This paper addresses the training of network models from data produced by systems with symmetry properties. It is argued that although general networks are global approximators, in practice some properties such as symmetry are very hard to learn from data. In order to guarantee that the final network will be symmetrical, constraints are developed for two types of models, namely, the multilayer perceptron (MLP) network and the radial basis function (RBF) network. In global modeling problems it becomes crucial to impose conditions for symmetry in order to stand a chance of reproducing symmetry-related phenomena. Sufficient conditions are given for MLP and RBF networks to have a set of fixed points that are symmetrical with respect to the origin of the phase space. In the case of MLP networks such conditions reduce to the absence of bias parameters and the requirement of odd activation functions. This turns out to be important from a dynamical point of view since some phenomena are only observed in the context of symmetry, which is not a structurally stable property. The results are illustrated using bench systems that display symmetry, such as the Duffing-Ueda oscillator and the Lorenz system.

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The present study investigated the influence of high proportions of pellet feed (two different particle sizes) on the cold agglomeration behaviour of a sinter mixture and the properties of the granules. Using high proportions of adherent particles (pellet feed) lead to a decrease in the mixtures' mean diameter, producing wider size distributions with higher contents of granules below 1 mm. The bed permeability was impaired for higher additions of pellet feed, which correlated with the alterations of granules size distribution. Degradation tests so simulate handling and transported sharply affected granules size distribution and permeability, showing that larger granules are more susceptible to degradation. Moreover, both the ratio and the size distribution of the pellet feed were found to influence the granulation mechanism to different extents. Using finer adherent particles at adherents/nuclei ratios bigger than 50% changed the agglomeration mechanism from layering towards a combination of coalescence and layering.

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