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

Abstract

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.

Comparison of Neural Network Error Measures for Simulation of Slender Marine Structures

“…The idea with the hybrid method is to first perform a response analysis for a structure using a FEM model and then subsequently to use these results to train an ANN to recognize and predict the response for future loads. As demonstrated by Ordaz-Hernandez et al [6] an ANN can be trained to predict the deformation of a nonlinear cantilevered beam. A similar approach was used by Hosseini and Abbas [7] when they predicted the deflection of clamped beams struck by a mass.…”

Survey of Finite Element Method-Based Real-Time Simulations

“…This development aimed at a virtual reality simulator including a haptic device with force-feedback. Ordaz-Hernandez et al [38] used a multi-layer feed-forward neural network to produce a reduced model for geometrically nonlinear deformations of a cantilever beam.Ćojbašić et al [39] reported on a similar work for shell structures. Torano et al [40] used fuzzy logic, neural networks and three-dimensional (3D) finite element calculations to develop a numerical model that allows fast predictions of the response of longwall coal mining installation to changing operation conditions.…”

Towards real-time simulation of deformable structures by means of co-rotational finite element formulation

“…Such approach consists in using the nonlinear FEM computations to provide a set of results for the training phase and can thus be classified as model reduction technique. It was applied to a number of problems such as real-time simulation of impact [16], geometrically nonlinear deformation of a cantilever beam [38] and a shell structure [8], etc. Dulong et al [12] proposed a similar approach for real-time interaction between a designer and a virtual prototype as a support to design optimization.…”