Patent ID: 7899652

Claim:
A method of providing an optimized model of a nonlinear system, the method comprising: providing a support vector machine, the support vector machine having a wavelet kernel, support vectors being provided by a family of multidimensional wavelets and providing a model of the nonlinear system; providing training data to the support vector machine; and using the training data to optimize the support vectors through an optimization of the number of support vectors, weights of a support vector expansion, and translation factors of the support vectors using a linear programming algorithm, the optimized support vectors providing the optimized model of the nonlinear system, linear programming support vector regression (LP-SVR) with the wavelet kernel being used for modeling the nonlinear system, the support vector expansion having the form f ⁡ ( x ) = ∑ i = 1 l ⁢ β i ⁢ ∏ k = 1 n ⁢ ⁢ ϕ ( x k - x k ′ d ) = ∑ i = 1 l ⁢ ( α i + - α i - ) ⁢ ∏ k = 1 n ⁢ ⁢ ϕ ( x k - x k ′ d i ) and the linear programming algorithm having the form minimize ⁢ ⁢ c T ⁡ ( α + α - ξ ) subject ⁢ ⁢ to ⁢ ⁢ ( K - K - I - K K - I ) · ( α + α - ξ ) ≤ ( y + ɛ ɛ - y ) where c = ( 1 , 1 , … ⁢ , 1 ︸ l , 1 , 1 , … ⁢ , 1 ︸ l , 2 ⁢ C , 2 ⁢ C , … ⁢ , 2 ⁢ C ︸ l ) T , and where φ is a wavelet function, β i is a support vector ratio factor decomposable as β i =α i + −α i − , |β i |=α i + +α i − , x′ k is a translation factor, d i is a dilation factor, ε is a model deviation parameter, y is a data value, K is a wavelet kernel matrix, ζ is a slack variable, I is an identity matrix, C is a constant, α i + , α i − ≧0, α + =(α 1 + , α 2 + , . . . , α l + ) T and α − =(α 1 − , α 2 − , . . . , α 1 − ) T .