Due to the uncertain and dynamic parameters from design, manufacturing, and working conditions, many engineering structures usually show uncertain and dynamic properties. During the product design and development stages, designers often encounter reliability and robustness measures of dynamic uncertain structures. Time-varying and high nonlinear performance brings a new challenge for the 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 integrated framework is first established by minimizing the mean value and coefficient of variation of the objective performance at the same time subject to time-dependent probabilistic constraints. The time-dependent probabilistic constraints are then converted into deterministic constraints using the dimension reduction 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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