ANN structure optimisation using analysis of error variance

Summary Artificial neural networks (ANN) are extensively utilized in structural health monitoring. Nevertheless, the definition of a rigorous method for the optimization of their structure is still an unresolved issue, especially when applied to safety critical systems. In this paper, an approach typically adopted in the design of experiments and based on the analysis of variance (ANOVA) is used to statistically determine the number of hidden neurons in a three-layer ANN structure. Repeated trainings of the same network structure provide multiple observations of the performance index here, based on the root mean square error. Different levels of network structure complexity are statistically compared, based on the number of hidden nodes. ANOVA is used to determine whether there is statistical evidence that the network performance is influenced by the number of hidden nodes. This analysis allows defining the threshold number of hidden nodes above which there is no statistical evidence of a performance benefit by the increase of the ANN structure complexity. The method is applied to the optimization of a set of algorithms for the diagnosis of fatigue damage on a typical aeronautical structure, consisting of a metallic panel with a riveted skin-stringer construction. The ANNs for damage detection, localization, and quantification are trained and validated with finite element simulated strain data and are finally tested on experimental strain signals, acquired in real-time in a fatigue crack growth laboratory test program including a skin crack artificially initiated in a panel bay and two stringers that had failed naturally under fatigue load