• Title, Summary, Keyword: quadratic form

Log-density Ratio with Two Predictors in a Logistic Regression Model (로지스틱 회귀모형에서 이변량 정규분포에 근거한 로그-밀도비)

• Kahng, Myung Wook;Yoon, Jae Eun
• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.141-149
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• 2013
• We present methods for studying the log-density ratio that enables the selection of the predictors and the form to be included in the logistic regression model. Under bivariate normal distributional assumptions, we investigate the form of the log-density ratio as a function of two predictors. If two covariance matrices are equal, then the crossproduct and quadratic terms are not needed. If the variables are uncorrelated, we do not need the crossproduct terms, but we still need the linear and quadratic terms. We also explore other conditions in which the crossproduct and quadratic terms are not needed in the logistic regression model.

Fundamental Study for the Development of an Optimum Hull Form (최적선형개발에 대한 기초연구)

• Seo, Kwang-Cheol;Choi, Hee-Jong;Chun, Ho-Hwan;Kim, Moon-Chan
• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• pp.37-42
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• 2003
• Fundamental Study for optimizing ship hull form using SQP(sequential quadratic programming) method in a resistance point of view is presented. The Wigley hull is used as an initial hull and numerical calculations are carried out according to various froude numbers. To obtain the ship resistance the wave resistance is evaluated by a Rankine source panel method with nonlinear free surface conditions and the ITTC 1957 friction line is used to predict the frictional resistance coefficient. The geometry of a hull surface is represented and modified by B-spline surface patch. The displacement and the waterplane transverse 2nd moment of inertia of the hull is fixed during the optimization process. And the shp design program called EzHULL is used to draw the lines of the optimized hull form to perform the model test.

A Globally Stabilizing Model Predictive Controller for Neutrally Stable Linear Systems with Input Constraints

• Yoon, Tae-Woong;Kim, Jung-Su;Jadbabaie, Ali;Persis, Claudio De
• 제어로봇시스템학회:학술대회논문집
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• pp.1901-1904
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• 2003
• MPC or model predictive control is representative of control methods which are able to handle physical constraints. Closed-loop stability can therefore be ensured only locally in the presence of constraints of this type. However, if the system is neutrally stable, and if the constraints are imposed only on the input, global aymptotic stability can be obtained; until recently, use of infinite horizons was thought to be inevitable in this case. A globally stabilizing finite-horizon MPC has lately been suggested for neutrally stable continuous-time systems using a non-quadratic terminal cost which consists of cubic as well as quadratic functions of the state. The idea originates from the so-called small gain control, where the global stability is proven using a non-quadratic Lyapunov function. The newly developed finite-horizon MPC employs the same form of Lyapunov function as the terminal cost, thereby leading to global asymptotic stability. A discrete-time version of this finite-horizon MPC is presented here. The proposed MPC algorithm is also coded using an SQP (Sequential Quadratic Programming) algorithm, and simulation results are given to show the effectiveness of the method.

Sufficient Conditions for the Admissibility of Estimators in the Multiparameter Exponential Family

• Dong, Kyung-Hwa;Kim, Byung-Hwee
• Journal of the Korean Statistical Society
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• v.22 no.1
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• pp.55-69
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• 1993
• Consider the problem of estimating an arbitrary continuous vector function under a weighted quadratic loss in the multiparameter exponential family with the density of the natural form. We first provide, using Blyth's (1951) method, a set of sufficient conditions for the admisibility of (possibly generalized Bayes) estimators and then treat some examples for normal, Poisson, and gamma distributions as applications of the main result.

Stability of time-delayed Linear Systems Based on Augmented LKF Including Time-delay Product Quadratic Terms (시간지연 곱 이차항을 포함하는 LKF에 기초한 시간지연 선형 시스템의 안정성)

• Kim, Jin-Hoon
• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.5
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• pp.651-655
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• 2018
• In this paper, based on an augmented Lyapunov-Krasovskii functional(LKF) with time-delay product quadratic terms, the stability result in the form of linear matrix inequality(LMI) is proposed. In getting an LMI result, the free matrix based integral inequality is used. Finally, two well-known numerical examples are given to demonstrate the usefulness of the proposed result.

A Study on Hull-Form Design for Ships Operated at Two Speeds (두 가지 속도에서 운항하는 선박의 형상설계에 관한 연구)

• Kim, Tae Hoon;Choi, Hee Jong
• Journal of the Korean Society of Marine Environment & Safety
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• v.24 no.4
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• pp.467-474
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• 2018
• The purpose of this study is related to automatic hull-form design for ships operating at two speeds. Research was conducted using a series 60 ($C_B=0.6$) ship as a target, which has the most basic ship hull-form. Hull-form development was pursued from the viewpoint of improving resistance performance. In particular, automatic hull-form design for a ship was performed to improve wave resistance, which is closely related to hull-forms. For this purpose, we developed automatic hull-form design software for ships by combining an optimization technique, resistance prediction technique and hull-form modification technique, appling the software developed to a target ship. A sequential quadratic programming method was used for optimization, and a potential-based panel method was used to predict resistance performance. A Gaussian-type modification function was developed and applied to change the ship hull-form. The software developed was used to design a target ship operating at two different speeds, and the performance of the resulting optimized hull was compared with the results of the original hull. In order to verify the validity of the program developed, experimental results obtained in model tests were compared with calculated values by numerical analysis.

Discrete-Time Robust $H_{\infty}$ Filter Design via Krein Space

• Lee, T.H.;Jung, S.Y.;Seo, J.E.;Shin, D.H.;Park, J.B.
• 제어로봇시스템학회:학술대회논문집
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• pp.542-547
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• 2003
• A new approach to design of a discrete-time robust $H_{\infty}$ filter in finite horizon case is proposed. It is shown that robust $H_{\infty}$ filtering problem can be cast into the minimization problem of an indefinite quadratic form, which can be solved by implementing the Kalman filter defined in Krein space. The proposed filter is readily derived by simply augmenting the state space model and has the robustness property against the parameter uncertainties of a given system.

An efficient solution algorithm of the optimal load distribution for multiple cooperating robots

• Choi, Myoung-Hwan;Lee, Hum-Hee
• 제어로봇시스템학회:학술대회논문집
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• pp.501-506
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• 1993
• An efficient solution algorithm of the optimal load distribution problem with joint torque constraints is presented. Multiple robot system where each robot is rigidly grasping a common object is considered. The optimality criteria used is the sum of weighted norm of the joint torque vectors. The maximum and minimum bounds of each joint torque in arbitrary form are considered as constraints, and the solution that reduces the internal force to zero is obtained. The optimal load distribution problem is formulated as a quadratic optimization problem in R, where I is the number of robots. The general solution can be obtained using any efficient numerial method for quadratic programming, and for dual robot case, the optimal solution is given in a simple analytical form.

A New Method for Generating Structural Configurations of Modular-Reconfigurable Machine Tool (모듈러 RMT의 구조형태 생성을 위한 새로운 방법)

• Choi Y. H.;Park H. M.;Jang S. H.;Choi E. Y.;Kim I. S.;Park J. K.
• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• pp.435-440
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• 2005
• This study describes a new method of constructing Reconfigurable machine tools configurations from a set of modules or components. This proposed method defines combinability vector for each module and mutual combinability coefficient matrix for adjacent two modules. All of machine configurations possible to be generated from any two adjacent modules can be determined by quadratic form of two associated combinability vectors. Furthermore, all of possible RMT configurations generating from a series of multiple modules also can be obtained by multiplying quadratic form of two adjacent conbinability vectors recursively. Our proposed RMT configuration generating method can be successfully applied to determining all of possible machine configurations from several modules or components at conceptual- or preliminary- design stage.

An estimator of the mean of the squared functions for a nonparametric regression

• Park, Chun-Gun
• Journal of the Korean Data and Information Science Society
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• v.20 no.3
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• pp.577-585
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• 2009
• So far in a nonparametric regression model one of the interesting problems is estimating the error variance. In this paper we propose an estimator of the mean of the squared functions which is the numerator of SNR (Signal to Noise Ratio). To estimate SNR, the mean of the squared function should be firstly estimated. Our focus is on estimating the amplitude, that is the mean of the squared functions, in a nonparametric regression using a simple linear regression model with the quadratic form of observations as the dependent variable and the function of a lag as the regressor. Our method can be extended to nonparametric regression models with multivariate functions on unequally spaced design points or clustered designed points.