Revised GMDH Algorithm Estimating Degree of the Complete Polynomial

Abstract

In this paper, a revised GMDH (Group Method of Data Handling) algorithm, which can estimate directly degree of the complete polynomial, is developed. In the previous GMDH algorithms, the optimal partial polinomials, which are generated by using the second degree polynomials of two variables in each selection layer, are accumulated in multilayered structure to construct the complete polynomial, and so, degrees of the variables which construct the complete polynomial become positive integral multiples of the input variables. Therefore, the system, which can be described by the complete polynomials with degrees of the non-integers, are very difficult to be identified by the previous GMDH algorithm. The revised GMDH algorithm in this paper generates optimal partial polynomials, which can estimate directly degree of the complete polynomial in each selection layer, and constructs the complete polynomial by the combinations of them. Therefore, over the many kinds of the nonlinear systems can be identified by the revised GMDH algorithm. The revised GMDH algorithm is applied to a simple illustrative example and compared with the result obtained by the previous GMDH algorithm.