Minimum Degrees Of Freedom Research Articles

Solution of a multidimensional inverse radiation problem by means of mode reduction

AbstractThe Karhunen–Loève Galerkin procedure is employed to solve an inverse radiation problem of determining the time‐varying strength of a heat source, which mimics flames in a furnace, from temperature measurements in three‐dimensional participating media where radiation and conduction occur simultaneously. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, using a conjugate gradient method. Through the Karhunen–Loève Galerkin procedure, one can represent the system dynamics with a minimum degree of freedom, and consequently the amount of computation required in the solution of the inverse problem is reduced drastically when the present technique is adopted. Copyright © 2004 John Wiley & Sons, Ltd.

Solution of inverse radiation problems using the Karhunen–Loève Galerkin procedure

The low-dimensional model obtained by the Karhunen–Loève Galerkin procedure is employed to solve the inverse radiation problem of estimating radiative parameters from the temperature measurement in three-dimensional participating media, where radiation and conduction occur simultaneously. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, utilizing the conjugate gradient method. The low-dimensional model based on the Karhunen–Loève Galerkin procedure can represent a given system with a minimum degree of freedom, and consequently the number of equations to be solved in the estimation of parameters is minimized when the present technique is used. It is shown that the present technique of solving inverse radiation problems employing the Karhunen–Loève Galerkin procedure yields results as accurate as those using the S 4 method at a drastically reduced computational cost.

Control of Navier–Stokes equations by means of mode reduction

AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In a previous work (Park HM, Lee MW. An efficient method of solving the Navier–Stokes equation for the flow control. International Journal of Numerical Methods in Engineering 1998; 41: 1131–1151), the authors proposed an efficient method of solving the Navier–Stokes equations by reducing their number of modes. Employing the empirical eigenfunctions of the Karhunen–Loève decomposition as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear sub-space that is sufficient to describe the observed phenomena, and consequently, reduce the Navier–Stokes equations defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom. In the present work, we apply this technique, termed the Karhunen–Loève Galerkin procedure, to a pointwise control problem of Navier–Stokes equations. The Karhunen–Loève Galerkin procedure is found to be much more efficient than the traditional method, such as finite difference method in obtaining optimal control profiles when the minimization of the objective function has been done by using a conjugate gradient method. Citing Literature Volume33, Issue430 June 2000Pages 535-557 RelatedInformation

Solution of an inverse heat transfer problem by means of empirical reduction of modes

An efficent method of solving the inverse heat transfer problem of estimating the unknown function of wall heat flux for laminar flow inside a duct is proposed in the present paper. It is based on the Karhunen—Loeve Galerkin procedure which employs the empirical eigenfunctions of the Karhunen—Loeve decomposition as basis functions of a Galerkin procedure. With the empirical eigenfunctions, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and thus convert the governing equations to a model with a minimum degree of freedom, resulting in a drastic reduction of computation time without loss of accuracy. The performance of the present technique of inverse analysis using the Karhunen—Loeve Galerkin procedure is evaluated by several numerical experiments, and is found to be very accurate as well as efficient.

Control of Navier-Stokes equations by means of mode reduction

In a previous work (Park HM, Lee MW. An efficient method of solving the Navier–Stokes equation for the flow control. International Journal of Numerical Methods in Engineering 1998; 41: 1131–1151), the authors proposed an efficient method of solving the Navier–Stokes equations by reducing their number of modes. Employing the empirical eigenfunctions of the Karhunen–Loève decomposition as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear sub-space that is sufficient to describe the observed phenomena, and consequently, reduce the Navier–Stokes equations defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom. In the present work, we apply this technique, termed the Karhunen–Loève Galerkin procedure, to a pointwise control problem of Navier–Stokes equations. The Karhunen–Loève Galerkin procedure is found to be much more efficient than the traditional method, such as finite difference method in obtaining optimal control profiles when the minimization of the objective function has been done by using a conjugate gradient method.

On the solution of inverse heat transfer problem using the Karhunen–Loève Galerkin method

An efficient method based on the Karhunen–Loève Galerkin procedure is proposed for the solution of inverse problem of estimating the time-varying strength of a heat source in a two-dimensional heat conduction system. The Karhunen–Loève Galerkin procedure converts a given system into a model with the minimum degree of freedom, and consequently the number of equations to be solved in the inverse analysis is minimized, resulting in the drastic reduction of computation time. The performance of the present technique of inverse analysis using the Karhunen–Loève Galerkin procedure is evaluated by several numerical experiments, and is found to be very accurate as well as efficient.

Estimation of parameters in flow reactors using the Karhunen–Loève decomposition

The empirical eigenfunctions obtained from the Karhunen–Loève decomposition are employed as trial functions of a Galerkin method to construct a dynamic model of a flow reactor (the Karhunen–Loève Galerkin method). This dynamic model is then used for the purpose of parameter estimation of the flow reactor and the performance of the model is compared to a conventional method such as the method of lines. The dynamic model based on the Karhunen–Loève Galerkin method can represent a given system with a minimum degree of freedom, and consequently the number of equations to be solved in the estimation of parameters is minimized. It is demonstrated that, for a flow reactor of complicated shape, the present technique of parameter estimation using the Karhunen–Loève Galerkin procedure is far more efficient than the method of lines.

An efficient computational method of boundary optimal control problems for the Burgers equation

The Burgers equation is a simple one-dimensional model of the Navier-Stokes equation. In the present paper, we suggest an efficient method of solving optimal boundary control problems of the Burgers equation, which is practical as well as mathematically rigorous. Our eventual purpose is to extend this technique to the control problems of viscous fluid flows. The present method is based on the Karhunen-Loève decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system. Employing these empirical eigenfunctions as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and consequently reduce the Burgers equation to a set of ordinary differential equations with a minimum degree of freedom. The resulting low-dimensional model of Burgers equation is shown to simulate the original system almost exactly. The present algorithm is well suited for the problems of control or optimization, where one has to solve the governing equation repeatedly but one can also estimate the approximate solution space based on the range of control variables. The present method of solving boundary control problems of Burgers equation employing the lowdimensional model obtained by the Karhunen-Loève Galerkin procedure is found to yield accurate results in a very efficient way, when the minimization of the objective function is performed using a conjugate gradient method.

A method of solving inverse convection problems by means of mode reduction

Determination of wall heat flux for laminar flow inside a duct from the temperature measurement within the flow is a typical inverse heat convection problem which is ill-posed. In the present paper, an efficient method based on the Karhunen–Loève Galerkin procedure (Park and Cho, 1996, Chem. Engng Sci. 51, 81–98) is proposed for the solution of this kind of inverse heat transfer problems. Employing the Karhunen–Loève Galerkin procedure, which is a Galerkin method employing empirical eigenfunctions of the Karhunen–Loève decomposition, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and thus convert a given system into a model with a minimum degree of freedom, resulting in drastic reduction of computation time. The performance of the present technique of inverse analysis using the Karhunen–Loève Galerkin procedure is evaluated by numerical experiments on the identification of unknown functions of wall heat flux, and is found to be very accurate as well as efficient.

An efficient method of solving the Navier–Stokes equations for flow control

A new method of solving the Navier–Stokes equations efficiently by reducing their number of modes is proposed in the present paper. It is based on the Karhunen–Loève decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system. Employing these empirical eigenfunctions as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and consequently reduce the Navier–Stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom. The present algorithm is well suited for the problems of flow control or optimization, where one has to compute the flow field repeatedly using the Navier–Stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables. The low-dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the Navier–Stokes equation. © 1998 John Wiley & Sons, Ltd.

An efficient method of solving the Navier-Stokes equations for flow control

A new method of solving the Navier–Stokes equations efficiently by reducing their number of modes is proposed in the present paper. It is based on the Karhunen–Loeve decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system. Employing these empirical eigenfunctions as basis functions of a Galerkin procedure, one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena, and consequently reduce the Navier–Stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom. The present algorithm is well suited for the problems of flow control or optimization, where one has to compute the flow field repeatedly using the Navier–Stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables. The low-dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the Navier–Stokes equation. © 1998 John Wiley & Sons, Ltd.

Identifiability of hidden markov processes and their minimum degrees of freedom

AbstractThere exists a class of stochastic processes based on a finite‐state discrete‐time Markov chain, where the states are not directly observable and only the output symbols generated by the states are observable. If different states produce the same output symbol, the process is called a hidden Markov process. It is very important both in theory and applications. It is known that two Markov processes with different transition matrices are equivalent hidden Markov processes. The problem has been considered interesting concerning by what structures such a situation can arise.This paper gives a complete solution to the identification problem of the hidden Markov process, which has long been proposed and is still unsolved. At the same time, a structure of this kind of process, which has been unknown, is revealed. An n algebraic technique is used in the discussion, where new concepts called Δ‐subspace and Δ‐cy‐clic subspace are introduced into the framework of subspace and cyclic subspace in the usual linear algebra.In this paper, a Δ‐subspace is actually constructed which gives the effective minimum degree of the hidden Markov process. It is shown also that two stochastic processes are equivalent if and only if there exists an isomorphism between the Δ‐sub‐spaces.

Coupled rotor/tower stability analysis of horizontal-axis wind turbines.

A mathematical model of a large-scale wind turbine composed of a flexible two-bladed rotor and a flexible tower is described, and results of the stability analysis are presented in this paper. The model includes each component's property as well as blade aeroelasticity, and is described with minimum degrees of freedom using the Rayleigh-Ritz approach : a rotor is modeled as two degrees of freedom and a tower as three degrees of freedom. Aerodynamic forces are predicted quasi-statically with the annular momentum theory including angular momentum. Floquet theory is used to evaluate the stability of a periodic coefficient system. Applying this model to a 100 kW class wind turbine with a rigid-hub rotor, existence of stall instability, parametric instability and gyrostatic instabilitiy and their conditions of occurence are clarified, and whirl flutter, aerodynamic divergence and mechanical instability are also examined.

Current Studies of the Decision Process: Automation Versus Creativity

A REMARKABLE convergence of interest on the study of is occurring in political science and in the behavior sciences generally. Among political scientists this is reflected in the volume of publication devoted to the theory and practice of decision-making and execution.' The purpose of the present discussion is to call attention to many lines of approach now current among behavior scientists and to raise issues of particular concern to the professional student of government. We begin by outlining a set of categories that appear to be consonant with the modern study of decisions by political scientists and jurists and proceed then to look into more technical questions of method. It is recognized that the term choice is appropriately applied to situations in which the individual or the group has at least a minimum degree of freedom in selecting or interpreting goals and strategies. Political scientists use the conception of a process in two senses. Broadly conceived, a is the political act of the whole body politic. Narrowly viewed, it is the face-to-face determination of controversial or uncertain courses of action. In the broader sense, the body politic is making decisions when legislatures, executives, administrative agencies, and judicial organs vote; when wars and uprisings succeed or fail; and when the entire electorate commits itself at the polls. All decisions are interactions in the social process; and they involve community coercion. The role of coercion is obvious in the case of victory or defeat in war or revolution. It is less evident in the case of legislation or court decision; however, it is usually assumed that community coercion will be applied against the violator of a statute. Coercion in the name of the community takes many forms, such as deprivations of life, liberty, and property. When speaking technically we may reserve the word decision for the choices made in the political process. They involve sanctions (that is, severe actual or potential deprivations). Whether we are thinking of a body politic as a whole or of face-to-face situations we are considering arenas in which participants are striving to accomplish their purposes by influencing outcomes. The purposes are directed toward preferred events (values and interpretations of