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论文:2013,Vol:31,Issue(2):259-265 |
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引用本文： |
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兑红炎, 司书宾, 蔡志强, 孙树栋. 综合重要度的梯度表示方法[J]. 西北工业大学 |
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Dui Hongyan, Si Shubin, Cai Zhiqiang, Sun Shudong. Representation Method of Integrated Importance Measure in Gradient[J]. Northwestern polytechnical university |
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| 综合重要度的梯度表示方法 |
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| 兑红炎, 司书宾, 蔡志强, 孙树栋 |
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| 西北工业大学 机电学院工业工程系, 陕西 西安 710072 |
| 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。 |
| 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
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| Representation Method of Integrated Importance Measure in Gradient |
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| Dui Hongyan, Si Shubin, Cai Zhiqiang, Sun Shudong |
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| School of Mechatronics,Northwestern Polytechnical University,Xi'an 710072,China |
| Abstract: |
| Aim. The introduction of the full paper reviews a number of papers in the open literature and then pro-poses the representation method in the title,which is explained in sections 1 and 2. Section 1 briefs the system as-sumptions and the equation of integrated importance measure (IIM). The core of section 2 consists of: (1) we usethe gradient method,which is given by eq. (4) to describe the IIM as in eq. (5); (2) we analyze the physicalmeaning of the geometry of IIM and the relationships between IIM and gradient as indicated in Theorem 1; (3) wediscuss the characteristics of IIM in gradient for typical systems in Theorems 2 and 3 and their respective Corollaries1 and 2; (4) we get that IIM can be determined by the inner product of gradient and vector. Section 3 presents thenumerical 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 dimension-al space. |
| Key words:
computer simulation
geometry
gradient methods
parallel architectures
space applications
threedimensional
two dimensional
vectors;inner product
integrated importance measure (IIM)
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| 收稿日期: 2012-06-02
修回日期:
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| DOI: |
| 基金项目: 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 |
| 通讯作者:
Email： |
| 作者简介: 兑红炎(1982-),西北工业大学博士研究生,主要从事可靠性和重要度的研究。
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