ABSTRACT
GMDH (group method of data handling), originated by Ivakhnenko (1968), is a useful data analysis technique for the identification of nonlinear complex systems, especially when few data are available. The primary advantage of GMDH is that it self-selects the structure (degree of nonlinearity) of the model without using a priori information on the relationship among input/ output variables. In the original GMDH (Ivakhnenko, 1968, 1971; Ivakhnenko et al., 1969), the concept of regularization is used to avoid overfitting the model to past data- In this concept, available input/output data are divided into two sets: training data for estimating unknown parameters in the partial polynomials, and checking data for selecting the intermediate variables in each layer. Much research was done within Ivakhnenko's group (Ivakhnenko et al., 1979) on the best method of dividing the data into two data sets. In the original GMDH we need the following heuristics:
H1: Predetermination of the structure of the partial polynomials
H2: Division of the original data into two sets; training data and checking data
H3: Predetermination of the number of intermediate variables selected in each layer
226These heuristics are to be changed so as to find their optimal combination. Therefore, the computational procedure of the original GMDH must be repeated many times, but the final model obtained is rarely for the optimal combination of the heuristics. Furthermore, the results identified depend heavily on the heuristics adopted.