Modeling of systems using canonical form functions and symbolic regression

• US 8,332,188 B2
• Filed: 03/05/2007
• Issued: 12/11/2012
• Est. Priority Date: 03/03/2006
• Status: Active Grant

• Current Assignee: Siemens Industry Software Limited (Siemens AG)
• Original Assignee: Solido Design Automation (Siemens AG)
• Inventors: McConaghy, Trent Lorne
• Primary Examiner(s): Alhija, Saif
• Assistant Examiner(s): GEBRESILASSIE, KIBROM K
• Application Number:
  US11/682,089
• Publication Number:
  US 20070208548A1
• Time in Patent Office: 2,108 Days
• Field of Search: 703/2, 716/4, 716/5, 716/18
• US Class Current: 703/2
• CPC Class Codes: G06F 30/367 Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods

Abstract

An apparatus and method to generate and evolve canonical form expressions representing a characteristic of a given system. Static and dynamic behavior of non-linear electrical circuits can be modeled. Searching of canonical form expressions can use evolutionary algorithms, simulated annealing and Tabu searching.

Claims

1. A tangible computer-readable medium having recorded thereon statements and instructions for execution by a computer of a method to generate at least one mathematical expression describing a performance characteristic of a system, the system associated with variables and with pre-determined data related to the performance characteristic of the system, the method comprising steps of:

generating at least one initial mathematical expression having a pre-defined canonical form and being a function of the variables, the at least one initial mathematical expression having operators operating on the variables, the operators being selected from a pre-defined group of operators, the at least one initial mathematical expression describing the performance characteristic of the system;

wherein, the variables of the system are representable as a vector {right arrow over (x)} and the canonical form of an expression F({right arrow over (x)}) is representable as

2. The tangible computer-readable medium of claim 1 wherein, the goal function is a single objective goal function for minimizing error.

3. The tangible computer-readable medium of claim 1 wherein, the goal function is a multi-objective goal function for minimizing error and for minimizing complexity.

4. The tangible computer-readable medium of claim 1 wherein, the goal function is a multi-objective goal function for minimizing error and for constraining complexity.

5. The tangible computer-readable medium of claim 1 wherein, the goal function is a multi-objective goal function for constraining error and for constraining complexity.

6. The tangible computer-readable medium of claim 1 wherein, the goal function is at least for minimizing a normalized root mean square error between the pre-determined data and either the calculated data generated using the at least one initial mathematical expression or the additional calculated data generated using the at least one modified mathematical expressions.

7. The tangible computer-readable medium of claim 1 wherein, the step of modifying the at least one input mathematical expression in accordance with a search algorithm includes modifying the at least one input mathematical expression in accordance with an evolutionary search algorithm to produce the at least one modified mathematical expression.

8. The tangible computer-readable medium of claim 1 wherein, the step of modifying the at least one input mathematical expression in accordance with a search algorithm includes modifying the at least one input mathematical expression in accordance with a simulated annealing search algorithm to produce the at least one modified mathematical expression.

9. The tangible computer-readable medium of claim 1 wherein, the step of modifying the at least one input mathematical expression in accordance with a search algorithm includes modifying the at least one input mathematical expression in accordance with a Tabu search algorithm to produce the at least one modified mathematical expression.

10. The tangible computer-readable medium of claim 7 wherein, the goal function is an evolutionary multi-objective goal function.

11. The tangible computer-readable medium of claim 1 wherein, a step of simplifying the at least one modified mathematical expression is performed before generating additional calculated data.

12. The tangible computer-readable medium of claim 11, wherein the step of simplifying is done in accordance with a predicted sum of squares statistic process.

13. The tangible computer-readable medium of claim 7 wherein, the at least one initial mathematical expression and the at least one modified mathematical expressions are representable as trees, the trees having a pre-determined depth and a pre- determined branchiness, some of the at least one initial mathematical expression and the at least one modified mathematical expressions having introns.

14. The tangible computer-readable medium of claim 7 wherein, the step of generating at least one initial mathematical expression and the step of modifying the at least one input mathematical expression are performed in accordance with genetic programming principles.

15. The tangible computer-readable medium of claim 1 wherein, the system is an electrical system.

16. The tangible computer-readable medium of claim 1 wherein, the variables associated with the system include at least one of design variables, environmental variables and random variables.

17. A tangible computer-readable medium having recorded thereon statements and instructions for execution by a computer of a method to model an electrical circuit, the electrical circuit associated with circuit variables, with pre-determined data, with at least one pre-determined transient input waveform and with at least one pre-determined transient output waveform the method comprising steps of:

generating at least one initial mathematical expression dependent on at least one of at least one of the variables, at least one of the at least one pre-determined transient input waveform and at least one of the least one pre-determined transient output waveform, the at least one initial mathematical expression having a pre-defined canonical form, the at least one initial mathematical expression having operators operating on the variables, the operators selected from a pre-defined group of operators, the at least one initial mathematical expression describing a transient behavior of the electrical circuit;

wherein, the variables of the system are representable as a vector {right arrow over (x)} and the canonical form of an expression F({right arrow over (x)}) is representable as

18. The tangible computer-readable medium of claim 17 wherein, the pre-determined data includes at least one of steady-state electrical circuit data, transient electrical circuit data and noise electrical circuit data.

19. The tangible computer-readable medium of claim 17 wherein, the electrical circuit is nonlinear.

20. The tangible computer-readable medium of claim 17 wherein, the at least one initial mathematical expression and the at least one modified mathematical expression are independent of a connectivity topology of the electrical circuit.

21. The tangible computer-readable medium of claim 17 wherein, the at least one initial mathematical expression and the at least one modified mathematical expression are symbolic models of the electrical circuit.

22. The tangible computer-readable medium of claim 17 wherein, the at least one initial mathematical expression and the at least one modified mathematical expression are behavioral models of the electrical circuit.