A weighted extreme value moment method using adaptive sparse grids for time-variant reliability-based design optimization
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Time-variant reliability-based design optimization (t-RBDO) usually involves a nested-loop structure, in which repeated time-variant reliability analyses are required during design optimization. This paper proposes a weighted extreme value moment method using adaptive sparse grids for efficient t-RBDO. First, the extreme value method transforms the time-variant reliability constraints into equivalent reliability constraints based on extreme responses. The failure probability functions of the extreme responses are then constructed from their first three central moments using a three-parameter lognormal transformation. These central moment functions are obtained from raw extreme value moment functions. Next, a complete auxiliary density is introduced to express the raw moment functions as weighted integrals over the entire design domain, allowing evaluated extreme responses to be reused for different candidate designs. Subsequently, the weighted approach based on adaptive sparse grid collocation (WA-ASGC) evaluates the raw extreme value moment functions, with hierarchical surpluses guiding local refinement of the sparse grid. Finally, the resulting failure probability functions replace the time-variant probabilistic constraints, and the t-RBDO problem is solved through sequential deterministic optimization with reference point updating and local collocation point replenishment. The proposed method is non-intrusive and can be coupled with black-box numerical models. A nonlinear time-variant numerical example with two modified cases is presented to demonstrate its accuracy and efficiency.
