METHOD AND SYSTEM FOR EMPIRICAL MODELING OF TIME-VARYING, PARAMETER-VARYING, AND NONLINEAR SYSTEMS VIA ITERATIVE LINEAR SUBSPACE COMPUTATION

• US 20110054863A1
• Filed: 09/03/2010
• Published: 03/03/2011
• Est. Priority Date: 09/03/2009
• Status: Active Grant

• Current Assignee: Adaptics, Inc.
• Original Assignee: Adaptics, Inc.
• Inventors: Larimore, Wallace E.
• Granted Patent: US 8,898,040 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06F 2111/10 Numerical modelling
• CPC Class Codes: G06F 2218/00 Aspects of pattern recognition specially adapted for signal processing
• CPC Class Codes: G06F 30/23 using finite element methods [FEM] or finite difference methods [FDM]
• CPC Class Codes: G06F 9/48 Program initiating; Program switching, e.g. by interrupt

Abstract

Methods and systems for estimating differential or difference equations that can govern a nonlinear, time-varying and parameter-varying dynamic process or system. The methods and systems for estimating the equations may be based upon estimations of observed outputs and, when desired, input data for the equations. The methods and systems can be utilized with any system or process that may be capable of being described with nonlinear, time-varying and parameter-varying difference equations and can used for automated extraction of the difference equations in describing detailed system or method behavior for use in system control, fault detection, state estimation and prediction and adaptation of the same to changes in a system or method.

Claims

1. A system for identifying nonlinear, linear parameter varying and time varying models, comprising:

a linear subspace algorithm that receives at least one of a first output signal and a first input signal, the first output signal and the first input signal comprising at least one of a second output signal of the linear subspace algorithm and augmented input signals in combination with at least one of the Kronecker product the first input signal and a scheduling function, the Kronecker product of a state function and the scheduling function and substantially equivalent signals.

2. The system of claim 1, further comprising at least one iteration of the linear subspace algorithm that refines parameter estimates and state estimates.

3. The system of claim 2, further comprising the evaluation of a likelihood function that determines convergence of an iteration.

4. The system of claim 1, wherein an optimal state order is selected using at least one of a likelihood computation and an AIC computation.

5. The system of claim 1, further comprising a likelihood ratio test that determines if at least one of failures or changes in the system have occurred.

6. The system of claim 1, wherein at least one of the state function and the Kronecker product of a state function and the scheduling function scheduling function is absent upon initialization.

7. The system of claim 2, further comprising outlier censoring to ignore data when the use of such data results in unstable computation.

8. The system of claim 7, wherein the outlier censoring is achieved through a monitoring of an ARX modeling computation.

9. The system of claim 1, further comprising the utilization of experimental design to stabilize computation.

10. A system for estimating a set of equations governing nonlinear, time-varying and parameter-varying processes, comprising:

a first input;

a second input;

a feedback box; and

a time delay box,

wherein the first input and the second input are passed through the feedback box to the time delay box and produce an output.

11. The system of claim 11, wherein the system iterates until the variation from consecutive outputs reaches a predetermined threshold.

12. The system of claim 11, wherein the output of the system is used as at least one of the first input and the second input during iterations of the system.

13. The system of claim 11, wherein the system iterates until the variation from consecutive outputs reaches a predetermined threshold.

14. The system of claim 11, wherein the time delay box is a predetermined sample duration.

15. The system of claim 14, wherein the time delay box comprises at least one of a plurality of linear, time-invariant coefficients.

16. The system of claim 11, wherein the feedback box comprises at least one of the Kronecker products of a plurality of basis functions, a plurality of scheduling functions and a plurality of state functions.

17. The system of claim 11, wherein the first input is at least one of a plurality of scheduling parameters.

18. The system of claim 11, wherein the second input is at least one of a plurality of basis functions.