization problem of which constraint is the statistical consistency between the measured temperature and the estimated temperature. The successive quadratic programming facilitates the maximum entropy estimation. The gradient required fur the optimization procedure is provided by solving the adjoint problem. The characteristic feature of the maximum entropy method is discussed with the illustrated results. The presented results show considerable resolution enhancement and bias reduction in comparison with the conventional methods.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• Nuclear Engineering and Technology
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• v.21 no.3
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• pp.193-204
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• 1989

This paper develops a new method for reconstructing neutron flux distribution, that is based on the maximum entropy Principle in information theory. The Probability distribution that maximizes the entropy Provides the most unbiased objective Probability distribution within the known partial information. The partial information are the assembly volume-averaged neutron flux, the surface-averaged neutron fluxes and the surface-averaged neutron currents, that are the results of the nodal calculation. The flux distribution on the boundary of a fuel assembly, which is the boundary condition for the neutron diffusion equation, is transformed into the probability distribution in the entropy expression. The most objective boundary flux distribution is deduced using the results of the nodal calculation by the maximum entropy method. This boundary flux distribution is then used as the boundary condition in a procedure of the imbedded heterogeneous assembly calculation to provide detailed flux distribution. The results of the new method applied to several PWR benchmark problem assemblies show that the reconstruction errors are comparable with those of the form function methods in inner region of the assembly while they are relatively large near the boundary of the assembly. The incorporation of the surface-averaged neutron currents in the constraint information (that is not done in the present study) should provide better results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.7 s.250
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• pp.787-793
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• 2006

Recently kriging model has been widely used in the DACE (Design and Analysis of Computer Experiment) because of prominent predictability of nonlinear response. Since DACE has no random or measurement errors contrast to physical experiment, space filling experimental design that distributes uniformly design points over whole design space should be employed as a sampling method. In this paper, we examine the maximum entropy experimental design that reveals the space filling strategy in which defines the maximum entropy based on Gaussian or exponential. The influence of these two correlation functions on space filling design and their model parameters are investigated. Based on the exploration of numerous numerical tests, enhanced maximum entropy design based on exponential correlation function is suggested.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.11a
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• pp.571-572
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• 2007

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.54 no.1
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• pp.38-53
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• 2018

The purpose of this study is to estimate potential yield (PY) for Korean west coast fisheries using the holistic production method (HPM). HPM involves the use of surplus production models to apply input data of catch and standardized fishing efforts. HPM compared the estimated parameters of the surplus production from four different models: the Fox model, CYP model, ASPIC model, and maximum entropy model. The PY estimates ranged from 174,232 metric tons (mt) using the CYP model to 238,088 mt using the maximum entropy model. The highest coefficient of determination ($R^2$), the lowest root mean square error (RMSE), and the lowest Theil's U statistic (U) for Korean west coast fisheries were obtained from the maximum entropy model. The maximum entropy model showed relatively better fits of data, indicating that the maximum entropy model is statistically more stable and accurate than other models. The estimate from the maximum entropy model is regarded as a more reasonable estimate of PY. The quality of input data should be improved for the future study of PY to obtain more reliable estimates.

• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.125-137
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• 2005

Many discriminant analysis models for binary data have been used in real applications, but none of the classification models dominates in all varying circumstances(Asparoukhov & Krzanowski(2001)). Lee and Hwang (2003) proposed a new classification model by using multinomial distribution with the maximum entropy estimation method. The model showed some promising results in case of small number of variables, but its performance was not satisfactory for large number of variables. This paper explores to use the iterative cross entropy minimization estimation method in replace of the maximum entropy estimation. Simulation experiments show that this method can compete with other well known existing classification models.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 1993.07a
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• pp.125-129
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• 1993

학문의 어느 분야든, 어느 분야의 어느 한 가지든 그 출발점으로 거슬러 올라 가기란 결코 쉬운 일이 아니다. 불규칙 자료의 스펙트럼분석이야 고전적인 방법이지만 그 분석방법중 Burg(1967)에 의해 제안된 엔트로피(entropy) 개념을 이용한 방법은 그 출발점을 명확하게 이해하기가 손쉽지 않다. 차제에 최대엔트로피방법(Maximum Entropy Method： MIM)을 복습하고, 그것이 어떻게 스펙트럼 추정에 응용되는가를 정리함은 나름대로 의의가 있을 것이다. (중략)

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.6
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• pp.115-117
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• 1984

A method of calculating the maximum entropy per run in binary run-length coding is given when run-length is limited to a maximum of M. And Huang's bounds can be obtained from the present result as M tends to infinity.

• Structural Engineering and Mechanics
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• v.3 no.2
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• pp.135-144
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• 1995

Since structural systems may fail in any one of several failure modes, computation of system reliability is always difficult. A method using numerical quadrature for computing structural system reliability with either one or more than one failure mode is presented in this paper. Statistically correlated safety margin equations are transformed into a group of uncorrelated variables and the joint density function of these uncorrelated variables can be generated by using the Maximum Entropy Method. Structural system reliability is then obtained by integrating the joint density function with the transformed safety domain enclosed within a set of linear equations. The Gaussian numerical integration method is introduced in order to improve computational accuracy. This method can be used to evaluate structural system reliability for Gaussian or non-Gaussian variables with either linear or nonlinear safety boundaries. It is also valid for implicit safety margins such as computer programs. Both the theory and the examples show that this method is simple in concept and easy to implement.