System and method for constructing a mathematical model of a system in an artificial intelligence environment

Abstract

A system and method for constructing a mathematical model of a system. The method includes constructing an initial mathematical system representation with a combination of terms, the terms comprising mathematical functions including independent variables dependent on an input signal. A first set of known data is inputted to the initial mathematical representation to generate a corresponding set of output data. The corresponding set of output data of the initial mathematical representation and a second set of known data, correlated to the first set of known data, is fed to a comparator to generate error signals representing differences between output data and correlated members of the second set of known data. A parameter of the combination of terms is iteratively varied to produce a refined mathematical representation of the system until a measure of the error signals is reduced to a value wherein the set of corresponding output data of the refined mathematical representation over a desired range is approximately equivalent to the second set of known data.

1 . A method in an artificial intelligence (AI) system of constructing a mathematical model of a system, comprising:
 constructing an initial mathematical representation of said system with a combination of terms, said terms comprising mathematical functions including independent variables dependent on an input signal;   inputting a first set of known data to said initial mathematical representation to generate a corresponding set of output data;   feeding said corresponding set of output data of said initial mathematical representation and a second set of known data correlated to said first set of known data, to a comparator, said comparator generating error signals representing a difference between members of said set of output data and correlated members of said second set of known data; and   iteratively varying a parameter of at least one of said combination of terms comprising said initial mathematical representation to produce a refined mathematical representation of said system until a measure of said error signals is reduced to a value wherein the set of corresponding output data of said refined mathematical representation over a desired range is approximately equivalent to said second set of known data.   
     
     
         2 . The method recited in  claim 1 , wherein said iteratively varying a parameter of at least one of said combination of terms includes setting a coefficient of each term to a value between 0 and 1 such that all coefficients sum to 1. 
     
     
         3 . The method recited in  claim 1 , wherein said combination of terms comprises at least one of a transcendental function, a polynomial function, and a Boolean function. 
     
     
         4 . The method recited in  claim 1 , wherein said first set of known data and said second set of known data respectively comprise known input data and corresponding known output data for said real system. 
     
     
         5 . The method recited in  claim 1 , wherein said first set of known data and said second set of known data both comprise known output data for said real system. 
     
     
         6 . The method recited in  claim 1 , wherein said first set of known data and said second set of known data both comprise known input data for said real system. 
     
     
         7 . The method as recited in  claim 1 , wherein said first set of known data and said second set of known data are a subset of all known data for said real system. 
     
     
         8 . The method recited in  claim 7 , wherein said subset of all known data is utilized to produce said refined mathematical representation of said system and remaining data of said all known data is utilized to test said refined mathematical representation for coherence over a fuller range of data. 
     
     
         9 . The method recited in  claim 1 , wherein said measure of said error signals corresponds to a maximum error signal for the first and second sets of known data. 
     
     
         10 . The method recited in  claim 1 , wherein said measure of said error signals is a root-mean-square (RMS) value of said error signals. 
     
     
         11 . A system for constructing an artificial intelligence (AI) mathematical model of a system, comprising:
 a processor; and,   a memory, said memory storing instructions which, when executed by said processor, are operative to:
 construct an initial mathematical representation of said system with a combination of terms, said terms comprising mathematical functions including independent variables dependent on an input signal; 
 input a first set of known data to said initial mathematical representation to generate a corresponding set of output data; 
 feed said corresponding set of output data of said initial mathematical representation and a second set of known data, correlated to said first set of known data, to a comparator, said comparator generating error signals representing a difference between members of said set of output data and correlated members of said second set of known data; 
 iteratively vary a parameter of at least one of said combination of terms comprising said initial mathematical representation to produce a refined mathematical representation of said system until a measure of said error signals is reduced to a value wherein the set of corresponding output data of said refined mathematical representation over a desired range is approximately equivalent to said second set of known data. 
   
     
     
         12 . The system recited in  claim 11 , wherein iteratively varying a parameter of at least one of said combination of terms includes setting a coefficient of each term to a value between 0 and 1 such that all coefficients sum to 1. 
     
     
         13 . The system recited in  claim 11 , wherein said combination of terms comprises at least one of a transcendental function, polynomial function, and a Boolean function. 
     
     
         14 . The system recited in  claim 11 , wherein said first set of known data and said second set of known data respectively comprise known input data and corresponding known output data for said real system. 
     
     
         15 . The system recited in  claim 11 , wherein said first set of known data and said second set of known data both comprise known output data for said real system. 
     
     
         16 . The system recited in  claim 11 , wherein said first set of known data and said second set of known data both comprise known input data for said real system. 
     
     
         17 . The system as recited in  claim 11 , wherein said first set of known data and said second set of known data are a subset of all known data for said real system. 
     
     
         18 . The system recited in  claim 17 , wherein said subset of all known data is utilized to produce said refined mathematical representation of said system and remaining data of said all known data is utilized to test said refined mathematical representation for coherence over a fuller range of data. 
     
     
         19 . The system recited in  claim 11 , wherein said measure of said error signals corresponds to a maximum error signal for the first and second sets of known data. 
     
     
         20 . The system recited in  claim 11 , wherein said measure of said error signals is a root-mean-square (RMS) value of said error signals.