Neurocomputing strategies in structural design — on analysing weights of feedforward neural networks

Abstract

The sequel of two papers explores the applicability of selected neurocomputing strategies in the optimization of structural systems. The present paper describes the use of interconnection weights of a multilayer, feedforward neural network to extract information pertinent to a design space modelled by such a network. It is shown that aweights analysis provides a technique to assess the effect of all input quantities on a given output. Such dependencies are expressed in the form of atransition matrix, and their evaluation is reduced to the inspection of elements of a matrix row. Explicit formulae are derived for networks with one and two hidden layers and can easily be generalized to networks with an arbitrary number of hidden layers. In addition to its use as a tool to partition design spaces, the weights analysis may be employed to assist in determining the size of hidden layers and an adequate number of training patterns (input-output pairs). Several numerical examples from the field of structural analysis are provided, and the paper underscores the utility of the present technique in decomposition driven optimal design; such optimization is treated in full in the companion paper.