Method and arrangement for designing a technical system

• US 7,444,312 B2
• Filed: 07/30/2003
• Issued: 10/28/2008
• Est. Priority Date: 08/14/2002
• Status: Expired due to Fees

• Current Assignee: Siemens AG
• Original Assignee: Siemens AG
• Inventors: Hillermeier, Claus, Stoehr, Annelie
• Primary Examiner(s): Holmes; Michael B
• Application Number:
  US10/524,556
• Publication Number:
  US 20050256683A1
• Time in Patent Office: 1,917 Days
• Field of Search: None
• US Class Current: 706/45
• CPC Class Codes: G05B 13/024 in which a parameter or coefficient is automatically adjusted to optimise the performance
• CPC Class Codes: G05B 13/026 using a predictor

Abstract

In a method for designing a technical system, a technical system is modeled by a predetermined quantity of target functions depending on parameters, each individual target function being weighted with a weighting factor. The method solves a system of equations comprising the parameters and the weighting factors as variables in a variable space, solutions of the system of equations forming working points of a solution space in the variable space. The working points are determined by a predictor-corrector method, according to which a predictor produced by a stochastic variable is determined in the variable space, from a first working point, and a second working point is then determined in a correcting step. The determined working points are used to design the technical system. The method can be used to redesign, modify or adapt an already existing technical system.

Claims

1. A method for designing a technical system having a predetermined set of target functions which are dependent on parameters, comprising:

weighting each individual target function with a weighting factor;

solving an equation system in a variable space to produce operating points in a solution space, the equation system having the parameters and the weighting factors as variables, the equation system being solved by a predictor-corrector method comprising;

generating a first operating point by determining a predictor as a stochastic variable in the variable space; and

after generating the first operating point, generating a second operating point using a corrector method; and

using the operating points to design the technical system.

2. The method as claimed in claim 1, wherein the predictor is determined by random numbers.

3. The method as claimed in claim 2, wherein the random numbers are normally distributed.

4. The method as claimed in claim 1, wherein the stochastic variable relates to a stochastic process Z_t which satisfies the following equation:

dZ_t=ε

P(Z_t)dB_t

where

P(z) is a projection matrix onto a space tangential to the solution space in a valid operating point z,

ε

is a scaling factor, and

B_t,tε

₀⁺ is a Brownian movement in the variable space.

5. The method as claimed in claim 1, wherein pareto-optimal points are determined as the operating points.

6. The method as claimed in claim 1, wherein the operating points are points with positive weighting factors in the solution space.

7. The method as claimed in claim 1, wherein the operating points satisfy one or more auxiliary conditions, with each auxiliary condition being represented by a further variable of the equation system in the variable space.

8. The method as claimed in claim 7, wherein the auxiliary conditions are equality auxiliary conditions and/or inequality auxiliary conditions.

9. The method as claimed in claim 8, wherein inequality auxiliary conditions are transformed into equality auxiliary conditions by a slack variable.

10. The method as claimed in claim 1, wherein the solution space is a submanifold in the variable space.

11. The method as claimed in claim 1, wherein the first operating point is generated by a weighting method.

12. The method as claimed in claim 1, wherein in generating the first operating point, plane tangential to the solution space is determined and the predictor is determined in said plane.

13. The method as claimed in claim 1, wherein if a negative predictor associated with a negative weighting factor occurs, a new predictor is determined by a reflection at a subplane of the solution space having the operating points.

14. The method as claimed in claim 13, wherein

a point of intersection of a trajectory which runs between the first operating point and the negative predictor with the subplane of the solution space is determined;

a tangential component of a vector spanned by the point of intersection and the negative predictor is determined at a subplane of the solution space, the weighting factor for the negative predictor now being equal to zero;

a normal component, associated with the tangential component, of the vector spanned by the point of intersection and the negative predictor is determined;

the new predictor is determined as twice the difference of the normal component from the negative predictor.

15. The method as claimed in claim 1, wherein the corrector method is a Newtonian method.

16. The method as claimed in claim 1, wherein the operating points are determined by iterations of the predictor-corrector method, with the second operating point of a preceding iteration step being used in a current iteration step as the first operating point of the predictor-corrector method.

17. The method as claimed in claim 16, wherein the iterations are terminated by an abort condition.

18. The method as claimed in claim 17, wherein the abort condition is satisfied when a predetermined number of operating points has been determined and/or a predetermined time limit has been reached.

19. A system for designing a technical system having a predeterminable set of target functions which are dependent on parameters, comprising;

a weighting unit to weight each individual target function with a weighting factor;

a processor to solve an equation system having the parameters and the weighting factors as variables in a variable space, the solutions of the equation system forming operating points of a solution space in the variable space, the operating points being determined by a predictor-corrector method comprising;

generating a first operating point by determining a predictor as a stochastic variable in the variable space; and

after generating the first operating point, generating a second operating point in a corrector step; and

an output unit to output the operating points for the design of the technical system.

20. The system as claimed in claim 19, further comprising a random number generator for generating the stochastic variable.

21. A computer readable medium on which is stored a computer program to perform a method for designing a technical system having a predetermined set of target functions which are dependent on parameters, the method comprising:

weighting each individual target function with a weighting factor;

solving an equation system in a variable space to produce operating points in a solution space, the equation system having the parameters and the weighting factors as variables, the equation system being solved by a predictor-corrector method comprising;

generating a first operating point by determining a predictor as a stochastic variable in the variable space; and

after generating the first operating point, generating a second operating point in a corrector step; and

using the operating points to design the technical system.