System-reliability-based sizing and shape optimization of trusses considering millions of failure sequences

System-Reliability-Based Design Optimization (S-RBDO) of structures considering progressive collapse is a complex problem, as the number of potential failure sequences increases geometrically with the degree of static indeterminacy of the structure. Existing methods for identifying failure sequences in structural systems are computationally expensive and prone to missing some critical failure sequences, especially within an optimization framework. In this context, identifying the most critical failure sequences to simplify the problem is fundamental. Herein, we propose a novel system-reliability-based framework for sizing and shape optimization of trusses. The procedure identifies minimal cut sets using the recently developed null space method, which has been proven more efficient than traditional failure path-based methods. The most probable failure sequence is selected from each identified minimal cut set. System reliability is estimated using the dominant failure sequences for the whole structure, selected based on their correlations using the Probabilistic Network Evaluation Technique (PNET). Craziness-Based Particle Swarm Optimization (CRPSO) is employed as the optimization algorithm. Numerical examples involving hundreds to millions of failure sequences demonstrate applicability and efficiency of the proposed framework on truss optimization problems with different material post-failure behaviors. Results suggest that, in a system-reliability analysis considering progressive collapse, the most critical failure sequences are those obtained from minimal cut sets. Furthermore, results show that the procedure proposed herein can outperform other frameworks based on traditional failure path-based methods. Simple truss sizing and shape optimization is considered herein, but the conclusions have immediate relevance to the optimal design of realistic structures considering progressive collapse.