• Title/Summary/Keyword: method of differential equation

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A Derivation of Sensitivity Equations of the Error Components to Analyze Performance in the Direct Fire Control System (직사화기 성능분석을 위한 오차요소별 민감도 식 유도)

  • Kim, Jaehun;Kim, Euiwhan;Lee, Jeongyeob;Kim, Gunkook
    • KIPS Transactions on Computer and Communication Systems
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    • v.4 no.12
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    • pp.399-408
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    • 2015
  • In the direct Gun Fire Control System(GFCS), it is essential to analyze the impact of the specific error components on the hit probability to optimize the system design. For this purpose the sensitivity equations of these error components are conveniently used, but it is too difficult to get those equations for the complex system with too many system elements. Normally sensitivity analysis is performed using numerical and statistical methods for the ground combat system. This method requires much computation, and makes us difficult to estimate the sensitivity change of specific error component intuitionally for the changing operating conditions. In this paper we propose a set of sensitivity equations deriving from closed form solution of the ballistic differential equation for the bullet. They are handy equations with very little computations, easy to understand the physical meaning of the related system variables. Some simulation results are shown to demonstrate usefulness of our algorithm for the 30mm projectile.

Local Parameterization of Polygonal Models Using Projection Level Set (투영 등위 집합을 이용한 다면체 모델의 부분 매개 변수화)

  • Lee, Yeon-Joo;Cha, Deuk-Hyun;Chang, Byung-Joon;Ihm, In-Sung
    • Journal of KIISE:Computer Systems and Theory
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    • v.34 no.12
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    • pp.641-655
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    • 2007
  • Parameterization has been one of very important research subjects in several application areas including computer graphics. In the parameterization research, the problem of mapping 3D polygonal model to 2D plane has been studied frequently, but the previous methods often fail to handle complicated shapes of polygonal surfaces effectively as well as entail distortion between the 3D and 2D spaces. Several attempts have been made especially to reduce such distortion, but they often suffer from the problem when an arbitrary rectangular surface region on 3D model is locally parameterized. In this paper, we propose a new local parameterization scheme based on the projection level set method. This technique generates a series of equi-distanced curves on the surface region of interest, which are then used to generate effective local parameterization information. In this paper, we explain the new technique in detail and show its effectiveness by demonstrating experimental results.

Modeling Framework for Continuous Dynamic Systems Using Machine Learning of Hypothetical Model (가설적 모델의 기계학습을 이용한 연속시간 동적시스템 모델링 프레임워크)

  • Hae Sang Song;Tag Gon Kim
    • Journal of the Korea Society for Simulation
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    • v.32 no.1
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    • pp.13-21
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    • 2023
  • This paper proposes a method of automatically generating a model through a machine learning technique by setting a hypothetical model in the form of a gray box or black box with unknown parameters, when the big data of the actual system is given. We implements the proposed framework and conducts experiments to find an appropriate model among various hypothesis models and compares the cost and fitness of them. As a result we find that the proposed framework works well with continuous systems that could be modeled with ordinary differential equation. This technique is expected to be used well for the purpose of automatically updating the consistency of the digital twin model or predicting the output for new inputs using recently generated big data.

Parameter Identification of Nonlinear Dynamic Systems using Frequency Domain Volterra model (비선형 동적 시스템의 파라미터 산정을 위한 주파수 영역 볼테라 모델의 이용)

  • Paik, In-Yeol;Kwon, Jang-Sub
    • Journal of the Earthquake Engineering Society of Korea
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    • v.9 no.3 s.43
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    • pp.33-42
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    • 2005
  • Frequency domain Volterra model is applied to nonlinear parameter identification procedure for dynamic systems modeled by nonlinear function. The frequency domain Volterra kernels, which correspond io linear, quadratic, and cubic transfer functions in lime domain, are incorporated in nonlinear parametric identification procedure. The nonlinear transfer functions, which can be derived from the Volterra series representation of the nonlinear differential equation of the system by Schetzen's method(1980), are directly used for modeling input output relation. The error is defined by the difference between the observed output and the estimated output which is calculated by substituting the observed input to nonlinear frequency domain model. The system parameters are searched by minimizing the error. Volterra model guarantees enough accuracy and convergence and the estimated coefficients have a good agreement with their actual values not only in the linear frequency region but also in the legion where the $2^{nd}\;or\;3^{rd}$ order nonlinearity is dominant.

Closed Integral Form Expansion for the Highly Efficient Analysis of Fiber Raman Amplifier (라만증폭기의 효율적인 성능분석을 위한 라만방정식의 적분형 전개와 수치해석 알고리즘)

  • Choi, Lark-Kwon;Park, Jae-Hyoung;Kim, Pil-Han;Park, Jong-Han;Park, Nam-Kyoo
    • Korean Journal of Optics and Photonics
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    • v.16 no.3
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    • pp.182-190
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    • 2005
  • The fiber Raman amplifier(FRA) is a distinctly advantageous technology. Due to its wider, flexible gain bandwidth, and intrinsically lower noise characteristics, FRA has become an indispensable technology of today. Various FRA modeling methods, with different levels of convergence speed and accuracy, have been proposed in order to gain valuable insights for the FRA dynamics and optimum design before real implementation. Still, all these approaches share the common platform of coupled ordinary differential equations(ODE) for the Raman equation set that must be solved along the long length of fiber propagation axis. The ODE platform has classically set the bar for achievable convergence speed, resulting exhaustive calculation efforts. In this work, we propose an alternative, highly efficient framework for FRA analysis. In treating the Raman gain as the perturbation factor in an adiabatic process, we achieved implementation of the algorithm by deriving a recursive relation for the integrals of power inside fiber with the effective length and by constructing a matrix formalism for the solution of the given FRA problem. Finally, by adiabatically turning on the Raman process in the fiber as increasing the order of iterations, the FRA solution can be obtained along the iteration axis for the whole length of fiber rather than along the fiber propagation axis, enabling faster convergence speed, at the equivalent accuracy achievable with the methods based on coupled ODEs. Performance comparison in all co-, counter-, bi-directionally pumped multi-channel FRA shows more than 102 times faster with the convergence speed of the Average power method at the same level of accuracy(relative deviation < 0.03dB).

Validity of Linear Combination Approach based on Net Damping Analysis of Cable-Damper System (케이블-댐퍼 시스템의 전체감쇠비 해석을 통한 선형조합 접근법의 유효성)

  • Kim, Hyeon Kyeom;Hwang, Jae Woong;Lee, Myeong Jae
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.5A
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    • pp.467-475
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    • 2009
  • Existing studies have suggested Universal Curve only for supplemental damping by damper. Therefore net damping has been determined by means of arithmetic summation between intrinsic, aero-damping of cable and supplemental damping of damper. However linear combination approach by means of the arithmetic summation is not enough theoretical background. So validity of this approach should be verified in order to design adequate cable-damper system by engineers. This study establishes governing differential equation which can consider intrinsic, aero-damping and supplemental damping as well. And also analysis method is solved by combination of muller method and successive iteration method. Consequently, this study succeeds in verification for validity of linear combination approach. As a result of this study, linear combination approach is limitedly effective in case of low stiffness and optimum damping coefficient of damper, short distance from support to damper, lower vibration mode, low aero-damping, and normal windy environment. Whereas this study will be effective in case of opposite conditions, and existing studies or linear combination approach occur to further error. Meaning of this study presents exact solution for net damping of cable-damper system, and verifies linear combination approach by means of the analysis method. In the future, if monitoring of optimum damping coefficient of a damper against aero-damping is feasible on time, algorithm of this study will be available for control of cable and semi-active damper system such as magneto-rheological damper.

Solution to Elasticity Problems of Structural Elements of Composite Materials (복합재료 구조 요소의 탄성문제에 대한 해)

  • Afsar, A.M.;Huq, N.M.L.;Mirza, F.A.;Song, J.I.
    • Composites Research
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    • v.23 no.3
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    • pp.19-30
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    • 2010
  • The present study describes a method for analytical solution to elastic field in structural elements of general symmetric laminated composite materials. The two dimensional plane stress elasticity problems under mixed boundary conditions are reduced to the solution of a single fourth order partial differential equation, expressed in terms of a single unknown function, called displacement potential function. In addition, all the components of stress and displacement are expressed in terms of the same displacement potential function, which makes the method suitable for any boundary conditions. The method is applied to obtain analytical solutions to two particular problems of structural elements consisting of an angle-ply laminate and a cross-ply laminate, respectively. Some numerical results are presented for both the problems with reference to the glass/epoxy composite. The results are highly accurate and reliable as all the boundary conditions including those in the critical regions of supports and loads are satisfied exactly. This verifies the method as a simple and reliable one as well as capable to obtain exact analytical solution to elastic field in structural elements of composite materials under mixed and any other boundary conditions.

Study on the Melting Point Depression of Tin Nanoparticles Manufactured by Modified Evaporation Method (수정된 증발법을 이용하여 제작된 주석 나노입자의 녹는점 강하에 관한 연구)

  • Kim, Hyun Jin;Beak, Il Kwon;Kim, Kyu Han;Jang, Seok Pil
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.38 no.8
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    • pp.695-700
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    • 2014
  • In the present study, the melting temperature depression of Sn nanoparticles manufactured using the modified evaporation method was investigated. For this purpose, a modified evaporation method with mass productivity was developed. Using the manufacturing process, Sn nanoparticles of 10 nm size was manufactured in benzyl alcohol solution to prevent oxidation. To examine the morphology and size distribution of the nanonoparticles, a transmission electron microscope was used. The melting temperature of the Sn nanoparticles was measured using a Differential scanning calorimetry (DSC) which can calculate the endothermic energy during the phase changing process and an X-ray photoelectron spectroscopy (XPS) used for observing the manufactured Sn nanoparticle compound. The melting temperature of the Sn nanoparticles was observed to be $129^{\circ}C$, which is $44^{\circ}C$ lower than that of the bulk material. Finally, the melting temperature was compared with the Gibbs Thomson and Lai's equations, which can predict the melting temperature according to the particle size. Based on the experimental results, the melting temperature of the Sn nanoparticles was found to match well with those recommended by the Lai's equation.

A Study on Shape Optimization of Distributed Actuators using Time Domain Finite Element Method (시간유한요소법을 이용한 분포형 구동기의 형상최적화에 관한 연구)

  • Suk, Jin-Young;Kim, You-Dan
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.33 no.9
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    • pp.56-65
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    • 2005
  • A dynamic analysis method that freezes a time domain by discretization and solves the spatial propagation equation has a unique feature that provides a degree of freedom on spatial domain compared with the space discretization or space-time discretization finite element method. Using this feature, the time finite element analysis can be effectively applied to optimize the spatial characteristics of distributed type actuators. In this research, the time domain finite element method was used to discretize the model. A state variable vector was used in the discretization to include arbitrary initial conditions. A performance index was proposed on spatial domain to consider both potential and vibrational energy, so that the resulting shape of the distributed actuator was optimized for dynamic control of the structure. It is assumed that the structure satisfies the final rest condition using the realizable control scheme although the initial disturbance can affect the system response. Both equations on states and costates were derived based on the selected performance index and structural model. Ricatti matrix differential equations on state and costate variables were derived by the reconfiguration of the sub-matrices and application of time/space boundary conditions, and finally optimal actuator distribution was obtained. Numerical simulation results validated the proposed actuator shape optimization scheme.

2-D Axisymmetric Non-linear Finite Strain Consolidation Model Considering Self-weight Consolidation of Dredged Soil (준설매립지반의 자중압밀을 고려한 2차원 축대칭 비선형 유한변형 압밀 모델)

  • Kwak, Tae-Hoon;Lee, Dong-Seop;Lim, Jee-Hee;Stark, T.D.;Choi, Eun-Seok;Choi, Hang-Seok
    • Journal of the Korean Geotechnical Society
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    • v.28 no.8
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    • pp.5-19
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    • 2012
  • Vertical drains along with the preloading technique have been commonly used to enhance the consolidation rate of dredged placement formation. In practice, vertical drains are usually installed in the process of self-weight consolidation of a dredged soil deposit because this process takes considerable time to be completed, which makes conventional analytical or numerical models difficult to quantify the consolidation behavior. In this paper, we propose a governing partial differential equation and develop a numerical model for 2-D axisymmetric non-linear finite strain consolidation considering self-weight consolidation to predict the behavior of a vertical drain in the dredged placement foundation which is installed during the self-weight consolidation. In order to verify the developed model in this paper, results of the numerical analysis are compared with that of the lab-scaled self-weight consolidation test. In addition, the model verification has been carried out by comparing with the simplified method. The comparisons show that the developed model can properly simulate the consolidation of the dredged placement formation with the vertical drains installed during the self-weight consolidation. Finally, the effect of construction schedule of vertical drains and of pre-loading during the self-weight consolidation is examined by simulating an imaginary dredged material placement site with a thickness of 10 m and 20 m, respectively. This simulation infers the applicability of the proposed method in this research for designing a soil improvement in a soft dredged deposit when vertical drains and pre-loading are implemented before the self-weight consolidation ceases.