Reliability-based synthesis of non-linear stochastic dynamical systems: a global approximation approach

The paper presents an efficient methodology to carry out reliability-based structural optimisation of non-linear systems under stochastic loading. The optimisation problem is formulated as the minimisation of an objective function subject to multiple reliability constraints. The reliability constraints are given in terms of first excursion probabilities with large state-space dimensions. A sequential approximate optimisation scheme based on global approximations of the reliability constraints is implemented in the proposed formulation. The approximations of the first excursion probabilities in terms of the design variables are constructed by combining a global mixed linearisation approach with a reliability sensitivity analysis. The sensitivity of the first excursion probabilities are estimated by considering some statistics of an augmented reliability problem. The number of reliability estimations required during the optimal design process is generally very small. Two numerical examples are presented to illustrate the effectiveness of the method.