A Reliability-Based Design Optimization Method for Geotechnical Engineering Problem Based On Active-Learning Kriging Metamodeling

Abstract

Using an expensive-to-evaluate numerical model, such as a finite element method (FEM) model, is deemed unavoidable in solving modern geotechnical engineering problems. At the same time, the application of reliability analysis in dealing with uncertainties (e.g. soil properties) is increasing rapidly. This could pose a time-wise problem for an FEM model since reliability analysis normally takes much more than only one realization (function call) of the model. It becomes a bigger problem when a design optimization process is taking place. More often than not, design optimization is performed by a ”trial-and-error” method in practice, which the process itself would even take longer just to give engineers the ”sense” of achieving an optimal design (in terms of safety and economy). Therefore, the actual optimality of the design is not systematically proven and quantified. This research proposes a novel reliability-based design optimization (RBDO) method by combining existing theories regarding active-learning Kriging-based Monte Carlo Simulation (AK-MCS) and (1+1)-Covariance Matrix Adaptation evolution scheme ((1+1)-CMA-ES). To achieve accuracy and efficiency, the method consists of four enrichment stages. These enrichment stages ensure the method accurately and efficiently predicts the optimal design combination by considering the reliability constraint. The chosen case study is the reinforcement design of the Starnmeer polder dyke in the Netherlands, which is simulated as an FEM model. Within a limited number of function calls, the proposed RBDO method could accurately predict the optimal dimensions of the dyke that delivers the targeted reliability index. The reliable performance of the proposed method is further demonstrated by solving three analytical optimization problems.