• Title/Summary/Keyword: linear error equation

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Whole learning algorithm of the neural network for modeling nonlinear and dynamic behavior of RC members

  • Satoh, Kayo;Yoshikawa, Nobuhiro;Nakano, Yoshiaki;Yang, Won-Jik
    • Structural Engineering and Mechanics
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    • v.12 no.5
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    • pp.527-540
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    • 2001
  • A new sort of learning algorithm named whole learning algorithm is proposed to simulate the nonlinear and dynamic behavior of RC members for the estimation of structural integrity. A mathematical technique to solve the multi-objective optimization problem is applied for the learning of the feedforward neural network, which is formulated so as to minimize the Euclidean norm of the error vector defined as the difference between the outputs and the target values for all the learning data sets. The change of the outputs is approximated in the first-order with respect to the amount of weight modification of the network. The governing equation for weight modification to make the error vector null is constituted with the consideration of the approximated outputs for all the learning data sets. The solution is neatly determined by means of the Moore-Penrose generalized inverse after summarization of the governing equation into the linear simultaneous equations with a rectangular matrix of coefficients. The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified in three types of problems to learn the truth table for exclusive or, the stress-strain relationship described by the Ramberg-Osgood model and the nonlinear and dynamic behavior of RC members observed under an earthquake.

GA-LADRC based control for course keeping applied to a mariner class vessel (GA-LADRC를 이용한 Mariner class vessel의 선수각 제어)

  • Jong-Kap AHN
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.59 no.2
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    • pp.145-154
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    • 2023
  • In this study, to control the heading angle of a ship, which is constantly subjected to various internal and external disturbances during the voyage, an LADRC (linear active disturbance rejection control) design that focuses more on improving the disturbance removal performance was proposed. The speed rate of change of the ship's heading angle due to the turn of the rudder angle was selected as a significant factor, and the nonlinear model of the ship's maneuvering equation, including the steering gear, was treated as a total disturbance. It is the similar process with an LADRC design for the first-order transfer function model. At this time, the gains of the controller included in LADRC and the gains of the extended state observer were tuned to RCGAs (real-coded genetic algorithms) to minimize the integral time-weighted absolute error as an evaluation function. The simulation was performed by applying the proposed GA-LADRC controller to the heading angle control of the Mariner class vessel. In particular, it was confirmed that the proposed controller satisfactorily maintains and follows the set course even when the disturbances such as nonlinearity, modelling error, uncertainty and noise of the measurement sensor are considered.

A Study on the Analysis of Incompressible and Looped Flow Network Using Topological Constitutive Matrix Equation (위상구성행렬식을 이용한 비압축성 순환망 형태의 유로망 해석에 관한 연구)

  • Yoo, Seong-Yeon;Kim, Bum-Shin
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.22 no.8
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    • pp.573-578
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    • 2010
  • Topological matrix which reflects characteristics of network connectivity has been widely used in efficient solving for complicated flow network. Using topological matrix, one can easily define continuity at each node of flow network and make algorithm to automatically generate continuity equation of matrix form. In order to analyze flow network completely it is required to satisfy energy conservation in closed loops of flow network. Fundamental cycle retrieving algorithm based on graph theory automatically constructs energy conservation equation in closed loops. However, it is often accompanied by NP-complete problem. In addition, it always needs fundamental cycle retrieving procedure for every structural change of flow network. This paper proposes alternative mathematical method to analyze flow network without fundamental cycle retrieving algorithm. Consequently, the new mathematical method is expected to reduce solving time and prevent error occurrence by means of simplifying flow network analysis procedure.

Practical Study on Adjustment of Load Correlation Equations of Pole Transformer (주상변압기 부하 상관식 조정에 관한 실증적 연구)

  • 박창호;김두봉;김기현;배주천;윤상윤;김재철
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.14 no.1
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    • pp.102-108
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    • 2000
  • This paper presents a result of practical study about the adjustment of load correlation equation for the load management of pole transformer. For adjusting the load correlation equation, we analyze the correlative relation between working electric energy[kWh] and peak load[A]. To enhance the accuracy of correlation equation, we classify the 12 representative area patterns. And then, we select the 24 sample pole transformer for each area pattern. For the reliability of the data using the load correlation equation, load management equipment is utilized for each sample pole transformer. Through the on-line data acquisition, we construct the database. For adjusting the load correlation equation, we consider the two points. One is the goodness of fitness for load correlation equation and the other is prevention of pole transformer damage due to the overload. Finally, we propose the correlation equation using the linear and quadratic equation all at once. Through the case studies, we verify that the proposed load correlation equation is reduced the error ratio than conventional correlation equation.

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Correlation Analysis Using Precipitation Radar of TRMM Satellite and Ground Observed Value : YONG-DAM Watershed (TRMM/PR 관측치와 지상 관측치와의 상관분석 - 용담댐 유역을 대상으로 -)

  • Jang, Choul-Hee;Park, Guen-Ae;Kim, Seong-Joon
    • Proceedings of the Korean Society of Agricultural Engineers Conference
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    • 2001.10a
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    • pp.335-339
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    • 2001
  • The Tropical Rainfall Measuring Mission(TRMM) Satellite was launched in November 1997, carrying into orbit the first space-borne Precipitation Radar(PR). The purpose of this study is to identify the relationship between TRMM/PR and AWS raingage data, and test the possibility to apply storm runoff prediction. Four TRMM/PR data in 1999 for Yongdam watershed was adopted and made a simple linear regression equation using AWS data. By using the equation, the storm runoff was estimated with the adjusted rainfall. TRMM/PR rainfall and runoff was overall underestimated by the carry-over effect of rainfall error and SCS-CN value selection.

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Maneuverability Analysis of a Ship by System Indentification technique (시스템검증법에 의한 조종성능해석연구)

  • Gang, Chang-Gu;Seo, Sang-Hyeon
    • 한국기계연구소 소보
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    • s.10
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    • pp.35-48
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    • 1983
  • When the hydrodynamic coefficients of the ship maneuvering equation are estimated by captive model test, it is difficult to take account of the scale effect between model and full scale ship. This scale effect problem can be overcome by processing the sea trial data with system identification. Extended Kalman filter is used as a system identification technique for the modification of the simulation equation as well as the estimation of hydrodynamic coefficients. The phenomena of simultaneous drifting of linear coefficients occur. It is confirmed that two coefficients in each pair-($Y_v$', $Y_r$' -m' u'), ($N_v$', $N_r$' )-are simultaneously drifting and all 4 coefficients are simultaneously drifting together. Particularly simultaneous drifting of 2 coefficients in each pair is more significant. It is also shown that the simultaneous drifting of 4 coefficients can be reduced by choosing the input data which have the random v'/r' curve and 4 coefficients are estimated within 2-4% error, which may be noise level. So, it is recommended to operate the rudder randomly in sea trial or model test for the application of system identification technique.

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Dynamic Modeling of an Fine Positioner Using Magnetic Levitation (자기 부상 방식 미세 운동 기구의 동적 모델링)

  • Jeong, Gwang-Seok;Baek, Yun-Su
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.5 s.176
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    • pp.1166-1174
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    • 2000
  • In this paper, we introduce a positioner based on magnetic levitation to eliminate the friction which is the most severe effect to limit high resolution on the micro level. Differently from existing electromagnetic device, the proposed positioner consists of air core solenoid and permanent magnet. Although the combination produces small magnetic force, it is suitable for realizing micro motion repeatedly without the accumulation of error because there is no hysteresis caused by ferromagnetic materials, no eddy current loss, no flux saturation. First, the approximate modeling of stiffness and damping effects between the magnetic elements is made and verified experimentally. Then, we have formulated the dynamic equation of one d.o.f magnetic levitation positioner using linear perturbation method and discussed the necessity of optimization for the chief design parameters to maximize the stability performance.

Determination of Camera System Orientation and Translation in Cartesian Coordinate (직교 좌표에서 카메라 시스템의 방향과 위치 결정)

  • 이용중
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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    • 2000.04a
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    • pp.109-114
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    • 2000
  • A new method for the determination of camera system rotation and translation from in 3-D space using recursive least square method is presented in this paper. With this method, the calculation of the equation is found by a linear algorithm. Where the equation are either given or be obtained by solving five or more point correspondences. Good results can be obtained in the presence if more than the eight point. A main advantage of this new method is that it decouple rotation and translation, and then reduces computation. With respect to error in the solution point number in the input image data, adding one more feature correspondence to required minimum number improves the solution accuracy drastically. However, further increase in the number of feature correspondence improve the solution accuracy only slowly. The algorithm proposed by this paper is used to make camera system rotation and translation easy to recognize even when camera system attached at end effecter of six degrees of freedom industrial robot manipulator are applied industrial field.

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Adaptive Fuzzy Control of Helicopter (헬리콥터의 적응 퍼지제어)

  • 김종화;장용줄;이원창;강근택
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2001.05a
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    • pp.144-147
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    • 2001
  • This paper presents adaptive fuzzy controller which is uncertainty or unknown variation in different parameters with nonlinear system of helicopter. The proposed adaptive fuzzy controller applied TSK(Takagi-Sugeno-Kang) fuzzy system which is not only low number of fuzzy rule, and a linear input-output equation with a constant term, but also can represent a large class of nonlinear system with good accuracy. The adaptive law was designed by using Lyapunov stability theory. The adaptive fuzzy controller is a model reference adaptive controller which can adjust the parameter $\theta$ so that the plant output tracks the reference model output. First of all, system of helicopter was considered as stopping state, and design of controller was simulated from dynamics equation with stopping state. Results show that it is controlled more successfully with a model reference adaptive controller than with a non-adaptive fuzzy controller when there is a modelling error between system and model or a continuous added noise in such unstable system.

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AN EFFICIENT SECOND-ORDER NON-ITERATIVE FINITE DIFFERENCE SCHEME FOR HYPERBOLIC TELEGRAPH EQUATIONS

  • Jun, Young-Bae;Hwang, Hong-Taek
    • The Pure and Applied Mathematics
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    • v.17 no.4
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    • pp.289-298
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    • 2010
  • In this paper, we propose a second-order prediction/correction (SPC) domain decomposition method for solving one dimensional linear hyperbolic partial differential equation $u_{tt}+a(x,t)u_t+b(x,t)u=c(x,t)u_{xx}+{\int}(x,t)$. The method can be applied to variable coefficients problems and singular problems. Unconditional stability and error analysis of the method have been carried out. Numerical results support stability and efficiency of the method.