# Effects of epistemic uncertainties on truss topology optimization considering progressive collapse

## Palavras-chave:

structural reliability, progressive collapse, latent failure probability, risk optimization## Resumo

The history of engineering contains many examples of structural failures. Despite being related to

diverse causes, these collapses can be attributed to the existence of uncertainties, which are usually classified as

aleatory and epistemic. In this context, optimization techniques can be employed in order to obtain optimal

structural solutions that are robust to the effects of uncertainty. Additionally, the progressive collapse phenomenon

has raised engineers' and researchers' awareness in recent years. However, there are still very few papers addressing

the optimal structural design under uncertainty considering progressive collapse. Hence, this paper aims to

investigate the effect of aleatory and epistemic uncertainties on truss topology optimization considering

progressive collapse. Uncertainties are considered in the optimization problems through the RBDO (Reliability-

Based Design Optimization) and RO (Risk Optimization) formulations. Non-structural factors, which are

epistemic in nature and can lead to progressive collapse, are considered using a formulation based on the latent

failure probability concept. Through a simple six-bar truss problem, the huge impact of epistemic uncertainties on

optimal topologies is shown. The variation of the latent failure probability indicates the existence of two transition

points in the optimal solutions, named Hyperstatic and Redundancy Thresholds. We conclude that these bounds

are mainly controlled by the magnitude of epistemic uncertainties, having a strong effect on the reliability and

costs of the optimal solutions. These results reveal something that has already been recognized in practice:

engineering structures need to be redundant in order to cope with the effect of epistemic uncertainties. Therefore,

despite being an idealized concept, the latent failure probability proves to be a simple tool to impose minimal

redundancy in optimal structural solutions.