Enhancement of Reliability-Based Probabilistic Solutions for Rotorcraft Structural Analysis and Optimization

This study addresses opportunities to dramatically increase computational efficiency of probabilistic solutions relevant to rotorcraft, i.e., focused on very low probabilities of failure (POF). Firstly, it is shown that down-selection of probabilistic solutions depends on problem definition, and a set of eight decision-based criteria is proposed. Next, limitations of typically used Monte Carlo simulation (MCS) and First- and Second-Order Reliability methods (FORM/SORM) are discussed in detail and demonstrated on numerical examples. Major efforts are focused on computational implementation of Cross-Entropy Importance Sampling (CE-IS) as an efficient alternative to both MCS and FORM/SORM. Remarkable computational enhancement in comparison with MCS is demonstrated on an example of probabilistic damage tolerance assessment for a representative composite structure: >1E+3 at POF = ∼1E-4; > 6E+4 at POF = ∼1E-6; and >1E+7 at POF = ∼1E-9. In addition, a simplified "engineering" variant is proposed based on estimation of a conservative, upper boundary of POF instead of its true value. Finally, possibilities of probabilistic optimization are highlighted according to the demonstrated CE-IS based capabilities.