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

大系统灵敏度分析统一技术研究

基本信息

批准号：
05452120
负责人：
IRI Masao
金额：
$ 4.16万
依托单位：
Chuo University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (B)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1995
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05452120/
关键词：
Sensitivity Analysis Automatic Differentiation Adjoint System Interval Computation Complexity

项目摘要

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.

在工程、科学、社会学等许多领域中，灵敏度分析是系统设计/运行以及验证解释自然或社会现象的数学模型的适用性的关键技术。然而，许多研究者对它进行了独立的研究，他们生活在不同的国家，他们的主题广泛传播，他们的术语也有很大的不同(例如，共轭系统，伴随系统，微扰计算)。结果，他们中的每一个人都在不同的背景下分别“找到”了几乎相同的想法。我们的研究目标是：(1)思想的统一化和系统化；(2)建立具有快速自动微分功能的“灵敏度分析综合理论”；(3)建立通用算法；(4)开发算法软件系统；(5)通过计算实验进行评价。首先，我们提出了一种新的非线性系统灵敏度分析理论，并建立了适用于任何模型的灵敏度分析算法。它可以进行灵敏度分析，也可以对数学模型进行分析。特别是，它的复杂性与单独分析模型的复杂性相同。其次，我们将共轭系统、共轭系统等概念与数值计算方法统一起来。我们正在开发一个可以处理区间数、指数长度可变的浮点数、自动微分数等的实验系统。最后，我们认识到了一个可以很容易地分析其敏感度的系统结构的表征问题，即通过它可以很容易地预测元件的扰动对整个系统的影响，并以串并系统的结构为例。这一认识对于通过系统分析设计系统的“结构”具有重要的工程意义。