During the product design and development stage, design engineers often encounter reliability and robustness of dynamic uncertain structures. Meanwhile, time-varying and high nonlinear performance are the basic characteristics of reliability analysis and design. Hence, the time-dependent reliability analysis and integrating reliability-based design with robust design become a primary challenge in reliability-based robust design optimization. This paper proposes a multi-objective integrated framework for time-dependent reliability-based robust design optimization and the corresponding algorithms. The multi-objective integrated framework, which minimizes the mean value and coefficient of variation for the objective function at the same time subject to time-dependent probabilistic constraints, is first established. The time-dependent probabilistic constraints are then converted into deterministic constraints using a combination of moment method and the sparse grid based stochastic collocation method. The evolutionary multi-objective optimization algorithm is finally employed for the deterministic multi-objective optimization problem. Several examples are investigated to demonstrate the effectiveness of the proposed method.

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