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Research on unifying techniques for sensitivity analysis of large-scale systems

Research Project

Project/Area Number 05452120
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field Engineering fundamentals
Research InstitutionChuo University

Principal Investigator

IRI Masao  Chuo Univ., Scien. & Eng, Prof.10DA01 : 90178046, 理工学部, 教授 (40010722)

Co-Investigator(Kenkyū-buntansha) KUBOTA Koichi  Chuo Univ., Scien. & Eng, Assoc.Prof., 理工学部, 助教授 (90178046)
Project Period (FY) 1993 – 1995
Project Status Completed (Fiscal Year 1995)
Budget Amount *help
¥6,500,000 (Direct Cost: ¥6,500,000)
Fiscal Year 1995: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1994: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1993: ¥3,100,000 (Direct Cost: ¥3,100,000)
KeywordsSensitivity Analysis / Automatic Differentiation / Adjoint System / Interval Computation / Complexity
Research Abstract

In many fields of engineering, science, sociology, etc., the sensitivity analysis is a key technique for system design/operation and verification of suitability of mathematical models explaining natural or sociological phenomena. Many researchers, however, had studied on it independently, who lived in different countries, whose themes were widely spread, whose terminologies were quite different (e.g., conjugate system, adjoint system, perturbation computation). As a result, each of them had separately "found" almost same idea in the different contexts. Our research aims were (1) unification and systematization of the proposed ideas, (2) construction of "synthetic theory on sensitivity analysis" with fast automatic differentiation, (3) establishment of a general algorithm, (4) development of software system for the algorithm, and (5) evaluation through computational experiments.
We have obtained the following expected results. Firstly, we proposed a new theory for the sensitivity analysis on nonlinear systems, and established an algorithm which could be generally applied to any model. It can perform the sensitivity analysis as well as analyzing the mathematical model. In particular its complexity was the same order as that for analyzing the model alone. Secondly, we unified the concepts referred as adjoint system, conjugate system, etc. with a numerical computational approach. We are developing an experimental system by which we can treat interval numbers, floating-point numbers with variable length of exponent, automatic differentiation numbers, etc. Finally, we have recognized an issue for characterizing system structures whose sensitivity can be easily analyzed, i.e., by which influences of perturbation of elements to the whole system can be easily anticipated, giving the structure of the serial-parallel system as an example. This recognition is significance in engineering in order to design "structure" of system through system analysis.

Report

(4 results)
  • 1995 Annual Research Report   Final Research Report Summary
  • 1994 Annual Research Report
  • 1993 Annual Research Report
  • Research Products

    (38 results)

All Other

All Publications (38 results)

  • [Publications] M.Iri: "Guaranteed accuracy and fast automatic differentiation" KITE Journal of Electronics Engineering. 4. 34-40 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 伊理正夫: "計算の品質向上を目指して" 日本機会学会誌. 98. 4-5 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri and J.Amemiya: "Experimental studies on guaranteed-accuracy solutions of the initial-value problem of nonlinear ordinary differential equations" T.Mitsui and Y.Shinohara (eds.) : Numerical Analysis of Ordinary Differential Equations and Its Applications,World Scientific. 195-212 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Kubota: "Matrix inversion algorithms by means of antomatic differentiation" Applied Mathematics Letters. 7. 19-22 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 久保田光一: "浮動小数点数の加減算における丸め誤差の分布について" 日本応用数理学会論文誌. 5. 37-46 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 伊理正夫: "高速自動微分法の立場からみた線形系の感度解析および随伴系の役割の再考" 第22回数値解析シンポジウム講演予稿集(1993年6月9日-11日 於 蔵王ハイツ). 102-106 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 伊理正夫: "非線形素子を含むシステムの感度解析" 第23回数値解析シンポジウム講演予稿集(1994年6月8日-10日 於 仙台ホテルクレセント). 47-49 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 伊理正夫: "信頼区間の厳密な計算法と直並列回路-奥村の問題への適用" 電子情報通信学会非線形理論とその応用学術研究集会ワークショップ論文集(1995年1月26日-27日). 1-6 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 伊理正夫: "感度解析・最適化と自動微分-算法の複雑度,変動幅の保証,随伴系の役割" 第44回応用力学連合講演会,講演番号451,予稿集(1995年1月30日-2月1日 於 日本学術会議). 419-420 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 伊理正夫: "随伴系の概念への数値計算論的アプローチ" 第24回数値解析シンポジウム講演予稿集(1995年6月14日-16日 於 熱川ハイツ). 36-40 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri and J.Amemiya: "Eamples of the solution of the initial-value problem of nonlinear ordinary differential equations with guaranteed accuracy" Proceedings of 1994 Symposium on Nonlinear Theory and its Applications,Research Society of Nonlinear Theory and its Applications,IEICE,October 6-8,1994.231-234 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 久保田光一: "常微分方程式の区間解法について" 京都大学数理解析研究所研究集会「科学技術における数値計算の理論と応用」(研究代表者三井斌友),1995年10月25日-27日. (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri: "Guaranteed accuracy and fast automatic differentiation" KITE Journal of Electoronics Engineering. Vol.4, No.1A. 34-40 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri: "Towards high-quality computation" Journal of JSME. Vol.98, No.920. 4-5 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Kubota: "Matrix inversion algorithms by means of automatic differentiation" Applied Mathematics Letters. Vol.7, No.4. 19-22 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] K.Kubota: "On distribution of rounding errors generated in additions and subtractions of floating-point numbers" Transactions of the Japan Society for Industrial and Applied Mathematics. Vol.5, No.1. 37-46 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri: "Computational methods for the sensitivity analysis of linear systems and the re-evaluation of the role of the adjoint system from the viewpoint of fast automatic differentiation" Proceedings of the 22nd symposium on numerical analysis (Zao, Jun 6-11, 1993). 102-106

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri: "A unifying approach to the sensitivity analysis of large systems containing nonlinear elements" Proceedings of the 23nd symposium on numerical analysis (Sendai, Jun 8-10, 1994). 47-49

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri: "Efficient rigorous computation of the confidence interval for series-parallel networks-Application to Okumura's problem" Proceedings of the Fifth Workshop on Nonlinear Theory and Its Applications, January 26-27. 1-6 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri: "Automatic differentiation in sensitivity analysis and optimization-Computational complexity, guaranteed interval of variation and the role of adjoint systems" The 44th Nat.Cong.of Theoretical and Applied Mechanics 1995, (January 30-February 1, 1995). 419-420

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri: "A numerical-computational approach to the concept of adjoint system" Proceedings of the 24th symposium on numerical analysis (Atagawa, Jun 14-16, 1995). 36-40

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri and J.Amemiya: "Examples of the solution of the initialvalue problem of nonlinear ordinary differential equations with guaranteed accuracy" Proceedings of 1994 Symposium on Nonlinear Theory and its Applications, Research Society of Nonlinear Theory and its Applications, IE-ICE, October 6-8, 1994. 231-234

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] M.Iri and J.Amemiya: T.Mitsui and Y.Shinohara (eds.) : Numerical Analysis of Ordinary Differential Equations and Its Applications (Experimental studies on guaranteed-accuracy solutions of the initial-value problem of nonlinear ordinary differential equations). World Scientific, 195-212 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1995 Final Research Report Summary
  • [Publications] 伊理正夫: "計算の品質向上を目指して" 日本機会学会誌. 98. 4-5 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 伊理正夫: "随伴系の概念への数値計算論的アプローチ" 第24回数値解析シンポジウム講演予稿集. 36-40 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] M.Iri and Amemiya: "Experimental studies on guaranteed-accuracy solutions of the initial-value problem of nonlinear ordinary differential equations" T.Mitsui and Y.Shinohara (eds.):Numerical Analysis of Ordinary Differential Equations and Its Applications,World Scientific.195-212 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 久保田光一: "常微分方程式の区間解法について" 京都大学数理解析研究講究録「科学技術における数値計算の理論と応用」(研究代表者三井斌友). (発表予定). (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] 伊理正夫,久保田光一: "アルゴリズムの自動微分" コロナ社(発表予定), 200 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] K.Sugihara and M.Iri: "A robust topology-oriented incremental algorithm for Voronoi diagrams" International Journal of Computational Geometry and Applications. 4. 179-228 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 伊理正夫: "Mohrの応力円,確率分布,線形計画法" 応用数理. 4. 316-326 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 伊理正夫: "感度解析・最適化と自動微分-算法の複雑度,変動幅の保証,随伴系の役割" 第44回応用力学連合講演会論文集. 416-420 (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] 伊理正夫: "信頼区間の厳密な計算法と直並列回路-奥村の問題への適用" 第5回非線形理論とその応用学術研究集会(NOLTA). 1-6 (1995)

    • Related Report
      1994 Annual Research Report
  • [Publications] 伊理正夫: "非線形素子を含むシステムの感度解析" 第23回数値解析シンポジウム講演予講集. 47-49 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] 伊理正夫: "線形代数II" 岩波書店(講座 応用数学[基礎1]), 291 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Masao IRI: "Guaraanteed accuracy and fast automatic differentiation" KITE Journal of Electronic Engineering. 4. 34-40 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 伊理 正夫: "高速自動微分法の立場から見た線形系の感度解析および随伴系の役割の再考" 第22回数値解析シンポジウム講演予稿集. 102-106 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] Koichi KUBOTA: "Matrix inversion algorithms by means of automatic differentiation" Applied Mathematics Letters. (to appear).

    • Related Report
      1993 Annual Research Report
  • [Publications] 久保田 光一: "自動微分の精度保証問題への応用" 日本応用数理学会平成5年度年会講演予稿集. 25-26 (1993)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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