Studies on Development of A Software System for Qualitative Analysis of Dynamical Systems

动力系统定性分析软件系统的开发研究

• 批准号: 02680024
• 负责人: NISHIDA Toyoaki
• 金额: $ 1.15万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1990
• 资助国家: 日本
• 起止时间: 1990 至 1991
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02680024/
• 关键词: qualitative reasoning; dynamical systems; commonsense reasoning; engineering problem solving; artificial intelligence; differential equations

In engineering problem solving, analysis of nonlinear differential equations plays a crucial part. This research aimed at development of a software system which can analyze the qualitative behavior of nonlinear ordinary differential equations with two unknowns, by integrating knowledge-based and numerial methods using qualitative reasoning techniques.We have achieved the following accomphshments with respect to the above research goal :1. We have devised flow patterns as a means for representing geometric features of solution curves of ordinary differential equations. In addition, we have formulated a flow grammar which is a grammatical characterization of flow patterns one may observe in phase spaces of ordinary differential equations.2. We have devised a new method of reasoning about qualitative behaviors which operates in both bottom-up and top-down mode. The bottom-up mode follows a prescribed procedure to collect information to capture the behavior. In contrast. the top-down mode is strongly guided by the domain knowledge, attempting to derive most plausible interpretation from partial information. In normal situations, the bottom-up mode is used, which will be switched to the top-down mode once logical failure is recognized.3. We have designed and implemented a prototype system called PSX2NL and have tested it against typical. examples to evaluate the method from experimental points of view.4. We have discussed about technical issues involved in a system which can analyze more complex ordinary differential equations with three unknowns. We have partly implemented the idea.

在工程问题求解中，非线性微分方程的分析起着至关重要的作用。本研究旨在利用定性推理技术，将知识方法与数值方法相结合，开发一个能够分析两未知量非线性常微分方程定性行为的软件系统。针对上述研究目标，我们取得了以下成果：我们设计了流型来表示常微分方程解曲线的几何特征。此外，我们还制定了一种流动语法，它是人们可以在常微分方程的相空间中观察到的流动模式的语法表征。我们设计了一种新的定性行为推理方法，这种方法可以自下而上和自上而下两种模式运行。自底向上模式遵循规定的过程来收集信息以捕获行为。相比之下。自顶向下模式强烈地以领域知识为指导，试图从部分信息中得出最合理的解释。正常情况下采用自底向上的方式，一旦发现逻辑故障，就会切换到自顶向下的方式。我们设计并实现了一个名为PSX2NL的原型系统，并对其进行了典型的测试。从实验的角度对方法进行评价。我们讨论了一个可以分析更复杂的三未知数常微分方程的系统所涉及的技术问题。我们已经部分实现了这个想法。

项目成果

Toyoaki Nishida and Shuji Doshita: "A Geometric Approach to Total Envisioning" Proc.IJCAI-91. 1150-1155 (1991)

Toyoaki Nishida 和 Shuji Doshita：“总体构想的几何方法”Proc.IJCAI-91。

Atsushi Yamada,Toyoaki Nishida and Shuji Doshita: "Qualitative Interpreter for the Sense Teaching of the Spatial Descriptions" Proceedings of International Conference on Advanced Research on Computers in Education. 255-266 (1990)

Atsushi Yamada、Toyoaki Nishida 和 Shuji Doshita：“空间描述意义教学的定性解释器”教育计算机高级研究国际会议论文集。

Toyoaki Nishida,Kenji Mizutani,Atsushi Kubota,and Shuji Doshita: "Automated Phase Portrait Analysis by Integrating Qualitative and Quantitative Analysis" Proc.AAAI-91. 811-816 (1991)

Toyoaki Nishida、Kenji Mizutani、Atsushi Kubota 和 Shuji Doshita：“通过集成定性和定量分析进行自动相图分析”Proc.AAAI-91。

Toyoaki Nishida, Kinji Mizutani, Atsushi Kubota, and Shuji Doshita: "Automated Phase Portrait Analysis by Integrating Qualitative and Quantitative Analysis" Proc. AAAI-91. 811-816 (1991)

Toyoaki Nishida、Kinji Mizutani、Atsushi Kubota 和 Shuji Doshita：“通过集成定性和定量分析进行自动相图分析”Proc。

Toyoaki Nishida,Kenji Mizutani,Atsushi Kubota,and Shuji Doshita: "Automated Phase Portrait Analysis by Integrating Qualitative and Quantitative Analysis" Proc.AAAIー91. 811-816 (1991)

Toyoaki Nishida、Kenji Mizutani、Atsushi Kubota 和 Shuji Doshita：“通过集成定性和定量分析进行自动相图分析”Proc.AAAI-91 (1991)。