Extend trajectory splitting to geometric failure-domain challenges

Investigate whether trajectory splitting methods can reliably discover important failure regions when time-variant structural reliability problems involve bifurcations, uncertain bifurcation parameters, discontinuous performance functions, or rapidly varying failure domains.

Background

Particle splitting methods have been studied extensively for complex failure geometries, but trajectory splitting methods have received less attention in this setting. The review notes that uncertain bifurcation parameters can produce qualitatively different dynamical responses and make the discovery of relevant failure trajectories particularly difficult.

The unresolved issue is whether trajectory-based algorithms can maintain adequate exploration under these geometric and dynamical complications, rather than merely estimating rare-event probabilities efficiently once the relevant failure regions are known.