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Method for constructing composite response surfaces by combining neural networks with polynominal interpolation or estimation techniques

  • US 7,191,161 B1
  • Filed: 07/31/2003
  • Issued: 03/13/2007
  • Est. Priority Date: 07/31/2003
  • Status: Expired due to Fees
First Claim
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1. A method for constructing a composite response surface based on neural networks and selected functions, the method comprising providing a computer that is programmed:

  • (1) to provide a set of h initial parameters that determine variation of provided data for a target variable, where each parameter corresponds to a coordinate in an h-dimensional parameter space G;

    (2) to decompose the h parameters into a first set of s simple parameters fi, numbered i=1, . . . , s, that may be used to describe the provided data with polynomials of total degree no greater than a selected number Ms, and a second set of c complex parameters gj, numbered j=1, . . . , c, that may be used to describe the provided data using neural networks, and with s+c=h, where s, c and Ms are selected positive integers;

    (3) to provide a simplex, having s+1 vertices, numbered k=1, . . . , s+1, and centered at a selected point in the space G;

    (4) to apply a neural network for each of the s+1 vertices, and to train each of the s+1 neural networks, using selected simulation data obtained by varying the parameters gj to generate a first sequence of network functions Rk(g1, . . . , gc);

    (5) to provide a second sequence of shape functions Pk(f1, . . . , fs) that satisfy the conditions Pk(f1, . . . , fs)=1 at the vertex numbered k and Pk(f1, . . . , fs)=0 at any vertex other than vertex number k, and Σ

    Pk(f1, . . . , fs)=1 for all values of f1, . . . , fs; and

    (6) to form a composite function CRS(fi, gj) defined by CRS

    { f i

    g j
    }
    =

    k = 1 s + 1




    P k

    ( f 1 ,



    , f s
    )
    ·

    R k

    ( g 1 ,



    , g c
    )
    .

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