• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.4
• /
• pp.293-305
• /
• 2009

In this article, we study a reduced-order modelling for distributed feedback control problem of the Burgers equations. Brief review of the centroidal Voronoi tessellation (CVT) are provided. A weighted (nonuniform density) CVT is introduced and low-order approximate solution and compensator-based control design of Burgers equation is discussed. Through weighted CVT (or CVT-nonuniform) method, obtained low-order basis is applied to low-order functional gains to design a low-order controller, and by using the low-order basis order of control modelling was reduced. Numerical experiments show that a solution of reduced-order controlled Burgers equation performs well in comparison with a solution of full order controlled Burgers equation.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.2
• /
• pp.141-159
• /
• 2009

In this article, we consider a weighted CVT-based reduced-order modelling for Burgers equation. Brief review of the CVT (centroidal Voronoi tessellation) approaches to reduced-order bases are provided. In CVT-reduced order modelling, we start with a snapshot set just as is done in a POD (Proper Orthogonal Decomposition)-based setting. So far, the CVT was researched with uniform density ($\rho$(y) = 1) to determine the basis elements for the approximatin subspaces. Here, we shall investigate the technique of CVT with nonuniform density as a procedure to determine the basis elements for the approximating subspaces. Some numerical experiments including comparison of two CVT (CVT-uniform and CVT-nonuniform)-based algorithm with numerical results obtained from FEM(finite element method) and POD-based algorithm are reported.

• Journal of the Korean Society for Precision Engineering
• /
• v.6 no.4
• /
• pp.52-60
• /
• 1989

In order to control the transient torsional vibration of rotational shaft system, the torsional stiffness of it has been taken into account in modelling the plant. In this paper the observer and controller has been designed in two ways. One is to consider the torsional stiffness and the other is to idealize the rotational shaft as rigid body. The third order observer considering torsional stiffness shows stable response on computer simulation. When the observer is designed on assumption of the rotational shaft being rigid body, the reduced order observer shows stable response whereas the full order observer shows unstable response.

• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.3
• /
• pp.261-280
• /
• 2019

We apply a reduced-order method based on B-spline Galerkin finite elements formulation to Rosenau-RLW equation for the first time and explain their process in detail. The ensemble of snapshots is very large generally, and it is difficult to apply POD to the ensemble of snapshots directly. Hence, we try to pick up important snapshots among the whole data. In this paper, we represent three different reduced-order schemes. First, the classical POD technique is examined. Second, (equally sampled snapshots) are exploited for POD technique. Finally, afterward sampling snapshots by CVT, for those snapshots, POD technique is implemented again.

• International Journal of Computer Science & Network Security
• /
• v.21 no.7
• /
• pp.297-304
• /
• 2021

In a duopoly situation, one firm can gain competitive advantage by attracting the price-sensitive customers from its competitor leading to higher profits through higher sale revenue for the competing company. A simulation study in which there are two electric car manufacturers with agent based modelling was conducted in order to verify this contention. The first step consisted of defining the baseline. Simulations of 1000 times and agent-based modelling were conducted with the assumption that company 1 reduced its price to the maximum of 20% thereby contributing to the switch-over of a maximum of 40% of the price sensitive customers of company 2. The results of 1000 simulations and agent-based modelling highlighted that price reduction by company 1 resulted in a significant increase in the number of customers, presumably due to switch-over from company 2 and there was a corresponding increase in revenues from both of the sales avenues. Thus, Company 1 achieved competitive advantage by marketing its cars to the customers of Company 2 using price reduction strategy to attract them. This study has ramifications for companies that aim to sway the price sensitive customers from a competitor.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.10 no.2 s.48
• /
• pp.21-29
• /
• 2006

It is impractical to install sensors on every floor of a tall building to measure the full state vector because of the large number of degrees of freedom. This makes it necessary to introduce reduced order control. A kind of system reduction scheme (dynamic condensation method) is proposed in this paper. This method is iterative and Guyan condensation is looked upon as an initial approximation of the iteration. Since the reduced order system is updated repeatedly until a desired one is obtained, the accuracy of the reduced order system resulting from the proposed method is much higher than that obtained from the Guyan condensation method. An eigenvalue shilling technique is applied to accelerate the convergence of Iteration. Two schemes to establish the reduced order system by using the proposed method are also presented and discussed in this paper. The results for a tail building with active tuned mass damper show that the proposed method is efficient for the reduced order modelling and the accuracy is very close to exact only after two iterations.

• Journal of the Korean Geographical Society
• /
• v.39 no.4
• /
• pp.633-642
• /
• 2004

This study tries to generalize the stream network by constructing rule-based modelling. A study on the map generalization tends to be concentrated on development of algorithms for modification of linear features and evaluations to the limited cartographic elements. Rule-based modelling can help to improve previous algorithms by application of generalization process with the results that analyzing mapping principles and spatial distribution patterns of geographical phenomena. Rule-based modelling can be applied to generalize various cartographic elements, and make an effective on multi-scaling mapping in the digital environments. In this research, nile-based modelling for stream network is composed of generalization rule, algorithm for centerline extraction and linear features. Before generalization, drainage pattern was analyzed by the connectivity with lake to minimize logical errors. As a result, 17 streams with centerline are extracted from 108 double-lined streams. Total length of stream networks is reduced as 17% in 1:25,000 scale, and as 29% in 1:50,000. Simoo algorithm, which is developed to generalize linear features, is compared to Douglas-Peucker(D-P) algorithm. D-P made linear features rough due to the increase of data point distance and widening of external angle. But in Simoo, linear features are smoothed with the decrease of scale.

• 한국전산유체공학회:학술대회논문집
• /
• 2010.05a
• /
• pp.40-42
• /
• 2010

Unsteady CFD results of the backward facing step (BFS) flow field is reconstructed by the low-dimenstional modes using the POD (Proper Orthogonal Decomposition) technique. Flow responses to the blowing or suction with various frequencies and amplitudes applied at the edge of the BFS can also be analysed using the same technique. The present technique can be effectively applied to the feedback flow control device.

• Structural Engineering and Mechanics
• /
• v.28 no.1
• /
• pp.107-127
• /
• 2008

Wind turbine blades are increasing in magnitude without a proportional increase of stiffness for which reason geometrical and inertial nonlinearities become increasingly important. Often these effects are analysed using a nonlinear truncated expansion in undamped fixed base mode shapes of a blade, modelling geometrical and inertial nonlinear couplings in the fundamental flap and edge direction. The purpose of this article is to examine the applicability of such a reduced-degree-of-freedom model in predicting the nonlinear response and stability of a blade by comparison to a full model based on a nonlinear co-rotating FE formulation. By use of the reduced-degree-of-freedom model it is shown that under strong resonance excitation of the fundamental flap or edge modes, significant energy is transferred to higher modes due to parametric or nonlinear coupling terms, which influence the response and stability conditions. It is demonstrated that the response predicted by such models in some cases becomes instable or chaotic. However, as a consequence of the energy flow the stability is increased and the tendency of chaotic vibrations is reduced as the number of modes are increased. The FE model representing the case of infinitely many included modes, is shown to predict stable and ordered response for all considered parameters. Further, the analysis shows that the reduced-degree-of-freedom model of relatively low order overestimates the response near resonance peaks, which is a consequence of the small number of included modes. The qualitative erratic response and stability prediction of the reduced order models take place at frequencies slightly above normal operation. However, for normal operation of the wind turbine without resonance excitation 4 modes in the reduced-degree-of-freedom model perform acceptable.

• Asia-Pacific Journal of Business
• /
• v.9 no.4
• /
• pp.99-117
• /
• 2018

This study has investigated Linear Programming (LP) applications to special decision making problems in managerial accounting with the help of spreadsheet Solver tools. It uses scenario approaches to case examples having three products and three resources in make-and-supply business operations, which is applicable to cases having more variables and constraints. Integer Programmings (IP) are applied in order to model situations when products are better valued in integer values or logical constraints are required. Three cases in one-time-only special order decisions include Goal Programming approach, Knapsack problems with 0/1 selections, and fixed-charge 0/1 integer modelling techniques for set-up operation costs. For the decisions in outsourcing problems, opportunity-costs of resources expressed by shadow-prices are considered to determine their precise contributions. It has also shown that the improvement in work-shop operation for an unprofitable product must overcome its 'reduced cost' by the sum of direct manufacturing cost savings and its shadow-price contributions. This paper has demonstrated how various real situations of special decision problem in managerial accounting can be approached without mistakes by using LP's and IP's, and how students both in accounting and management science can acquire LP skills in their education.