Statistics on reliability of neural network estimates

It has been demonstrated that artificial neural networks can be used to infer estimates of variables infrequently measured in many applications. These estimates have been used in closed-loop control applications, however, the reliability of the estimates have not been used to improve the controller's performance. This work focuses on the generation of an appropriate statistic for the reliability of the estimate, the confidence interval. This statistic is calculated from an empirical sampling distribution obtained using the bootstrap technique. A demonstration of the bootstrap method in the context of an ANN to estimate of a distillation process bottoms' composition is provided. A discussion on the use of the bootstrap estimate and its confidence interval to the practical problem of controller tuning and process performance follows.