摘要
以区间代数为工具的灰色数学与有限单元模型相结合所形成的灰色有限元数学模型 ,可以充分表达模型输入参数的灰色特性 ,通过求解区间线性方程组可以得出一个用区间数表示的灰色温度场 ,能够更好地符合工程实际需要。考虑到区间代数的扩张性 ,从最佳逼近的意义出发将区间线性方程组转换成极大极小值类型的优化数学模型 ,所推荐使用的基于李兴斯方法的二次优化策略较之通用的序列二次规划算法计算效率更高。文中叙述了温度场灰色有限元模型及其优化模型的建立过程 ,介绍了两种极大极小值优化的求解方法 ,并给出了数值算例。
The finite element method (FEM),with its flexibility in dealing with complex geometries,is an ideal approach to employ in the solution of such problems.Exact values for the parameters of FEM,such as geometrical dimensions,properties of the material,or heat transfer coefficients,should be available to achieve reliable results.In practice,due to the measurement errors and the lack of information,some specific crisp values of them could not be obtained,or considered to be representative for the whole spectrum of possible results. Stimulated by the ideal combination of interval arithmetic and finite difference model presented by the authors,a gray finite element method (gFEM) model is constructed in this paper for transient thermal analysis.Considering the unavoidable interval expanding due to intrinsic characteristics of interval arithmetic,especially when iterating large scale sparse linear equations,we convert the model in the optimal sense to a minimax programming.A twice applied Li method,which tries to substitute the minimax programming to an unconstrained optimization,is found more efficient than the general sequential quadratic programming (SQP).By numeral examples shown at the end of this paper,it is believed that the gFEM model is applicable in practice if the computing time is confirmed to be more acceptable.
出处
《中国电机工程学报》
EI
CSCD
北大核心
2002年第3期113-117,共5页
Proceedings of the CSEE
关键词
汽轮机
转子
热分析
灰色理论
有限元
数学模型
tempratue field
thermal stresses
gray theory
interval arithmetic
steam turbine
