基于偏好序的桥梁结构全寿命抗震设计多目标优化模型

Preference-based Multi-objective Optimization Model for Life-cycle Seismic Design of Bridge

为综合考虑地震作用下结构的经济及性能等因素,将基于偏好序的交互式多目标综合优化决策方法应用于梁式桥梁全寿命抗震性能设计中。以单柱桥墩为例,令全寿命费用最低、强度安全及变形可靠指标最高为设计目标;根据工程经验分别引入考虑位移延性的经济偏好和安全偏好,并建立相应的价值函数,此交互式多目标优化问题的最终解可逐步收敛到与经济或安全偏好序一致的优化区域。研究结果表明:在桥梁全寿命抗震性能设计中,基于偏好序的交互式多目标优化决策模型可同时满足不同设防水准下多个性能目标的要求;较传统多目标优化算法中存在的问题,即优化结果分布广泛致使设计者无从选择,以及目标过多时无法获取全局Pareto前沿,该模型可通过逐步引入设计者偏好序以获得相应的全局最优解;该模型克服了规范算法反复试算和被动校核的缺点,通过指引其解沿当前价值函数的梯度方向主动搜索,最终可获取满足预期费用最低或安全最高偏好序,且兼顾位移延性需求的最终满意解。

Considering the economy, structural performance and other factors under the earthquake, the preference-based multi-objective optimization and decision-making method was applied to the life-cycle seismic design of beam bridge. A single-column pier was regarded as an application example, and the seismic design was to minimize the life-cycle cost and maximize the seismic capacity and the deformation index. Based on theoretical analysis and engineering judgment, the cost preference and safety preference information under the reasonable displacement ductility was used to construct corresponding value functions, progressively directing at the multi-objective optimization algorithm to the corresponding preferred solutions. The results indicate that the preference-based multi-objective optimization decision model can, in the life-cycle seismic design of bridge, meet the multiple performance requirements at various seismic hazard levels. Compared with the traditional multi-objective optimization algorithm which faces difficulties in obtaining a full approximation of the entire Pareto optimal front for large-dimensional problems and cognitive difficulty in selecting one preferred solution from all these solutions, the proposed model is available to find the global Pareto front to satisfy the corresponding preference. Furthermore, to overcome the shortcomings of repeated trial and passive verification in the classical code-compliant algorithm, the proposed model is used to actively strive the search for the more preferred solution space along the gradient of the current value function, and ultimately converge to the expected Pareto front which meets not only the needs of the lowest cost or the highest safety preference but also the rational displacement ductility.