Robust fuzzy structural safety assessment using mathematical programming approach

This paper presents a robust safety assessment for engineering structures involving fuzzy uncertainties. Uncertain applied loads and yielding capacities of structural elements are modelled as fuzzy variables with associated membership functions representing possibility distributions. A new computation-orientated methodology, namely the α-level collapse assessment (α-level CA) approach, is developed to provide structural safety profile by constructing membership function of the structural collapse load limit accommodating fuzzy uncertainties. The proposed method firstly utilizes the α-level strategy to transform the fuzzy limit analysis into a series of interval limit analyses. By implementing the concept of robust and optimistic optimizations, a mathematical programming (MP) scheme is proposed to explicitly capture the upper and lower bounds of the collapse load limit at each α-sublevel. Subsequently, the membership function of the collapse load limit is established by using the upper and lower bounds obtained from the series of α-sublevel calculations. The proposed α-level mathematical programming scheme preserves the quality of sharpness of the bounds of collapse load limit at each α-sublevel, which consequently provides a rigorous evaluation on the fuzzy profile of the safety of engineering structures against structural collapse. Numbers of numerical examples, motivated by real-world engineering applications, have been investigated to illustrate the accuracy, efficiency and applicability of the proposed method.