考虑偶然和认知混合不确定性的高维多输出时变可靠性设计优化研究

新能源、航空航天和基础设施建设等重要工程领域的工程结构具有高维、多输出、时变及偶然和认知不确定性共存的特点，其可靠性设计优化研究是当前的热点和难点。如何有效处理偶然和认知混合不确定性，快速识别关键参数、降低模型复杂度，发展高效求解策略，是该项研究急需解决的关键科学问题。本项目构建混合不确定性统一时变概率分析模型；提出双层自适应Kriging模型，内层近似极限状态函数，外层直接近似概率约束函数，将双循环优化退化为单循环；发展混合不确定性高维多输出时变全局灵敏度分析新方法，实现关键参数快速识别和模型复杂度简化；提出可靠性设计优化新求解策略，其时变概率约束由复合极限状态方程结合广义子集模拟高效评估，搜索策略采用子集模拟优化结合序列二次规划，既不易陷入局部最优又能快速收敛。最后，采用复合材料风力机叶片工程实例，验证该方法的有效性。项目成果可为重要工程领域的可靠性设计优化研究提供参考。

Engineering structures in key engineering fields, such as new energy, aerospace and infrastructure construction, are characterized as high dimensional, multi-output, and time-dependent models under aleatory and epistemic (mixed) uncertainty. Research on Reliability-Based Design Optimization (RBDO) of these structures is currently the hotspot and difficult point. How to deal with the mixed uncertainty, how to identify the key inputs and reduce the complexity of the model, and how to develop an efficient RBDO solving strategy for the high dimensional, multi-output and time-dependent problem under mixed uncertainty, are the key scientific problems on this research project. To address these issues, the project is firstly to construct a unique probabilistic model for the time-dependent problem under mixed uncertainty. A two-level adaptive Kriging model is provided, where the inner level is to approximate the limit-state functions and the outer one is to directly approximate the probabilistic constraints, degenerating the two-loop RBDO into a single loop. A variance-based global sensitivity analysis method for the time-dependent problem under mixed uncertainty is developed to efficiently identify the key input parameters and reduce the complexity of the model. As to the search strategy, a subset simulation optimization is firstly run for the corresponding deterministic optimization to pick up a global optimum. Next, the single loop problem will be efficiently solved by the sequential quadratic programming with the global optimum as a proper initial design point. By doing this, the search algorithm can quickly converge and avoid being trapped into a local optimum. The time-dependent probabilistic constraints will be then evaluated in an effective and robust way with the help of the composite limit-state function method and the generalized subset simulation. Finally, a wind turbine blade made of composite materials in real practice is used to test the performance of the proposed method. It provides a novel way for the relevant studies on RBDO in key engineering fields.