An optimised product-unit neural network with a novel PSO–BP hybrid training algorithm: Applications to load–deformation analysis of axially loaded piles

• We coupled both PSO and BP algorithms to develop a robust hybrid training algorithm.
• A more efficient hybrid algorithm based on the L–M algorithm and the particle swarm optimiser.
• This model provides a better prediction of the load–deformation curve of axially loaded piles.

In general, neural network training is a nonlinear multivariate optimisation problem. Unlike previous studies, in the present study, particle swarm optimisation (PSO) and back-propagation (BP) algorithms were coupled to develop a robust hybrid training algorithm with both local and global search capabilities. To demonstrate the capacity of the proposed model, we applied the model to the predictions of the load–deformation behaviour of axially loaded piles. This is a soil–structure interaction problem, involving a complex mechanism of load transfer from the pile to the supporting geologic medium. A database of full scale pile loading tests is used to train and validate the product-unit network. The results show that the proposed hybrid learning algorithm simulates the load–deformation curve of axially loaded piles more accurately than other BP, PSO, and existing PSO–BP hybrid methods. The network developed using the proposed algorithm also turns out to be more accurate than hyperbolic and t−zt−z models.