Method and apparatus for rapid approximation of system model

1 . A computer implemented method for generating an improved System Under Study (SUS) characterizing mathematical model (SCMM), the SUS being characterized comprising one of a mechanical system, an electrical system, a chemical system, a biological system, and an electromechanical system, the SUS operative to exhibit at least one output adapted in response to a plurality of input parameters, the SCMM configured to represent SUS behavior responsive to the plurality of input parameters and resulting in the exhibiting of at least one output, the method comprising:

loading, into a non-transitory computer readable storage medium of a computer, data representing a list of candidate input parameters associated with the SUS;

loading, into the non-transitory computer readable storage medium, data representing an initial SCMM; and

generating an improved SCMM comprising a summation of the initial SCMM and a plurality of polynomials, each polynomial being associated with a respective N-tuplet of candidate input parameters for greater than zero integer values of N;

wherein polynomials included within said improved SCMM are generated by iteratively performing the following steps until an evaluated difference between respective sets of output parameters generated in response to a common set of input parameters by a current SCMM (CSCMM) and the SUS being characterized is below a threshold level:

rank ordering the N-tuplets of input parameters to be processed;

selecting model generation points for a highest ranking N-tuplet of input parameters from among the rank ordered N-tuplets of input parameters to be processed;

causing the SUS to generate a set of output parameters in response to input parameters associated with the selected model generation points,

fitting a polynomial involving the selected N-tuplet of input parameters to the SUS generated set of output parameters;

updating the CSCMM by adding the fitted polynomials; and

evaluating fit of the CSCMM to the SUS by:

selecting a set of stress points by varying the input parameters,

causing the CSCMM and the SUS to generate respective sets of output parameters in response to the selected stress points, and

comparing the CSCMM generated set of output parameters to the SUS generated set of output parameters to determine a difference therebetween.

2 . The computer implemented method of claim 1 , wherein fitting a polynomial involving the selected N-tuplet of input parameters to the SUS generated set of output parameters comprises:

iteratively performing the following steps until an evaluated difference between respective sets of output parameters generated in response to a common set of input parameters by the CSCMM and the SUS being characterized is below a threshold level:

selecting a plurality of model generation points in the N-dimensional space defined by axis parallel lines of the selected N-tuplet of input parameters, where the selected model generation points are incremented by one or more for subsequent iterations in the N-dimensional space;

evaluating the CSCMM at the selected model generation points;

fitting a polynomial involving input parameters from the N-tuplet of input parameters to the CSCMM evaluation;

evaluating a fit of the polynomial to the SUS; and

removing polynomial terms that do not involve all input parameters from said N-tuplet of input parameters.

3 . The computer implemented method of claim 1 , wherein rank ordering is determined according to a difference between evaluations of the set of output parameters generated by the CSCMM to the outputs of the SUS at a plurality of selected ranking stress points, the ranking stress points generated using at least one of orthogonal array design, fractional factorial design, full factorial design, design of experiments, and space filling designs.

4 . The computer implemented method of claim 1 , wherein rank ordering is determined according to at least one of importance, presumed importance, random order, past data, alphabetical order, and order of entry.

5 . The computer implemented method of claim 4 , wherein importance of input parameters is determined by main effects analysis of the difference between the set of output parameters generated by the CSCMM to the outputs of the SUS at ranking stress points.

6 . The computer implemented method of claim 4 , wherein importance of N-tuplets of input parameters is determined by analyzing effects of interactions among the N-tuplets of input parameters for each corresponding output parameter of the CSCMM and the SUS at ranking stress points.

7 . The computer implemented method of claim 1 , wherein fitting a polynomial involving input parameters in the selected N-tuplet of input parameters is performed using at least one of orthogonal polynomials, matrix inversion, Lagrange polynomials, and solving simultaneous equations.

8 . The computer implemented method of claim 1 , wherein evaluated difference is determined by goodness of fit criteria comprising at least one of a maximum absolute difference, a sum of absolute differences, a mean square of selected top absolute differences, and a mean square error.

9 . The computer implemented method of claim 1 , wherein the SUS comprises a machine and the model comprises a machine performance model, the machine comprising one of an engine, an automobile, and an aircraft.

10 . The computer implemented method of claim 1 , wherein the SUS comprises an article of manufacture having a plurality of assemblies, wherein each of the assemblies comprises a plurality of components, and wherein the model represents the article of manufacture, assemblies, and components.

11 . The computer implemented method of claim 1 , wherein the SUS comprises a product manufacturing system and the model comprises a product manufacturing model.

12 . The computer implemented method of claim 1 , wherein the SUS comprises a voice or video compression system and the model comprises a voice or video compression model.

13 . The computer implemented method of claim 1 , wherein the SUS comprises a weather prediction system and the model comprises a weather prediction model.

14 . A computer implemented method for generating an improved System Under Study (SUS) characterizing mathematical model (SCMM), the SUS being characterized comprising one of a mechanical system, an electrical system, a chemical system, a biological system, and an electromechanical system, the SUS operative to exhibit at least one output adapted in response to a plurality of input parameters, the SCMM configured to represent SUS behavior responsive to the plurality of input parameters and resulting in the exhibiting of the at least one output, the method comprising:

loading, into the non-transitory computer readable storage medium of a computer, data representing a list of candidate input parameters associated with the SUS;

loading, into a non-transitory computer readable storage medium, data representing an initial SCMM;

generating an improved SCMM comprising a summation of the initial SCMM and a plurality of complex function elements, each complex function element being associated with a respective N-tuplet of candidate input parameters for greater than zero integer values of N;

wherein complex function elements included within said improved SCMM are generated by iteratively performing the following steps until an evaluated difference between respective sets of output parameters generated in response to a common set of input parameters by a current SCMM (CSCMM) and the SUS being characterized is below a threshold level:

rank ordering the N-tuplets of input parameters to be processed;

selecting model generation points for a highest ranking N-tuplet of input parameters from among the rank ordered N-tuplets of input parameters to be processed;

causing the SUS to generate a set of output parameters in response to input parameters associated with the selected model generation points,

fitting a complex function element involving the selected N-tuplet of input parameters to the SUS generated set of output parameters;

updating the CSCMM by adding the fitted complex function elements; and

evaluating fit of the CSCMM to the SUS by:

selecting a set of stress points by varying the input parameters,

causing the CSCMM and the SUS to generate respective sets of output parameters in response to the selected stress points, and

comparing the CSCMM generated set of output parameters to the SUS generated set of output parameters to determine a difference therebetween.

15 . The computer implemented method of claim 14 , wherein the complex function elements are associated with one of a polynomial function, a wavelet function, a Fourier series, and a Walsh function.

16 . The computer implemented method of claim 1 , further comprising:

prior to evaluating fit of the SCMM to the SUS, adjusting a constant term to match the evaluations of the SUS and the CSCMM at a point.

17 . The computer implemented method of claim 14 , further comprising:

prior to evaluating fit of the SCMM to the SUS, adjusting a constant term to match the evaluations of the SUS and the CSCMM at a point.

18 . A computer implemented method of generating a model of a physical system, the physical system comprising one of a mechanical system, an electrical system, a chemical system, a biological system, and an electromechanical system, the method comprising:

receiving an input dataset comprising data representing a list of candidate input parameters associated with the physical system and data representing an initial model of the physical system, the initial model of the physical system comprising a plurality of polynomials, each polynomial being associated with a respective N-tuplet of candidate input parameters for greater than zero integer values of N; and

generating an output dataset associated with an improved model by iteratively performing the following steps until an evaluated difference between respective sets of output parameters generated in response to a common set of input parameters by a current model and the physical system is below a threshold level:

rank ordering the N-tuplets of input parameters to be processed;

selecting model generation points for a highest ranking N-tuplet of input parameters from among the rank ordered N-tuplets of input parameters to be processed;

causing the current model to generate a set of output parameters in response to input parameters associated with the selected model generation points,

fitting a polynomial involving the selected N-tuplet of input parameters to the set of output parameters generated by the current model;

updating the current model by adding the fitted polynomials; and

evaluating fit of the current model to the physical system by:

selecting a set of stress points by varying the input parameters,

causing the current model and the physical system to generate respective sets of output parameters in response to the selected stress points, and

comparing the set of output parameters generated by the current model to the set of output parameters generated by the physical system to determine a difference therebetween.