若干相似建模方和定性相图中相似性讨论.pdf

摘 要 摘 要 相似理论作为评估系统仿真质量的重要依据，在人们适应改造客观世界中， 发挥了巨大的作用，它在工程领域，物理实验，模型构造，数据挖掘等诸多方面 都有着研究和应用。 定性仿真是对系统定性建模的一种方法。它将系统各变量间的关系定性化， 通过方程中的约束关系，给出系统所有的可能行为。定性相图是基于定性仿真方 法构造的、能够表达系统全局行为的几何状态图。实际系统的行为往往由含有噪 声的时间序列所表示，它是系统的数值解析，而定性相图则是系统的定性状态的 表达。二者一个定量，一个定性，讨论它们的相似性，对定性相图模型做出评估， 具有必要性，也是个难点，需要对相似理论做深入探索。 本文首先讨论了若干领域内的相似理论，并对它们的优势和局限性提出自己 的看法。讨论这些领域内的相似理论，对讨论时间序列和定性相图间的相似性有 着借鉴作用。 接着，改进了常见的降噪方法，提出平滑降噪的方法，对表达系统行为的时 间序列进行降噪处理，使得系统特性能够从噪声干扰中凸显出来，以利于对时间 序列进行定性化处理。 最后，对时间序列和定性相图的相似性在变化趋势的粗粒度上进行讨论，并 给出一些相似指标，如鞍点，源点，汇点，分界线等，并在试验中对二者进行了 相似性对比。 关键词：相似理论 平滑降噪 相似指标 定性相图 定性仿真 I Abstract ABSTRACT Similarity theory, as an important basis of quality evaluation of simulation sys- tem, has played a huge role when people adapt and change the world. It has been re- searched and applied in wide areas such as engineering, physic experiments, model construction, data mining and so on. Qualitative simulation is a method for qualitative modeling of system. According to qualitative relationships between the variables of the system, it gives all the possi- ble behaviors. Qualitative phase portrait is a geometrical state portrait constructed based on qualitative simulation method ，which can express the global behavior of the system. The actual behaviors of the system are often represented by time series ob- scured with noise. The time series is a numerical analysis, while the qualitative phase portrait is a qualitatively expression of the system state. It is necessary to evaluate the quality of qualitative phase portrait and discuss their similarities, which is full of dif- ficulties and needs to make a further study on similarity theory. We firstly discusses similarity theory in several fields, and their a