Artificial neural networks in calibration of nonlinear mechanical models
This work provides a practical guide for engineers to select efficient calibration strategies, addressing a computationally intensive problem in material modeling, but it is incremental as it reviews and compares existing approaches.
The paper reviews and compares three neural network strategies for calibrating nonlinear mechanical models from noisy experimental data, demonstrating their advantages and drawbacks on a four-parameter affinity hydration model using both simulated and experimental measurements.
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.