基于自组织映射的高维优化参变量相关性研究  

SOM-Based High-Dimensional Design Spaces Mapping for Multi-Objective Optimization

作　　者：张泽斌[1] 张鹏飞[1] 李瑞珍[1] ZHANG Zebin;ZHANG Pengfei;LI Ruizhen(School of Mechanical and Power Engineering,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]郑州大学机械与动力工程学院,河南郑州450001

出　　处：《西北工业大学学报》2020年第3期677-684,共8页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(51575498)资助。

摘　　要：针对多目标优化中计算量大、以及难以提取分析高维数据中的复杂非线性关系的问题,借助自组织映射方法,将隐藏的高维多属性数据特征展现在低维可视空间中。利用NSGA-Ⅱ得到多目标优化问题中的Pareto最优解集,并通过对数据进行聚类分析,从而得到高维最优解集内目标与参数的特征分布、映射关系等特性。以动静压阶梯腔滑动轴承为应用对象,以单位承载力下的摩擦功耗、温升和失稳转速为优化目标,考虑几何结构等约束条件,结合DoE构建相应的低成本、高精度的多目标Kriging代理模型。利用自组织映射方法提取和分析最优特征区域中各目标与参数之间的相关性特征以及映射关系。结果表明,在设计范围内目标与轴向封油边宽度、供油压力之间相关性较强,而与深腔深度、浅腔包角相关性较弱。此方法可更直观地服务于设计人员对于多目标高维优化设计结果参变量的择优。Multi-objective optimization can reveal the complex parameter-objective relationships in the high-dimensional design problems.However,the data-extraction and data-presentation of the high-dimensional complex nonlinear system suffers from the increasing dimensionality.Key features and data-distribution of high-dimensional design spaces:parameter and objective spaces could be obtained by using Self-Organizing Maps(SOM)method,which re-clusters the high-dimensional multi-attribute data existing on the Pareto front into several low-dimensional maps.Correlations among all the design variables can be drawn according the colorized topological structure of the maps.Under the constraints including geometric structure and operating parameters,a low-cost and high accurate Kriging surrogate model was established to optimize a hybrid sliding bearing based on the sequential design method.Correlations between 3 objectives:“friction-to-load”ratio,temperature rise,instability threshold speed and 4 design parameters were extracted by SOM.Optimal feature regions were captured and analyzed.Results show that,within the specific feasible design space,supply pressure,axial bearing land width have important impact on the selected objectives,whereas the other parameters such as deep pocket depth and shallow pocket angle have relatively limited impact.A series of corresponding design decisions and optimization results help to understand the mechanism of the hybrid sliding bearing system in a much more intuitive way.

关 键 词：自组织映射 高维问题表达 克里金方法 帕累托前沿 多目标优化 滑动轴承 

分 类 号：TH122[机械工程—机械设计及理论] TH117.2