Optimum design of hydraulic water retaining structures incorporating uncertainty in estimating heterogeneous hydraulic conductivity utilizing stochastic ensemble surrogate models within a multi-objective multi-realisation optimisation model

In order to find optimum and reliable designs for hydraulic water retaining structures (HWRSs), a reliability based optimum design (RBOD) model was used to quantify uncertainty in estimates of seepage characteristics due to uncertainty in heterogeneous hydraulic conductivity (HHC). This included incorporating reliability measures into minimum-cost HWRS designs and utilising a multi-realisation optimisation technique based on various stochastic ensemble surrogate models. To improve the efficiency of the RBOD model and the direct search optimisation solver, a multi-objective multi-realisation optimisation (MOMRO) model was employed. Some of the stochastic optimisation constraints could be formulated as a second objective function to be minimised in the MOMRO model. This can significantly improve the search efficiency of the multi-objective non-dominated sorting genetic algorithm-II (NSGA-II) that was used, and help determine more feasible candidate solutions in the search space. Gaussian process regression was used to develop the surrogate models, which were trained on numerous datasets created from numerical seepage simulations. The effect of uncertainty was also considered for other HWRS safety factors and conditions, such as overturning, flotation, sliding and eccentric loading. The results demonstrate that uncertainty in HHC estimates significantly impacts optimum HWRS design. Therefore, deterministic optimum solutions that are created based on expected values of hydraulic conductivity are not adequate for reliable HWRS design. The developed MOMRO model, which was based on an ensemble approach, addresses some of the uncertainty in HHC values that affects HWRS design. Also, the MOMRO technique improves the efficiency of the optimisation search process and facilitates a direct search process to provide many optimum alternatives. (C) 2018 Society for Computational Design and Engineering. Publishing Services by Elsevier.