• Title/Summary/Keyword: Inverse Estimation

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A Study on the Estimation of One-dimensional Beat Fluxes on the Slab in Reheating Furnace by Using Inverse Analysis (역해석을 이용한 가열로 내 소재의 1차원 열유속 추정에 관한 연구)

  • Kang, Deok-Hong;Kwag, Dong-Seong;Kim, Woo-Seung;Lee, Yong-Kuk
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.27 no.1
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    • pp.61-68
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    • 2003
  • This study deals with the use of the conjugate gradient method for the simultaneous estimation of two unknown boundary heat fluxes on the slab in reheating furnace. Temperature measurements by the experiment are used in the inverse analysis. The heat flux estimations for three different cases of measurement locations in the slab are performed: non-skid, skid, and shift-skid zones. The estimated heat fluxes for three cases indicated the three regions having local peak values of heat fluxes. The estimated temperatures at measurement locations were in good agreements with the measured temperatures within 5% relative error.

A Study on the Estimation of One-dimensional Heat Fluxes on the Slab in Reheating Furnace by Using Inverse Analysis (열해석을 이용한 가열로 내 소재의 1차원 열유속 추정에 관한 연구)

  • Kwag, Dong-Seong;Kang, Deok-Hong;Kim, Ki-Hong;Lee, Yong-Kuk;Jeong, Hong-Gyu;Kim, Woo-Seung
    • Proceedings of the KSME Conference
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    • 2001.11b
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    • pp.254-259
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    • 2001
  • This study deals with the use of the conjugate gradient method for the simultaneous estimation of two unknown boundary heat fluxes on the slab in reheating furnace. Temperature measurements by the experiment are used in the inverse analysis. The heat flux estimations for three different cases of measurement locations in the slab are performed: non-skid, skid, and shift-skid zones. The estimated heat fluxes for three cases indicated the three regions having local peak values of heat fluxes. The estimated temperatures at measurement locations were in good agreements with the measured temperatures within 5% relative error.

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A Study on the Inverse Radiation Analysis in a Cylindrical Enclosure (원통형상에서의 역복사 해석에 관한 연구)

  • Kim, Ki-Wan;Baek, Seung-Wook;Ryou, Hong-Sun
    • Proceedings of the KSME Conference
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    • 2004.04a
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    • pp.1516-1521
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    • 2004
  • An inverse boundary analysis of surface radiation in an axisymmetric cylindrical enclosure has been conducted in this study. Net energy exchange method was used to calculate the radiative heat flux on each surface, and a hybrid genetic algorithm was adopted to minimize an objective function, which is expressed by sum of square errors between estimated and measured heat fluxes on the design surface. We have examined the effects of the measurement error as well as the number of measurement points on the estimation accuracy.

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Different estimation methods for the unit inverse exponentiated weibull distribution

  • Amal S Hassan;Reem S Alharbi
    • Communications for Statistical Applications and Methods
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    • v.30 no.2
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    • pp.191-213
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    • 2023
  • Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson-Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators.

인구 역 추정에 의한 시조의 연대를 추정하는 수리적 방법

  • 유동선;구자흥;이성철
    • Journal for History of Mathematics
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    • v.17 no.1
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    • pp.97-108
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    • 2004
  • There are so many methods in population estimation such as logistic estimation and compound interest estimation. If we have some pieces of information about population of one tribe, we can estimate progenitor chronology of that tribe used by inverse estimation. In this paper, we describe several theory of population estimation, and develop mathematical method for estimation progenitor chronology from prior general data and statistical estimation theory. Several examples are illustrated.

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Analysis of an Inverse Heat Conduction Problem Using Maximum Entropy Method (최대엔트로피법을 이용한 역열전도문제의 해석)

  • Kim, Sun-Kyoung;Lee, Woo-Il
    • 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.

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Iterative projection of sliced inverse regression with fused approach

  • Han, Hyoseon;Cho, Youyoung;Yoo, Jae Keun
    • Communications for Statistical Applications and Methods
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    • v.28 no.2
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    • pp.205-215
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    • 2021
  • Sufficient dimension reduction is useful dimension reduction tool in regression, and sliced inverse regression (Li, 1991) is one of the most popular sufficient dimension reduction methodologies. In spite of its popularity, it is known to be sensitive to the number of slices. To overcome this shortcoming, the so-called fused sliced inverse regression is proposed by Cook and Zhang (2014). Unfortunately, the two existing methods do not have the direction application to large p-small n regression, in which the dimension reduction is desperately needed. In this paper, we newly propose seeded sliced inverse regression and seeded fused sliced inverse regression to overcome this deficit by adopting iterative projection approach (Cook et al., 2007). Numerical studies are presented to study their asymptotic estimation behaviors, and real data analysis confirms their practical usefulness in high-dimensional data analysis.

Determinant Eigenvalue and Inverse Matrix of a Tridiagonal Matrix (삼대각선행열의 행열식 고유값 및 역행열)

  • Lee, Doo-Soo
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.23 no.4
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    • pp.455-459
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    • 1986
  • A large set of linear equations which arise in many applications, such as in digital signal processing, image filtering, estimation theory, numerical analysis, etc. involve the problem of a tridiagonal matrix. In this paper, the determinant, eigenvalue and inverse matrix of a tridiagoanl matrix are analytically evaluated.

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Inverted exponentiated Weibull distribution with applications to lifetime data

  • Lee, Seunghyung;Noh, Yunhwan;Chung, Younshik
    • Communications for Statistical Applications and Methods
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    • v.24 no.3
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    • pp.227-240
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    • 2017
  • In this paper, we introduce the inverted exponentiated Weibull (IEW) distribution which contains exponentiated inverted Weibull distribution, inverse Weibull (IW) distribution, and inverted exponentiated distribution as submodels. The proposed distribution is obtained by the inverse form of the exponentiated Weibull distribution. In particular, we explain that the proposed distribution can be interpreted by Marshall and Olkin's book (Lifetime Distributions: Structure of Non-parametric, Semiparametric, and Parametric Families, 2007, Springer) idea. We derive the cumulative distribution function and hazard function and calculate expression for its moment. The hazard function of the IEW distribution can be decreasing, increasing or bathtub-shaped. The maximum likelihood estimation (MLE) is obtained. Then we show the existence and uniqueness of MLE. We can also obtain the Bayesian estimation by using the Gibbs sampler with the Metropolis-Hastings algorithm. We also give applications with a simulated data set and two real data set to show the flexibility of the IEW distribution. Finally, conclusions are mentioned.

Estimation of the Properties for a Charring Material Using the RPSO Algorithm (RPSO 알고리즘을 이용한 탄화 재료의 열분해 물성치 추정)

  • Chang, Hee-Chul;Park, Won-Hee;Yoon, Kyung-Beom;Kim, Tae-Kuk
    • The KSFM Journal of Fluid Machinery
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    • v.14 no.1
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    • pp.34-41
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    • 2011
  • Fire characteristics can be analyzed more realistically by using more accurate properties related to the fire dynamics and one way to acquire these fire properties is to use one of the inverse property estimation techniques. In this study two optimization algorithms which are frequently applied for the inverse heat transfer problems are selected to demonstrate the procedure of obtaining pyrolysis properties of charring material with relatively simple thermal decomposition. Thermal decomposition is occurred at the surface of the charring material heated by receiving the radiative energy from external heat sources and in this process the heat transfer through the charring material is simplified by an unsteady 1-dimensional problem. The basic genetic algorithm(GA) and repulsive particle swarm optimization(RPSO) algorithm are used to find the eight properties of a charring material; thermal conductivity(virgin, char), specific heat(virgin, char), char density, heat of pyrolysis, pre-exponential factor and activation energy by using the surface temperature and mass loss rate history data which are obtained from the calculated experiments. Results show that the RPSO algorithm has better performance in estimating the eight pyrolysis properties than the basic GA for problems considered in this study.