有界不确定结构基于最小二乘支持向量机回归的动力特性分析方法  

Dynamic characteristics analysis method for uncertain-but-bounded structures based on least squares SVM regression

作　　者：莫延彧[1] 郭书祥[2] 唐承[2] 

机构地区：[1]空军工程大学航空航天工程学院,西安710038 [2]空军工程大学理学院,西安710051

出　　处：《振动与冲击》2017年第7期199-207,233,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(51175510)

摘　　要：针对不确定结构的动力特性分析问题展开研究,考虑仅已知结构参数变量变化范围的情况,建立不确定参数变量的区间模型。对不确定变量在其取值范围内进行改进的均匀试验设计抽样,并基于确定结构动力特性分析的有限元法和模态叠加理论,提出改进均匀试验设计抽样模拟方法;考虑到该算法计算效率较低,对其进行改进并提出基于最小二乘支持向量机回归的模拟方法,算法在不改变样本点数量的前提下,引入了支持向量机回归代理模型,用训练后的代理模型对不确定结构的动力特性进行了模拟分析。算法通过两个数值算例验证了其有效性。Dynamic properties analysis for uncertain-but-bounded structures was studied. To reach this goal, uncertain-but-bounded parameters were taken as interval variables, but the distributions of the variables were unknown, and then an interval model was built for each uncertain variable. After an improved uniform design sampling for each interval variable, a dynamic analysis simulation method for uncertain structures was proposed based on the deterministic structure,s dynamic properties analysis with the finite element method and the modal superposition theory. Considering the poor efficiency of the proposed method, an improved method was presented. The improved method was based on the least squares support vector machine （ SVM） regression in the premise of unchanged number of sampling points, a surrogate model of SVM regression was introduced. The dynamic characteristics of uncertain structures were simulated and analyzed with this surrogate model trained. Finally, two different numerical examples demonstrated the validity of the proposed approach.

关 键 词：均匀设计 区间模型 频率分析 频响分析 支持向量机回归 

分 类 号：O327[理学—一般力学与力学基础]