Model reduction technique for mechanical behaviour modelling: Efficiency criteria and validity domain assessment

The current paper presents the study of a neural network-based technique used to create fast, reduced, non-linear behavioural models. The studied approach is the use of artificial neural networks (ANNs) as a model reduction technique to create more efficient models, mostly in terms of computational speed. The test case is the deformation of a cantilever beam under large deflections (geometrical non-linearity). A reduced model is created by means of a multi-layer feed-forward neural network, a type of ANN reported as ‘universal approximator’ in the literature. Then it is compared with two finite-element models: linear (inaccurate for large deflections but fast) and non-linear (accurate but slow). Under large displacements, the reduced model approximates well the non-linear model while having similar speed to the linear model. Unfortunately, the resulting model presents a shortening of its validity domain, as being incapable of approximating the deformed configuration of the cantilever beam under small displacements. In other words, the ANN-based model provides a very good compromise between accuracy and speed within its validity domain, despite the low fidelity presented: accurate for large displacements but inaccurate for small displacements.