# Solution of Time-Variant Risk Optimization Problems using Two-Level Active Learning Kriging Approach

## Palavras-chave:

Risk-Based Optimization, Time-Dependent Reliability, Adaptive Kriging## Resumo

Risk optimization is a general approach for structural optimization regarding uncertainties.

Different life-cycle costs are considered, including expected failure costs, whose calculation requires

the computation of failure probabilities. Although more comprehensive than concurrent approaches,

the literature about this topic is scarce. Time-dependency can be considered, broadening the scope of

the analysis, but further complicating the solution. In this work, a numerical framework for solving

time-dependent risk optimization problems is proposed. It consists in a Monte Carlo simulation based

approach, where two adaptive coupled metamodels are employed. In the first level, objective functions

are approximated, and in the second, the limit state functions related to the computation of the failure

probabilities. An iterative procedure is developed for selecting candidate points to each surrogate model’s

design of experiment. The accuracy and generality of the method is shown in an example including

system-reliability and load-path dependent failures.