11 - Geotechnical Applications of Bayesian Neural Networks

Abstract

Empirical relationships are commonly used in geotechnical engineering design to estimate engineering properties of soils and evaluate the performance of geotechnical structures because the interacting factors and relationship between these factors are not precisely known. This chapter explores the use of a modified Bayesian back-propagation neural network to model the highly nonlinear relationships between interacting factors or variables. The main advantage of neural networks over conventional regression analysis techniques is that the neural network is able to find a best-fit solution without the need to specify the relationship or the form of the relationship between variables. It is, therefore, useful for analyzing problems where there is incomplete understanding of the problem to be solved, but where training data are available, as is the case for many geotechnical engineering problems. With the integration of the Bayesian framework into the back-propagation algorithm, error bars can be calculated for network output instead of just a single output value given in conventional back-propagation neural networks. These error bars indicate the confidence level of the predicted values in relation to the spatial density of the training data. This chapter describes the use of a hybrid neural network that incorporates the genetic algorithm search engine and Bayesian approach in quantifying the uncertainty of the learned model. Some practical examples of its application to pile foundation and retaining wall design are presented to demonstrate the usefulness of this hybrid model.