M.Sc. Thesis, Instituto Superior Técnico
September 1993, Lisboa, Portugal
© 1993 IST
Estimação de Limites de Confiança com Redes Neuronais
Pedro M. Q. Aguiar
Neural networks are nonlinear models whose parameters are adapted iteratively during the training phase, when the network is presented with the available data patterns. The reliability of a model of this kind is determined by two factors. First, it is important to know whether or not the network model is being applied in an area of the input space where training data were available, that is, to know whether or not the network is extrapolating. Second, if the network is not extrapolating, the reliability depends on the accuracy, or uncertainty, of the model for the current values of the input variables.
The work performed consists on the development and test of neural network models that include additional outputs indicating extrapolation and local accuracy. Extrapolation detection is based on the estimation of local training data density; the accuracy is indicated by confidence intervals, one for each model output. This kind of models, based on two kinds of networks (multilayer perceptron and radial basis function network), is applied to system modeling and fault detection.
This thesis begins by presenting the statistical decision theory and its application to fault detection. Then, it shows the relationship between this classical theory and the application of neural networks to data classification problems and presents the methods developed for confidence estimation.
Finally, experimental results of the application of the methods developed, to artificial data, as well as to real data obtained from sensors of a petrochemical industrial plant, are given.
Keywords: Neural networks, System modeling, Data classification, Fault detection, Nonparametric probability density estimation.