Time-variant reliability-based robust optimization for structures with material degradation

Time-variant reliability-based robust design optimization (TRBRDO) has achieved certain progress recently for its ability to ensure both robustness of design and feasibility of time-variant probabilistic constraints. However, the existing TRBRDO methods have not specifically addressed the dynamic uncertainty of material degradation, and there is lack of a universal and efficient approach for this class of time-variant robust design problems. For this reason, this paper proposes three solution strategies, namely the reliability index based double-loop method, performance measure based double-loop method, and sequential single-loop method. In these approaches, the minimum reliability of each time-variant probabilistic constraint is considered by obtaining the extremum in a series system. With use of the first-order reliability analysis technique, two different single-loop multivariate optimization models are established to obtain the minimum reliabilities and minimum performance measures through sequential quadratic programming algorithm, respectively. Following this, two different double-loop models and a sequential single-loop model are developed. Furthermore, an augmented step length adjustment technique is proposed for inverse reliability analysis, which is integrated into the performance moment integration and percentile difference method to derive the robustness indicators for the design objective. Finally, three illustrative numerical examples and one engineering problem are provided to demonstrate the effectiveness of the proposed solution strategies for reliable and robust design optimization with high computational efficiency.