NEUROCOMPUTING STRATEGIES IN STRUCTURAL DESIGN - ON ANALYZING WEIGHTSOF FEEDFORWARD NEURAL NETWORKS

The sequel of two papers explores the applicability of selected neuroc omputing strategies in the optimization of structural systems. The pre sent paper describes the use of interconnection weights of a multilaye r, feedforward neural network to extract information pertinent to a de sign space modelled by such a network. It is shown that a weights anal ysis provides a technique to assess the effect of all input quantities on a given output. Such dependencies are expressed in the form of a t ransition 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 networ ks with an arbitrary number of hidden layers. In addition to its use a s a tool to partition design spaces, the weights analysis may be emplo yed to assist in determining the size of hidden layers and an adequate number of training patterns (input-output pairs). Several numerical e xamples from the field of structural analysis are provided, and the pa per underscores the utility of the present technique in decomposition driven optimal design; such optimization is treated in full in the com panion paper.