基于稀疏变量不确定性表征的复杂装备结构稳健设计方法研究

The structural robust design is an effective means to reduce the deteriorative influences of multiple types of uncertain variables, and then improve the performance of complex equipment. In view of the difficulty in solving structural robust optimization problems caused by the imprecise representation of sparse variables, and the inaccurate correlation strengths between sparse variables and performance functions in complex equipment, this project proposes the structural robust design method of complex equipment based on uncertainty representation of sparse variables. The uncertainty analysis method of sparse variables under poor data, the unified uncertainty propagation method of sparse variables, interval variables and statistical variables, the construction method of surrogate model based on the self-learning of multiple uncertain variables, and the structural robust optimization method based on sparse variable regularization are researched. The quantitative representation of the uncertainty of sparse variables, the correlation rules between multiple types of uncertain variables and performance functions, and the structural robust optimization of complex equipment based on sensitivity area calculation of multiple uncertain variables are accomplished. A structural robust design system of complex equipment based on the uncertainty representation of sparse variables is developed, and then applies to the structural robust design of large plate-fin heat exchangers.

复杂装备结构稳健设计是减少性能在多类型不确定性变量下的波动、进而提高装备性能的有效手段。针对多类型不确定性变量中稀疏变量难以精确度量、稀疏变量与性能指标间关联关系不明确的问题，提出基于稀疏变量不确定性表征的复杂装备结构稳健设计方法。研究贫数据下稀疏变量不确定性分析、稀疏变量与区间变量和统计变量的统一不确定性传播计算、多类型变量自学习的性能代理模型构建、基于稀疏变量正则化的结构稳健求解等方法与技术，实现稀疏变量不确定性的定量化表征、多类型变量与性能指标的关联规律获取、基于多类型变量敏感度区域计算的复杂装备结构稳健优化设计。研制基于稀疏变量不确定性表征的复杂装备结构稳健设计系统，并在超大型板翅式换热器等复杂装备的结构稳健设计中对相关理论和技术进行应用验证。

结构稳健设计是改善装备可靠性、实现装备性能升级的有效手段。针对复杂装备的变量不确定性的表征数据难以获取、变量与性能间非线性耦合传播复杂等问题，本项目提出了基于稀疏变量不确定性表征的复杂装备结构稳健设计方法，从变量不确定性的精确度量、多类型不确定性精确传播、高维稳健优化求解等方面保证复杂装备结构稳健设计的精度，提高装备可靠度。提出了基于贫数据的稀疏变量不确定性定量表征方法，实现了稀疏变量的分布类型和分布参数的概率化计算；建立了基于贫数据的变量不确定性定量化表征函数；提出了贫数据的稀疏变量、无数据的区间变量、富数据的统计变量的统一不确定性传播分析方法，构建了多类型变量的统一不确定性传播分析模型，获取了多类型不确定性变量与性能指标不确定性的关联规律；建立了复杂装备自适应学习的性能高精度代理模型，实现了基于稀疏变量正则化转换的复杂装备结构稳健优化求解。提出的理论与方法在大型板翅式换热器、多尺度复合结构、高维桁架结构等复杂装备稳健设计中进行了应用，为工程领域复杂装备高精度、高可靠性设计提供了技术支持。项目资助在国内外学术期刊上发表论文28篇，授权国家发明专利3项、实用新型专利2项；毕业硕士4名。项目投入直接经费60万元，支出32.93万元，剩余经费27.07万元将用于本项目研究的后续支出。