Optimal design of stochastic complex systems with applications to deep excavations

Abstract

Modern geotechnical systems, like any other civil engineering systems, tend to have a remarkable increase in their complexity. Also, uncertainties arise due to incomplete knowledge about the system and its environment. Addressing explicitly these uncertainties for a complex system, which may involve high nonlinearity and/or a large number of uncertain parameters, can be very challenging. Particularly, in the optimal design of deep excavations, one should take into account the sophisticated soil mechanical behaviors, the complicated soil-structure interaction, and spatial variability of soil properties. Reliability-based design optimization (RBDO) aims to model the safety-under-uncertainty aspect of design optimization by introducing reliability constraints. Among many RBDO approaches, the stochastic-sampling-based ones provide the flexibility in the choice of stochastic sampling techniques and the complexity level of numerical models. However, the required computational efforts become prohibitively large especially when expensive-to-evaluate numerical physical models are involved. In this contribution, an efficient decoupling framework for RBDO called Design Optimization in the PArtitioned Design Space (DOPADS) has been proposed. DOPADS decouples reliability constraints from the optimization loop by approximating failure probability functions (FPF) in the partitioned design space. A sufficient number of failure samples are generated using Markov chain Monte Carlo methods in each subspace, ensuring the accuracy of the approximation over the entire design space. The major gain in efficiency comes from the decoupling that explores the design space in a single reliability analysis instead of performing the reliability analyses repeatedly as in nested RBDO approaches. In the vanilla version of DOPADS, an FPF is approximated for each reliability constraint separately, which makes its computational complexity linear to the number of reliability constraints. Therefore, another framework DOPADS_m has been proposed which is tailored to the cases with multiple reliability constraints. By taking advantage of the dependency between different failure events, DOPADS_m largely enhances the efficiency of DOPADS. Design optimization is an ongoing process in which the initial design may need to be modified based on model updating using observed data. In the traditional reliability updating methods, one needs to update the distribution of model parameters in a Bayesian approach, then calculate the failure probability based on the set of the updated models. This process takes a long time which may lead to lagged decision making regarding the current reliability state. Thus, a new framework INstant REliability Updating (INREU) for reliability updating has been presented. The updated failure probability function is constructed before collecting data, making the instant plug-in query of the updated reliability possible. The application of the proposed frameworks to the deep excavation cases in Singapore has been investigated. The…