Stochastic modelling and risk analysis of groundwater pollution using FORM coupled with automatic differentiation

The first order reliability method (FORM) has been widely used in probabilistic modelling of groundwater problems. The FORM approach requires an iterative optimization procedure to find out the system failure point (the most probable point). The advantages of this approach are that it does not require many computations in comparison with other methods when applied to simple problems, and it produces reasonably accurate results. However, it has been found that the computations of FORM can equal or exceed that of other methods in case of large number of variables. In this paper, a new implementation of FORM was proposed with more efficiency and accuracy than the traditional FORM method. In the proposed approach, automatic differentiation is used to obtain the gradient vector of the limit state function, which is required by FORM, instead of using finite difference estimation. This way, the first order derivative was obtained with a very good accuracy, and with less computational effort. Based on the obtained results, it is found that the proposed implementation of FORM is a very good tool for probabilistic risk assessment and uncertainty analysis in groundwater problems.