基于截尾变量的高效可靠性优化方法

The theory and method for reliability-based design optimization are one of the development frontiers of computational mechanics. Reliability-based design optimization with truncated random variables will enrich and develop the theory and method for reliability-based design optimization, and have an important meaning for application of engineering. This project will investigate formulating reliability analysis models, solving the nesting optimization problem for reliability optimization, and developing efficient algorithms. Firstly, by introducing interval convex model to truncated distribution model, a hybrid reliability model is constructed for the truncated distribution problems. Then based on the judgment method for the uncertainty domain and the failure surface according to whether their intersection set is non-empty or empty, the interval reliability analysis or the probability method will be employed to deal with these two cases. Secondly, the mathematical models for the reliability optimization can be formulated, then decoupled optimization method is established to solve the original nesting model based on modified sequential optimization and reliability assessment method, and an adaptive approximation method is extended into the reliability optimization for improving efficiency. Finally, the crashworthiness optimization design of structure of vehicle body for frontal impact is demonstrated to verify the effectiveness of the method presented. This project will develop theory of reliability analysis and optimization with truncated random variables and be propitious to innovative design of engineering structure.

可靠性优化理论与方法是目前计算力学的发展前沿之一。基于截尾变量可靠性优化设计是可靠性优化理论与方法的丰富与发展，有着重要的工程应用价值。本项目针对截尾变量的可靠度分析和两层嵌套优化问题的求解进行研究，开发高效的可靠性优化算法。首先，在截尾变量描述下，将区间凸模型引入到截尾概率模型中，构建一种混合可靠性模型。通过一种高效判定方法判断极限状态曲面与不确定域所形成的交集域是否为空，分别采用区间方法或概率方法求解两种情况下的结构可靠度。其次，建立在截尾分布下的可靠性优化数学模型，基于序列优化与可靠性评估方法研究原嵌套优化模型的解耦技术，并将自适应近似模型技术引入到截尾可靠性优化中，提高计算效率。最后，以车身正面耐撞性结构设计为例，验证提出的方法的有效性。本项目成果将推进截尾变量的可靠性分析及其优化理论发展，同时有利于工程结构的创新设计。

基于截尾变量可靠性优化设计是可靠性优化理论与方法的丰富与发展，有着重要的工程应用价值。本项目针对截尾变量的可靠度分析和两层嵌套优化问题的求解进行研究，开发高效的可靠性优化算法。本项目按照时间表围绕项目预定研究内容和目标进行研究，并在相关方面进行了扩展。首先，在截尾变量描述下，将区间凸模型可靠性分析方法引入到截尾概率分布问题中，构建混合可靠性模型，研究混合可靠性指标求解。其次，基于序列优化与可靠性评估方法将原嵌套优化模型进行解耦，研究高效解耦算法。同时，将自适应近似模型技术引入到可靠性优化中，研究近似模型的精度评价标准和近似模型的更新机制，提高优化求解精度和效率。最后，将算法应用于车身耐撞性结构设计领域中的一些实际问题，验证所提出方法的有效性。本项目成果将推进截尾变量的可靠性分析及其优化理论发展，同时有利于工程结构的创新设计。在项目执行期间，发表论文7篇，其中SCI索引论文6篇，EI索引论文4篇，培养研究生1名，取得发明专利1项。