Validity Domains of Beams Behavioural Models: Efficiency and Reduction with Artificial Neural Networks

In a particular case of behavioural model reduction by ANNs, a validity domain shortening has been found. In me- chanics, as in other domains, the notion of validity domain allows the engineer to choose a valid model for a particular analysis or simulation. In the study of mechanical behaviour for a cantilever beam (using linear and non-linear models), Multi-Layer Perceptron (MLP) Backpropagation (BP) networks have been applied as model reduction technique. This reduced model is constructed to be more efficient than the non-reduced model. Within a less extended domain, the ANN reduced model estimates correctly the non-linear response, with a lower computational cost. It has been found that the neural network model is not able to approximate the linear behaviour while it does approximate the non-linear behaviour very well. The details of the case are provided with an example of the cantilever beam behaviour modelling. situations (as in the reuse of mechanical models, see (40)), a model should always be accompanied of its validity domain in order to be used. Moreover, the validity domain must be verified if the model is modified: during the application of a model reduction to beam behavioural models, a modification of the resulting validity domain was noticed. While using model reduction techniques to create a more efficient model (lower time of response with a negligible loss of accuracy), changes in the validity domain must be expected. In this paper, the case of Artificial Neural Networks (ANN) employment as model reduction technique for beam behavioural models is considered. The efficiency and validity domain of the reduced model are studied to a means to support decision making in the successful use of models: • A shortening of validity domain after reduction of the original model is reported. • An improvement of the efficiency of the model after reduction is reported.

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