Abstract

Abstract

In this work a conceptual theory of neural networks (NNs) from the perspective of functional analysis and variational calculus is presented. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function, which is an extremal for some functional. Therefore, a variational formulation for NNs provides a direct method for the solution of variational problems.

This proposed method is then applied to distinct types of engineering problems. In particular a shape design, an optimal control and an inverse problem are considered. The selected examples can be solved analytically, which enables a fair comparison with the NN results. Copyright © 2008 John Wiley & Sons, Ltd.

Abstract

Predictive models are essential in dam safety assessment. Both deterministic and statistical models applied in the day-to-day practice have demonstrated to be useful, although they show relevant limitations at the same time. On another note, powerful learning algorithms have been developed in the field of machine learning (ML), which have been applied to solve practical problems. The work aims at testing the prediction capability of some state-of-the-art algorithms to model dam behaviour, in terms of displacements and leakage. Models based on random forests (RF), boosted regression trees (BRT), neural networks (NN), support vector machines (SVM) and multivariate adaptive regression splines (MARS) are fitted to predict 14 target variables. Prediction accuracy is compared with the conventional statistical model, which shows poorer performance on average. BRT models stand out as the most accurate overall, followed by NN and RF. It was also verified that the model fit can be improved by removing the records of the first years of dam functioning from the training set.

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Abstract

Second order systems are those that respond to a second order differential equation. The study of a second order system is proposed, given by an RC electric circuit. The transfer equation was determined and the transient response was analyzed using the method of the Geometric Place of the Roots, likewise the coefficients of the PID controller were determined. From the response of the PID controller, a backpropagation neural network was created and trained to later replace the classic PID controller. In this work, the analysis of a PID controller case study is carried out where an artificial neural network has been implemented to evaluate its response. It is observed that the results are acceptable and with a good transient response.

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Abstract