Advanced Polynomial Neural Networks Architecture with New Adaptive Nodes
Sung‐Kwun Oh, Dong-Won Kim, Byoung‐Jun Park, Hyung-Soo Hwang · Transaction on Control, Automation and Systems Engineering · 2001
In this paper, we propose the design procedure of advanced Polynomial Neural Networks(PNN) architecture fo r optimal model identification of complex and nonlinear system. The proposed PNN architecture is presented as the generic and advanced type. The essence of the design procedure dwells on the Group Method of Data Handling (GMDH). PNN is a flexible neural architecture whose structure is developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated in a dynamic way. In this sense, PNN is a self-organizing network. With the aid of three representative numerical examples, compari- sons show that the proposed advanced PNN algorithm can produce the model with higher accuracy than previous other works. And performance index related to approximation and generalization capabilities of model is evaluated and also discussed. The mathematical models to express dynamic analysis of nonlinear real system, have had lots of difficulties in the selec- tion of variables constructing the model among many input- output variables. Moreover, high-order equation requires a large amount of data for estimating all system parameters in mathematical models. So it needs the model designer who has had the specific and prior knowledge of the model architecture or its components. In that case, it is impossible to make the high performance model architecture or to perform process control very well when we depend on the specific and prior knowledge of designer and experiment too much. To deal with such a problem, GMDH(1) was developed in Russia in the late 1960's by Ivakhnenko as an analysis technique for identifying nonlinear relations between system inputs and outputs. The primary disadvantage of GMDH is that it not only can gener- ate a complex polynomial even for some simple system but also can not take into consideration of input -output relation- ship well because of its limited architecture, and if there is a sufficiently large number of training data, GMDH has a ten- dency to produce overly complex networks as it tries to stretch for the last bit of accuracy. So it can be shown that the GMDH is very in effective in modeling nonlinear systems having dif- ferent characteristics in different environments. In order to overcome the limitations of GMDH, we propose a PNN algorithm and show its design procedure for optimal PNN model. The number of input variables used in Partial Description(PD) of each node is extended and the order of regression polynomial used in PD is also extended as linear, quadratic, and cubic. And also the number of input variables and the order of regression polynomial are not fixed and can be changed in each layer of PNN. Through the extended re- gression polynomial, the architecture of PNN can be changed to adapt to system environment. Two types of architectures, the basic PNN and modified PNN architecture, are studied in this paper.