• Title/Summary/Keyword: State of equations

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An Efficient Blast Design using Reliability Index (신뢰성지수를 이용한 효율적인 발파설계)

  • 박연수;박선준;강성후
    • Journal of KSNVE
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    • v.8 no.5
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    • pp.821-831
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    • 1998
  • The actual ground vibrations due to NATM and foundation blasting at Seoul(weathered rock), Pusan(weathered rock) and Youngkwang(quartz andesite) have been measured, and the data were analyzed using reliability index($\beta$) to determinate the vibration equations and the maximum charge weight for efficient blast. These were suggested with the division of ultimate limit state($\beta$=0), serviceability limit state($\beta$=1.28) and safety state($\beta$=3), respectively. The reliability index 0 mean 50% data line obtained by the least squares best-fit line. The reliability index 1.28 and 3 represent bounds below 90% and 99.9% of the data, respectively. In this study, reliability index $\beta$=1.28 with security and economy was suggested. The maximum charge weight equations for efficient blast were obtained in W=(Vc/384.90)1.5151.D3(Seoul), W=(Vc/579.82)1.4706.D3(Pusan). W=(Vc/1654.01)1.3456.D3(Youngkwang), and the blast vibration equatiions in V=385(SD)-1.98(Seoul), V=580(SD)-2.04(Pusan), V=1654(SD)-2.23(Youngkwang), respectively. From this study, inference and analysis methods of vibration equations using reliability theory were established.

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A hierarchical approach to state estimation of time-varying linear systems via block pulse function (블럭펄스함수를 이용한 시스템 상태추정의 계층별접근에 관한 연구)

  • 안두수;안비오;임윤식;이재춘
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.45 no.3
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    • pp.399-406
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    • 1996
  • This paper presents a method of hierarchical state estimation of the time-varying linear systems via Block-pulse function(BPF). When we estimate the state of the systems where noise is considered, it is very difficult to obtain the solutions because minimum error variance matrix having a form of matrix nonlinear differential equations is included in the filter gain calculation. Therefore, hierarchical approach is adapted to transpose matrix nonlinear differential equations to a sum of low order state space equation from and Block-pulse functions are used for solving each low order state space equation in the form of simple and recursive algebraic equation. We believe that presented methods are very attractive nd proper for state estimation of time-varying linear systems on account of its simplicity and computational convenience. (author). 13 refs., 10 figs.

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Determination and Prediction of Digestible and Metabolizable Energy from the Chemical Composition of Chinese Corn Gluten Feed Fed to Finishing Pigs

  • Wang, T.T.;Liu, D.W.;Huang, C.F.;Liu, L.;Piao, X.S.;Wang, F.L.
    • Asian-Australasian Journal of Animal Sciences
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    • v.27 no.6
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    • pp.871-879
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    • 2014
  • Two experiments were conducted to determine the digestible energy (DE) and metabolizable energy (ME) contents of corn gluten feed (CGF) for finishing pigs and to develop equations predicting the DE and ME content from the chemical composition of the CGF samples, as well as validate the accuracy of the prediction equations. In Exp. 1, ten CGF samples from seven provinces of China were collected and fed to 66 finishing barrows (Duroc${\times}$Landrace${\times}$Yorkshire) with an initial body weight (BW) of $51.9{\pm}5.5$ kg. The pigs were assigned to 11 diets comprising one basal diet and 10 CGF test diets with six pigs fed each diet. The basal diet contained corn (76%), dehulled soybean meal (21%) and premix (3%). The ten test diets were formulated by substituting 25% of the corn and dehulled soybean meal with CGF and contained corn (57%), dehulled soybean meal (15.75%), CGF (24.25%) and premix (3%). In Exp. 2, two additional CGF sources were collected as validation samples to test the accuracy of the prediction equations. In this experiment, 18 barrows (Duroc${\times}$Landrace${\times}$Yorkshire) with an initial BW of $61.1{\pm}4.0$ kg were randomly allotted to be fed either the basal diet or two CGF containing diets which had a similar composition as used in Exp. 1. The DE and ME of CGF ranged from 10.37 to 12.85 MJ/kg of dry matter (DM) and 9.53 to 12.49 MJ/kg of DM, respectively. Through stepwise regression analysis, several prediction equations of DE and ME were generated. The best fit equations were: DE, MJ/kg of DM = 18.30-0.13 neutral detergent fiber-0.22 ether extract, with $R^2$ = 0.95, residual standard deviation (RSD) = 0.21 and p<0.01; and ME, MJ/kg of DM = 12.82+0.11 Starch-0.26 acid detergent fiber, with $R^2$ = 0.94, RSD = 0.20 and p<0.01. These results indicate that the DE and ME content of CGF varied substantially but the DE and ME for finishing pigs can be accurately predicted from equations based on nutritional analysis.

Evaluation of Energy Digestibility and Prediction of Digestible and Metabolizable Energy from Chemical Composition of Different Cottonseed Meal Sources Fed to Growing Pigs

  • Li, J.T.;Li, D.F.;Zang, J.J.;Yang, W.J.;Zhang, W.J.;Zhang, L.Y.
    • Asian-Australasian Journal of Animal Sciences
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    • v.25 no.10
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    • pp.1430-1438
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    • 2012
  • The present experiment was conducted to determine the digestible energy (DE), metabolizable energy (ME) content, and the apparent total tract digestibility (ATTD) of energy in growing pigs fed diets containing one of ten cottonseed meals (CSM) collected from different provinces of China and to develop in vitro prediction equations for DE and ME content from chemical composition of the CSM samples. Twelve growing barrows with an initial body weight of $35.2{\pm}1.7$ kg were allotted to two $6{\times}6$ Latin square designs, with six barrows and six periods and six diets for each. A corn-dehulled soybean meal diet was used as the basal diet, and the other ten diets were formulated with corn, dehulled soybean meal and 19.20% CSM. The DE, ME and ATTD of gross energy among different CSM sources varied largely and ranged from 1,856 to 2,730 kcal/kg dry matter (DM), 1,778 to 2,534 kcal/kg DM, and 42.08 to 60.47%, respectively. Several chemical parameters were identified to predict the DE and ME values of CSM, and the accuracy of prediction models were also tested. The best fit equations were: DE, kcal/kg DM = 670.14+31.12 CP+659.15 EE with $R^2$ = 0.82, RSD = 172.02, p<0.05; and ME, kcal/kg DM = 843.98+25.03 CP+673.97 EE with $R^2$ = 0.84, RSD = 144.79, p<0.05. These results indicate that DE, ME values and ATTD of gross energy varied substantially among different CSM sources, and that some prediction equations can be applied to predict DE and ME in CSM with an acceptable accuracy.

Performance measurement of safety-critical systems based on ordinary differential equations and Petri nets: A case study of nuclear power plant

  • Nand Kumar Jyotish;Lalit Kumar Singh;Chiranjeev Kumar
    • Nuclear Engineering and Technology
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    • v.55 no.3
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    • pp.861-869
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    • 2023
  • This article proposes a novel approach to measure the performance of Safety-Critical Systems (SCS). Such systems contain multiple processing nodes that communicate with each other is modeled by a Petri nets (PN). The paper uses the PN for the performance evaluation of SCS. A set of ordinary differential equations (ODEs) is derived from the Petri net model that represent the state of the system, and the solutions can be used to measure the system's performance. The proposed method can avoid the state space explosion problem and also introduces new metrics of performance, along with their measurement: deadlock, liveness, stability, boundedness, and steady state. The proposed technique is applied to Shutdown System (SDS) of Nuclear Power Plant (NPP). We obtained 99.887% accuracy of performance measurement, which proves the effectiveness of our approach.

An Equation of State for the PVT Behavior of Gaseous Refrigerants (기체냉매의 PVT 거동을 나타내기 위한 상태방정식)

  • Park, K.;Sonntag, R.E.
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.7 no.1
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    • pp.98-111
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    • 1995
  • The objective of this work is to investigate the form of equations of state for specific refrigerants. In particular, equations of the extended van der Waals form have been studied. As a result, a new equation of state has been developed and tested over ranges of pressure and density up to 5 and 1.5 times critical, respectively. The equation of state separates the compressibility factor into two parts. One is the repulsive compressibility factor and the other is attractive. The former is in the same form of Carnahan-Starling's repulsive term with constant hard-sphere volume. The latter is based on a combination of two different functions linear to density. The equation of state developed here has 12 adjustable parameters and correlates PVT data successfully. All properties are in reduced forms.

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Acoustic theory application in ultra short baseline system for tracking AUV

  • Ji, Daxiong;Liu, Jian;Zheng, Rong
    • Ocean Systems Engineering
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    • v.3 no.1
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    • pp.71-77
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    • 2013
  • The effective tracking area of ultra short baseline (USBL) systems strongly relates to the safety of autonomous underwater vehicles (AUVs). This problem has not been studied previously. A method for determining the effective tracking area using acoustic theory is proposed. Ray acoustic equations are used to draw rays which ascertain the effective space. The sonar equation is established in order to discover the available range of the USBL system and the background noise level using sonar characteristics. The available range defines a hemisphere like enclosure. The overlap of the effective space with the hemisphere is the effective area for USBL systems tracking AUVs. Lake and sea trials show the proposed method's validity.

Transient Response Analysis of Locally Nonlinear Structures Using Substructure-Based-State Equations (부분구조의 상태방정식을 이용한 국부 비선형계의 과도응답해석)

  • 김형근;박윤식
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.17 no.10
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    • pp.2457-2466
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    • 1993
  • A simple method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. Although the method is based upon the mode synthesis formulation procedure, the equations of the combined whole structure are not constructed compared with the conventional methods. Lagrange multi-pliers are used to enforce the conditions of geometric compatibility between the substructure interfaces and they are treated as external forces on each substructure itself. Substructure eigenvalue problem is defined with the substructure interface free of fixed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurated and efficient in calculating transient responses compared with the direct numerical integration method.

Transient Response Analysis of Locally Nonlinear Structures Using Substructure-Based State Equations (부분구조의 상태방정식을 이용한 국부 비선형계의 과도응답해석)

  • 김형근;박윤식
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1993.04a
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    • pp.52-56
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    • 1993
  • An efficient method is presented for determining transient responses of locally nonlinear structures using substructure eigenproperties and Lagrange multiplier technique. The method is based upon the mode synthesis formulation procedure, but does not construct the equations of motion of the combined whole structure compared with the conventional methods. For modal bases of each linear substructure, either fixed or free interface modes can be employed. The transient analysis is based upon the recurrence discrete-time state equations and offers the simplicity of the Euler integration method without requiring small time increment and iterative solution procedure. Numerical examples reveal that the method is very accurate and efficient in calculating transient responses compared with the direct numerical integration method.

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Application of the Modified Reactive SPH Method for Simulating Explosions

  • Sirotkin, Fedir V.;Yoh, Jai-Ick
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2011.11a
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    • pp.922-925
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    • 2011
  • Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method widely used for the modeling fluid flows. Simulations of explosions require, besides the hydrodynamic equations, a realistic equation of state, an energy source term, and a set of chemical kinetic equations to follow the composition changes of the gas during the explosion. The performance of the hydrodynamic equations is investigated in the framework of the Sedov-Taylor blast-wave. The implementation of chemical kinetic equations and equation of state is studied with 1D detonation of TNT slab. Our results are compared to those from analytical and experimental studies.

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