Modeling Tool for Stiff Heterogeneous Systems
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Transcript of Modeling Tool for Stiff Heterogeneous Systems
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Modeling Tool for Stiff Heterogeneous Modeling Tool for Stiff Heterogeneous SystemsSystems
Yury Shornikov1, Eugeny Novikov2
1 Design Technological Institute of Digital Techniques SB RAS,Novosibirsk, Russia, [email protected]
2 Institute of Computational Modeling SB RAS,Krasnoyarsk, Russia, [email protected]
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Class of SystemsClass of Systems
;
;
Discrete-continuous systems. For example, the constrained pendulum.
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Classes of HS Continuous BehaviorClasses of HS Continuous Behavior
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Systems Models of Continuous Modes
Electromechanical ODE
Automation ODE having retarded arguments
Chemical kinetics ODE
Biological ODE, PDE
Electrical DAE
Chemical-engineering PDE
Mechanical PDE
Others ODE, DAE, PDE
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Class of SystemsClass of Systems
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Traction Electric DriveTraction Electric Drive
Block diagram of traction electric drive of electric loader
Structural specification (visual model)
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Data ImportData Import
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Changing of the motor torque in time
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Solving Direct Problems of Solving Direct Problems of Chemical KineticsChemical Kinetics
s
N
1iiij
N
1i
k
iij N,1j,ccrr j
ri N,1i,c – reactants
sj N,1j,k – rate constants of stages
αij и βij – stoichiometric coefficients
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Unification of ISMA SoftwareUnification of ISMA Software::Integrated PreprocessorIntegrated Preprocessor
LISMALISMA GG
;S S
C SC S
S E aE
ida
cidO
T*OOT
ETTE SS
:LISMAG C
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Ethane PyrolysisEthane Pyrolysis
2 6 3 3
3 2 6 4 2 5
2 5 2 4
2 6 2 2 5
2 5 2 5 4 10
,
,
,
,
.
C H CH CH
CH C H CH C H
C H C H H
H C H H C H
C H C H C H
8,1j,y j - concentrations of reactants
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Biliary SystemBiliary System
Reception Ejection
Daily bile secretion
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Biliary SystemBiliary SystemOutput intensity of the bile in 12
duodenum Output intensity of the bile into
the bile duct
Mode «reception»
Mode «ejection»
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Class of SystemsClass of SystemsSystem of differential-algebraic equations (DAE) with constraints:
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0 0 0 0 0
, , ,
, , ,
: , , 0,
, , , ,
where , , ,
: ,
: ,
: .
yx
y yx
yx
yx
k
NN
N NN
NN Nx
NN S
y f x y t
x x y t
pr g x y t
t t t x t x y t y
x R y R t R
f R R R R
R R R R
g R R R R
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Ring Modulator*Ring Modulator*
*Kampowski W., Rentrop P., Schmidt W. Classication and numerical simulation of electric circuits // Surveys on Mathematics for Industry, 2(1):23 65, 1992
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Ring Modulator:Ring Modulator:Program Model in ISMAProgram Model in ISMA
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Practical Modeling of HSPractical Modeling of HSRing modulator: comparative evaluation
Characteristics ISMAMK22*
DLSODE
MVS AnyLogic
Simulink
Number of computing the right side
474213 496073 _ _ _
Number of returns 496073 16946 _ _ _
*Novikov А.Е., Novikov Е.А., Shornikov Y.V. Approximation of Jacobi matrix in (2,2)-method of solving hybrid systems // Report of Academy of Science of Higher School of Russian Federation, 2008, #1(10). – P. 31-44.
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Original Explicit, Semi-Explicit and Adaptive Integration Original Explicit, Semi-Explicit and Adaptive Integration Algorithms in the ISMAAlgorithms in the ISMA**
* Instrumental tools of computerized analysis (ISMA) / Yu.V. Shornikov, V.S. Druzhinin, N.А. Makarov, K.V. Omelchenko, and I.N. Tomilov // Official registration license for computers No. 2005610126, Мoscow, Rospatent, 2005.
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High-Dimensional ModelsHigh-Dimensional ModelsModel of penetration of radioactive labeled antibodies in a tumor affected tissue of a
living oragnism (Akzo Nobel Central Research)
20t0,Ry,g0y,y,tfdt
dy N2
,ykyf
,ykyyy2y
2
yyf
1j2j2j2
j21j221j21j23j2
j3j21j2
j1j2
.v,0,...,v,0,v,0g,Rg
,yy,tty,N
1
,Nj1,c1j,c1j2
T000
N2
1N21N21
24j
23j
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Text Model in ISMAText Model in ISMA
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Dependency of Calculation Time Dependency of Calculation Time From System DimensionFrom System Dimension
Simulation results from:http://www.dm.uniba.it/~testset/report/medakzo.pdf
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Comparison of Solutions Obtained Comparison of Solutions Obtained by Explicit and Implicit Methodsby Explicit and Implicit Methods
RADAU5
RADAU5, RKF78ST
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Extending a Class of SystemsExtending a Class of Systems
DAE systems with constraints unresolved for the derivative:
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0 0 0 0 0
, , , 0,
, , ,
: , , 0,
, , , ,
where , , ,
: ,
: ,
: .
yx
y y yx
yx
yx
k
NN
N N NN
NN Nx
NN S
F x y y t
x x y t
pr g x y t
t t t x t x y t y
x R y R t R
F R R R R R
R R R R
g R R R R
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Instrumental Simulation of EPSInstrumental Simulation of EPS
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Dostovalov D.N. Program of graphical sheme editor for electro-power systems ISMA EPS (ISMA Electric Power Systems) / Yu.V. Shornikov, A.N. Komarichev, D.N. Dostovalov // Certificate of state registration of computer programs #2013617771. M.: Federal Service for Intellectual Property. - 2013.
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Algorithm for Analysis of Implicit ProblemsAlgorithm for Analysis of Implicit Problems**
• Problem definition:
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* Novikov E.A., Yumatova L.A. A few methods for solving of ordinary differential equations unresolved for the derivative // Reports of the Academy of Sciences of the USSR, vol.295, №4, 1987. – pp.809-812.
0 0 0 0
, 0,
where ,
, .
F x y
y x
x t x y t y
• Numerical scheme:
1 1 1 1 1 1
1 1 1
, ,
,
1( ), ,
where , , , ,
1, 1.
x yn n n n
n ny nx
x y xn ny n n n
nx n n ny n n
x x p k y y p k
D F ahF
D k h F y F k k hyah
F F x y x F F x y y
a p
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Event Detection in HSEvent Detection in HS**
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* 1. Novikov E.A., Shornikov Yu.V. Computer simulation of stiff hybrid systems: monograph / Novosibirsk: Publishing house of the NSTU, 2012, 451p. 2. Esposito J., Kumar V., Pappas, G.J.: Accurate event detection for simulating hybrid systems. In: Hybrid Systems: Computation and Control (HSCC). Volume LNCS 2034, Springer–Verlag, 1998.
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Event Detection AlgorithmEvent Detection Algorithm
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Test of Event Detection AlgorithmTest of Event Detection Algorithm
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a) – without taking into account the dynamics of an event function, .b) – using the event-detection algorithm, .
Movement
Rebound:
: 0,
.
pr y
v v
Modal behavior:
0,
0.
y v
v a
a b
1 0 75. 2 0 06.
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Extending a Class of SystemsExtending a Class of SystemsContinuous behavior of HS is determined by the systems differential-algebraic equations and PDEs.
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2
2
0 0 0 0
0 0
2
, , , , , ,
, ,
: , 0,
, , , ,
, , , ,
,
, , , ,
: ,
: ,
: ,
px z
x x
p px z z
x
k m
p
NN N
N N
N NN N N
N S
z z zx z t p
t p p
x x t
pr g x t
x t p x z t p z
t t t p p p
zz p
n
x R z R t R p R
R R R
R R R R R R
g R R R
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Thank you for your attentionThank you for your attention!!
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Yury Shornikov1, Eugeny Novikov2
1 Design Technological Institute of Digital Techniques SB RAS,Novosibirsk, Russia, [email protected]
2 Institute of Computational Modeling SB RAS,Krasnoyarsk, Russia, [email protected]