Artificial neural networks in the calibration of nonlinear mechanical models

Abstract

Rapid development in numerical modelling of materials and the complexity of new models increase quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models from noisy experimental data remains a nontrivial and often computationally intensive task. Layered neural networks provide a robust and efficient technique for overcoming the time-consuming simulations of calibrated models. The potential advantages of neural networks include simple implementation and high versatility in approximating nonlinear relationships. Therefore, there were several approaches proposed in literature for accelerating the calibration of nonlinear models by neural networks. This contribution reviews and compares three possible strategies based on approximating (i) the model response, (ii) the inverse relationship between the model response and its parameters and (iii) an error function quantifying how well the model fits the data. The advantages and drawbacks of particular strategies are demonstrated with the calibration of four parameters of an affinity hydration model from simulated data as well as from experimental measurements. The affinity hydration model is highly nonlinear but computationally cheap, thus allowing its calibration without any approximation and better quantification of results obtained by the examined calibration strategies. This paper can be viewed as a guide for engineers to help them develop an appropriate strategy for their particular calibration problems.