基于稀疏网格的近似模型及其在轻量化设计中的应用  

Approximate Model Using Sparse Grid Approach and Its Application in Lightweight Design

作　　者：马石磊[1] 李方义[1] 李剑峰[1] 何洋[1] 

机构地区：[1]山东大学高效洁净机械制造教育部重点实验室,济南250061

出　　处：《机械工程学报》2013年第7期43-50,共8页Journal of Mechanical Engineering

基　　金：国家自然科学基金资助项目(51175312)

摘　　要：在复杂工程系统的多学科设计优化(Multidisciplinary design optimization,MDO)中,由于学科种类和设计变量多,学科分析中存在计算量大和优化效率低等难题。将稀疏网格方法引入多学科近似模型的建立过程,该方法集试验设计和近似模型建立于一体,可以缓解样本点数目对设计空间维度的指数依赖,因此在处理高维问题时仍有较高的效率,同时在近似模型的拟合精度方面具有先验性。将该近似模型应用于Haupt函数预测和NASA减速器优化设计实例,与传统多项式和Kriging近似模型方法进行对比分析,结果证明了该方法在拟合高维问题时的精确性、高效性和在高维优化设计中的适用性。构建基于稀疏网格近似模型的多学科设计优化流程,并以此为基础对某型驱动桥壳进行轻量化设计,所得设计方案减轻了驱动桥壳的质量,前六阶模态频率变化较小,且满足驱动桥壳静强度指标和疲劳寿命指标。In the multidisciplinary design optimization process of complex engineering system, the large amount of calculation and low computation efficiency resulting from various disciplines and high dimensionality of design space are critical problems to be solved. The sparse grid approach is applied to construct discipline approximate model, which includes experimental design and construction of approximate model, and it can relieve the curse of dimensionality. Also it has a high computing efficiency in solving problems of high dimensionality andhas the apriority of fitting precision. Then the approximate model based on sparse grid approach is applied to solve the prediction of Haupt function and optimization design of NASA reducer, compared with the traditional ploynomial response surface and Kriging approximate model, the sparse grid approach shows high precision and efficiency in solving high dimensionality problems and feasibility in design optimization. A multidisciplinary design optimization flow model using sparse grid approach is constructed, based on which the lightweight design of driving axle housing is implemented, and the results show all the design schemes reduced mass of driving axle housing with little change in modal frequencies as well as met criteria of driving axle strength and fatigue life.

关 键 词：稀疏网格 近似模型 多学科优化 轻量化设计 

分 类 号：U463[机械工程—车辆工程]