EP1390883A2 - Procede pour fournir des informations d'erreur sur des incoherences dans un systeme d'equations differentielles - Google Patents
Procede pour fournir des informations d'erreur sur des incoherences dans un systeme d'equations differentiellesInfo
- Publication number
- EP1390883A2 EP1390883A2 EP02737851A EP02737851A EP1390883A2 EP 1390883 A2 EP1390883 A2 EP 1390883A2 EP 02737851 A EP02737851 A EP 02737851A EP 02737851 A EP02737851 A EP 02737851A EP 1390883 A2 EP1390883 A2 EP 1390883A2
- Authority
- EP
- European Patent Office
- Prior art keywords
- computer program
- equation
- computer
- component
- meshes
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Withdrawn
Links
- 238000000034 method Methods 0.000 title claims abstract description 63
- 239000011159 matrix material Substances 0.000 claims description 56
- 238000004590 computer program Methods 0.000 claims description 36
- 238000004088 simulation Methods 0.000 claims description 24
- 239000013598 vector Substances 0.000 claims description 17
- 230000006399 behavior Effects 0.000 claims description 10
- 230000001419 dependent effect Effects 0.000 claims description 8
- 238000010998 test method Methods 0.000 claims 2
- 238000013024 troubleshooting Methods 0.000 description 5
- 238000004364 calculation method Methods 0.000 description 3
- 230000006870 function Effects 0.000 description 3
- 238000011161 development Methods 0.000 description 2
- 230000018109 developmental process Effects 0.000 description 2
- 235000002918 Fraxinus excelsior Nutrition 0.000 description 1
- 239000002956 ash Substances 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 230000009897 systematic effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B17/00—Systems involving the use of models or simulators of said systems
- G05B17/02—Systems involving the use of models or simulators of said systems electric
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
- G06F17/13—Differential equations
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
Definitions
- a set of column meshes of the dependency matrix ⁇ is determined, each of which has the numbers of those columns of the dependency matrix A, or those components of x or one of its derivatives, which are dependent on one another.
- a "line mesh” is understood here to mean the following.
- a set C z of natural numbers i, l ⁇ i ⁇ n is called a row mesh of a matrix with n rows and m columns if it fulfills the following conditions:
- a column mesh is understood to be a set C s of natural numbers i, l ⁇ i ⁇ m, a matrix ⁇ with n rows and m columns if it fulfills the following conditions:
- the "set of column indices of the transverse T" is understood to be a set Z which contains the column indices of the elements of the transverse T of the matrix A as elements.
- the set Z contains exactly those numbers j for which there is an i, so that the element (/ " , /) is an element of the transverse T of the matrix A ,.
- step 2 of the method according to the invention with the aim of determining row meshes and column meshes of the dependency matrix Y shown in FIG. 2, the transverse T of the dependency matrix given in FIG. 2 is first determined.
- Methods for determining transversals are in IS Duff, "On algorithms for obtaining a maximum transversal", ACM Trans. Math. Software, 7 (3): 315-330, 19-81 , in EL Lawler, "Combinatorial Optimization: Networks and Matroids", Holt, Rinehart and Winston, 1976, in L. Lovasz and MD Plummer, "Matching Theory", North-Holland Mathematics Studies 121 .. Annais of Discrete Mathematics, 29. North Holland, 1986, or in CC Pantelides, "The consistent initialization of differential algebraic systems", SIAM J. Sei. Statist. Co put., 9 (2): 213-231, Mar. 1988.
- steps for providing error information about inconsistencies in the system of equations are carried out before the equation system is actually solved.
- / j (t, x ⁇ i), x (t), ..., x (i) (t) j depends on the first element of x, i.e. on x x (t).
- the element A (3, l) selected as an example is set to the value "0" because the third element of f, that is f 3 ⁇ l, x (l), x ⁇ t), -. , x (l)), is from the first element of x, i.e. from
- step 2 of the method according to the invention with the aim of determining row meshes and column meshes of the dependency matrix A indicated in FIG. 4, the transverse T of the dependency matrix A indicated in FIG. 4 is first determined.
- Step 3 outputs the error information shown in FIG. 5.
- a prediction of the behavior of the underlying system with numerical means is not even attempted because errors will occur if a simulation is possible at all. Rather, the modeling of the system and the system itself must be checked again. This saves valuable computing time on the computer system not shown here. Troubleshooting is considerably simplified by knowing the error information output in step 3.
- the equation system is to be solved numerically, ie values for the unknown vector x (t) are to be calculated at one or more times t.
- Known numerical solution methods which are not illustrated here, are used for this purpose, which run as a computer program on a computer system not shown here.
- error information about inconsistencies in the relevant system of equations is provided as follows before the system of equations is actually solved.
- fl (xl (t), x2 (t), x3 (t), pl, p2, p3) is Kirchhoff's voltage equation for the mesh consisting of all three network elements of the network from FIG. 6.
- the quantity Z of the row meshes determined in FIG. 4 and the quantity S of the column meshes ascertained in FIG. 4 are determined.
- the error information specified in FIG. 8 is output using the equation meaning list G and the component meaning list K from FIG.
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Theoretical Computer Science (AREA)
- Pure & Applied Mathematics (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Computer Hardware Design (AREA)
- Data Mining & Analysis (AREA)
- General Engineering & Computer Science (AREA)
- Algebra (AREA)
- Operations Research (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- Geometry (AREA)
- Evolutionary Computation (AREA)
- Microelectronics & Electronic Packaging (AREA)
- Automation & Control Theory (AREA)
- Complex Calculations (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
- Testing And Monitoring For Control Systems (AREA)
Abstract
L'invention concerne un procédé pour fournir des informations d'erreur concernant des incohérences dans un système d'équations différentielles décrivant un système ou un processus technique.
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
DE10126018A DE10126018A1 (de) | 2001-05-28 | 2001-05-28 | Verfahren zum Bereitstellen von Fehlerinformationen über Inkonsistenzen in einem System von Differentialgleichungen |
DE10126018 | 2001-05-28 | ||
PCT/DE2002/001878 WO2002097679A2 (fr) | 2001-05-28 | 2002-05-23 | Procede pour fournir des informations d'erreur sur des incoherences dans un systeme d'equations differentielles |
Publications (1)
Publication Number | Publication Date |
---|---|
EP1390883A2 true EP1390883A2 (fr) | 2004-02-25 |
Family
ID=7686449
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
EP02737851A Withdrawn EP1390883A2 (fr) | 2001-05-28 | 2002-05-23 | Procede pour fournir des informations d'erreur sur des incoherences dans un systeme d'equations differentielles |
Country Status (7)
Country | Link |
---|---|
US (1) | US7490026B2 (fr) |
EP (1) | EP1390883A2 (fr) |
JP (1) | JP2004532483A (fr) |
KR (1) | KR100552639B1 (fr) |
CN (1) | CN1527979A (fr) |
DE (1) | DE10126018A1 (fr) |
WO (1) | WO2002097679A2 (fr) |
Families Citing this family (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US7415395B2 (en) * | 2001-12-21 | 2008-08-19 | Caterpillar Inc. | Symbolic evaluation engine for high-performance simulations |
DE102004040177A1 (de) * | 2004-08-18 | 2006-03-09 | Infineon Technologies Ag | Verfahren zur Verbesserung der Aussageschärfe von Diagnosen technischer Anordnungen |
US20080026968A1 (en) * | 2006-07-28 | 2008-01-31 | Deckman Douglas E | Lubricant compositions, their preparation and use |
US8483999B2 (en) | 2010-11-18 | 2013-07-09 | Toyota Motor Engineering & Manufacturing North America, Inc. | Method and system for simplifying models |
WO2013125118A1 (fr) * | 2012-02-22 | 2013-08-29 | カルソニックカンセイ株式会社 | Dispositif d'estimation de paramètres |
US8726203B1 (en) | 2013-04-25 | 2014-05-13 | Cydesign, Inc. | System and method for generating virtual test benches |
Family Cites Families (6)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH01307868A (ja) | 1988-06-06 | 1989-12-12 | Mitsubishi Electric Corp | 数値解析装置 |
JPH0944473A (ja) | 1995-07-26 | 1997-02-14 | Hitachi Ltd | 有限要素法による偏微分方程式解析手法 |
DE19626984C1 (de) * | 1996-07-04 | 1997-11-27 | Siemens Ag | Verfahren zur rechnergestützten Ermittlung einer Systemzusammenhangsfunktion |
EP1062604B1 (fr) * | 1998-03-18 | 2001-11-07 | Siemens Aktiengesellschaft | Procede et dispositif pour determiner une defaillance d'un systeme technique |
US6266630B1 (en) * | 1998-06-03 | 2001-07-24 | Mentor Graphics Corporation | Method and apparatus for providing a graphical user interface for simulating designs with analog and mixed signals |
US6230101B1 (en) * | 1999-06-03 | 2001-05-08 | Schlumberger Technology Corporation | Simulation method and apparatus |
-
2001
- 2001-05-28 DE DE10126018A patent/DE10126018A1/de not_active Ceased
-
2002
- 2002-05-23 KR KR1020037015502A patent/KR100552639B1/ko not_active IP Right Cessation
- 2002-05-23 WO PCT/DE2002/001878 patent/WO2002097679A2/fr active Application Filing
- 2002-05-23 CN CNA028109023A patent/CN1527979A/zh active Pending
- 2002-05-23 EP EP02737851A patent/EP1390883A2/fr not_active Withdrawn
- 2002-05-23 JP JP2003500789A patent/JP2004532483A/ja active Pending
-
2003
- 2003-11-26 US US10/723,642 patent/US7490026B2/en not_active Expired - Fee Related
Non-Patent Citations (1)
Title |
---|
See references of WO02097679A2 * |
Also Published As
Publication number | Publication date |
---|---|
JP2004532483A (ja) | 2004-10-21 |
KR100552639B1 (ko) | 2006-02-20 |
DE10126018A1 (de) | 2003-02-27 |
KR20040007612A (ko) | 2004-01-24 |
US20040133407A1 (en) | 2004-07-08 |
US7490026B2 (en) | 2009-02-10 |
WO2002097679A2 (fr) | 2002-12-05 |
CN1527979A (zh) | 2004-09-08 |
WO2002097679A3 (fr) | 2003-05-22 |
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Legal Events
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Effective date: 20091201 |