Reliability-based optimal design of linear structures subjected to stochastic excitations

• Transitional Markov chain Monte Carlo simulation is used for reliability-based optimal design of linear dynamic structures.
• Subset Simulation is utilized for exploring feasible space of designs satisfying deterministic and reliability constraints.
• The idea of 'Minimum computational effort' is presented for enhanced efficiency of the proposed method.

In this paper the problem of reliability-based optimal design of linear structures subjected to stochastic excitations is considered. A global optimization method based on Transitional Markov chain Monte Carlo (TMCMC) is used to address the problem, where the optimization problem is converted into the task of generating sample points (designs) according to a probability density function (PDF) suitably constructed on the feasible space of designs satisfying all the constraints. TMCMC is used for generating sample points, in order to get higher convergence rate of the stationary distribution of the Markov chain states to the constructed PDF. The generation of sample points uniformly distributed in the feasible space, which is required at the initial stage of TMCMC, is achieved by using Subset Simulation. To apply Subset Simulation and TMCMC in the concerned reliability-based optimization problem, Domain Decomposition Method (DDM) is used to examine the reliability constraint, that is, whether the failure probability at a given design exceeds a specified threshold. Based on the statistical properties of the failure probability estimator given by DDM, a ‘minimum’ computational effort, in terms of providing a reliable judgment on the reliability constraint, is defined so that a further reduction in the computational cost can be achieved in the proposed reliability-based optimization (RBO) algorithm. Illustrative examples are presented to show the application and the advantages of the proposed global RBO algorithm.