Artificial neural networks in calibration of nonlinear mechanical models

TL;DR

This paper reviews neural network strategies for calibrating complex nonlinear mechanical models, comparing their effectiveness and providing guidance for engineers to choose suitable methods based on model characteristics.

Contribution

It introduces and compares three neural network-based strategies for model calibration, offering practical insights and a guide for engineers dealing with nonlinear model calibration.

Findings

Neural networks can effectively approximate model responses and inverse relationships.

Different strategies have distinct advantages and limitations depending on the calibration context.

The calibration of a highly nonlinear but computationally inexpensive model demonstrates the practical application of these methods.

Abstract

Rapid development in numerical modelling of materials and the complexity of new models increases 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 exhaustive task. The layered neural networks thus represent a robust and efficient technique to overcome the time-consuming simulations of a calibrated model. The potential of neural networks consists in simple implementation and high versatility in approximating nonlinear relationships. Therefore, there were several approaches proposed to accelerate the calibration of nonlinear models by neural networks. This contribution reviews and compares three possible strategies based on approximating (i) model response, (ii) inverse relationship between the model response and its parameters and (iii) error function quantifying how well the model fits the data. The advantages and drawbacks of particular strategies are demonstrated on the calibration of four parameters of the affinity hydration model from simulated data as well as from experimental measurements. This 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. The paper can be thus viewed as a guide intended for the engineers to help them select an appropriate strategy in their particular calibration problems.