Bayesian artificial neural networks in water resources engineering.

Abstract

A new Bayesian framework for training and selecting the complexity of artificial neural networks (ANNs) is developed in this thesis, based on Markov chain Monte Carlo (MCMC) techniques. The primary motivation of the research presented is the incorporation of uncertainty into ANNs used for water resources modelling, with emphasis placed on obtaining accurate results, while maintaining simplicity of implementation, which is considered to be of utmost importance for adoption of the framework by practitioners in this field. By applying the Bayesian framework to a number of synthetic and real-world case studies and by comparison with a state-of-the-art ANN development approach, it is shown throughout this thesis how the Bayesian approach can be used to address the three most significant issues facing the wider acceptance of ANNs in this field; namely generalisability, interpretability and uncertainty. The state-of-the-art approach is devised through reviewing and, where necessary, improving current best practice deterministic ANN development methods, leading to the recommended use of the global SCE-UA optimisation algorithm, which has not been used before for ANN training, and the development of a modified connection weight approach for extracting knowledge from trained ANNs. The real-world case studies used in this research, which involve salinity forecasting in the River Murray at Murray Bridge, South Australia, and the forecasting of cyanobacteria (Anabaena spp.) in the River Murray at Morgan, South Australia, are used to demonstrate the practical value of the Bayesian framework, particularly when extrapolation is required and when the available data are of poor quality. These issues lead to poor model performance when deterministic ANN development methods are applied, yet as the generated predictions are deterministic, there is no direct way of assessing their quality. Application of the proposed Bayesian framework leads to better average performance of the ANN models developed, since a minimal ANN structure is selected and a more generalised input-output mapping is obtained. More importantly, prediction limits are provided which quantify the uncertainty in the predictions and enable management and design decisions to be made based on a known level of confidence.