Artificial neural networks in the calibration of nonlinear mechanical models

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.

Artificial Neural Networks-Based Material Parameter Identification for Numerical Simulations of Additively Manufactured Parts by Material Extrusion

“…These approaches are called HP tuning or HP optimization and a variety of different applicable libraries (e.g., scikit-learn , Hyperas ) with different algorithms exist. For more detailed information on these, please refer to [ 28 , 38 , 43 ].…”

“…Morand and Helm investigated in [ 6 ] problems occurring if the PI problem is non-unique and developed an approach using a mixture of expert model to partition the non-unique problem in subtasks. In [ 28 ] different strategies for calibrating non-linear mechanical models with NN are reviewed. Also, their advantages and disadvantages are demonstrated using a calibration of four parameters for an affinity hydration model.…”

BayCANN: Streamlining Bayesian Calibration With Artificial Neural Network Metamodeling

“…Since then, ANNs have been successfully implemented as emulators of all sorts of discrete-event and continuous simulation models in a wide variety of fields (Kilmer, 1996 ; Sabuncuoglu and Touhami, 2002 ; Fonseca et al, 2003 ; El Tabach et al, 2007 ). ANNs have also been proposed as proxies for non-linear and simulation models (Paiva et al, 2010 ; Mareš and Kučerová, 2012 ; Pichler et al, 2003 ). An example of ANNs as metamodels is estimating the mean and variance of patient time in emergency department visits (Kilmer, 1994 ; Kilmer et al, 1997 ).…”

Development of an Automated Assembly Process Supported With an Artificial Neural Network

“…For example, a failure of a sensor could be compensated by the ANN estimating a sensor value via the remaining inputs. The ability to learn, tolerance towards errors and generalization of correlations are arguments for the use of ANN in automated assembly [14].…”