Development of the Goodman Diagram for DD5 Composite Using a Modular ANN

Abstract

This work presents an analysis of how the learning rate in a modular Artificial Neural Network (ANN) influences the development of the Goodman Diagram for the DD5 composite material. Experimental data involving multiple S-N curves were collected, and a mathematical approach based on the Generalized Power Law was employed to determine the stress amplitude and the average number of cycles to failure. The Goodman Diagram was constructed by calculating the mean stress from the stress amplitude and fatigue ratio. Data normalization was applied to prevent neuron saturation and enhance the generalization capability of the ANN. For training, three fatigue ratio values (R = 0.1, 2, and 10) were chosen, while an additional value (R = 0.5) was reserved for validation purposes. The hidden layer neuron count varied from 5 to 25, with learning rates tested at 0.05, 0.1, and 0.5 over 3000 training epochs. Analysis of the mean squared error (MSE) demonstrated that learning rates of 0.05 and 0.1 yielded errors on the order of 10⁻⁴, whereas the 0.5 rate produced higher errors around 10⁻³. The best performance was achieved with the 0.1 learning rate, as its Goodman Diagram curves closely matched the experimental data, reflecting superior learning ability and robustness of the model. This methodology illustrates that modular ANNs provide an efficient, fast, and cost-effective alternative for fatigue life analysis of composite materials, supporting improvements in structural design with enhanced safety and reliability.