摘要
在对重要度理论及梯度计算方法研究的基础上,基于综合重要度的计算方法及物理意义,提出了基于梯度的综合重要度数学描述方法,探讨了综合重要度与梯度之间的关联关系,定理证明了综合重要度的几何意义,得出综合重要度值可以由梯度和向量的内积确定。通过典型串联和并联系统的数值仿真验证了综合重要度在多维空间中的几何意义,从梯度角度描述了其物理意义,为综合重要度在材料等领域的应用奠定了基础。
Aim. The introduction of the full paper reviews a number of papers in the open literature and then proposes the representation method in the title, which is explained in sections 1 and 2. Section 1 briefs the system assumptions and the equation of integrated importance measure （IIM）. The core of section 2 consists of： （ 1 ） we use the gradient method, which is given by eq. （4） to describe the IIM as in eq. （5） ; （2） we analyze the physical meaning of the geometry of IIM and the relationships between IIM and gradient as indicated in Theorem 1 ; （3） we discuss the characteristics of IIM in gradient for typical systems in Theorems 2 and 3 and their respective Corollaries 1 and 2 ; （4） we get that IIM can be determined by the inner product of gradient and vector. Section 3 presents the numerical examples of series and parallel systems. Computer simulation results, presented in Figs. 1 through 6, and their analysis verify the physical meaning of the geometry of IIM in two dimensional space and three dimensional space.
出处
《西北工业大学学报》
EI
CAS
CSCD
北大核心
2013年第2期259-265,共7页
Journal of Northwestern Polytechnical University
基金
国家自然科学基金(71271170
71101116)
国家高技术研究发展计划(2012AA040914)
西北工业大学基础研究基金(JC20120228)资助
关键词
综合重要度
梯度
几何意义
向量
内积
串联和并联系统
computer simulation, geometry, gradient methods, parallel architectures, space applications, three dimensional, two dimensional, vectors
inner product, integrated importance measure （ IIM ）
