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题名	DAE系统中两类指标约简修正算法的研究与实现
作者	饶锴
学位类别	硕士
答辩日期	2010-06-08
授予单位	中国科学院研究生院
授予地点	北京
导师	曹建文
关键词	Modelica
学位专业	计算机软件与理论
中文摘要	为了应对设计复杂产品的需求，研究者们提出了一些面向对象、基于组件的建模语言，比如说Modelica 语言。Modelica语言建模中采用了分治的思想，将大型的系统划分成一系列小型组件，极大程度地提高了模型复用性，简化了建模的过程。 Modelica语言构建的模型往往会被转化成一个DAE方程组。在一些情况中，这个DAE是指标数大于1的高指标问题。由于目前对高指标问题不存在通用的求解器，为了求解这类问题，通常的方法是先对问题进行指标约简。 指标约简有两类主流的方法，一类基于微分指标，如Gear算法；另一类基于结构指标，如Pantelides和哑导方法。Gear方法是解决一般高指标问题最为经典的方法，对它的研究和深入分析意义重大。在本文的第一部分，作者提出了一种Gear方法的修正实现。实验结果表明，对于一类特殊结构的DAE，修正实现比起经典实现做了更少的微分，最终得到了规模更小的方程组。 本文另一部分工作集中在对结构指标修正的方面。相比Gear算法，基于结构指标的指标约简算法是一类快速算法，但是并非百分之百有效。在少数情况下，当微分指标与结构指标不一致时，这类方法会失效。为了提高结构指标的适用性，必须首先消除这种不一致性。因此，作者深入分析了处理这一问题的组合松弛型算法，并做出了相应的实现。利用组合松弛型算法，作者进一步对几个Modelica模型导出的DAE方程组进行了处理。实验结果表明，作者所实现的算法解决了微分指标与结构指标不一致的问题。
英文摘要	To meet the needs of designing complex products, the researchers proposed some object-oriented, component-based modeling languages, such as Modelica. Modelica language uses the idea of “divide and conquer”, large system will be divided into a number of small components, which substantially improves model reusability and simplifies the modeling process. The model coming from Modelica language will often be transformed into DAE equations. Sometimes, the DAE is high-index problem whose differential index is larger than one. Current general purpose solvers can’t deal with such problem. Therefore, the problem should be performed index reduction first. There are two main kinds of methods for index reduction, one is based on differential index, such as Gear method, the other is based on structural index, such as Pantelides and Dummy Derivative method. Gear method is the most popularly adopted technique to solve high index problems, it’s significant to do research and in-depth analysis on it. The author proposes a modified implementation of Gear method. Experiments show that for a special class of DAEs, the modified method could reduce the number of differential computation, and decrease the magnitude of the final DAE system. Another part of this thesis focuses on the amendment of structural index. Compared with Gear method, the index reduction methods based on structural index are much faster. However, this kind of methods is not absolutely effective. In a few cases, when differential index is inconsistent with structural index, these methods are invalid. Therefore, the author does in-depth analysis on combinatorial relaxation algorithm to solve this problem. An implementation of this algorithm is given. Furthermore, several DAEs coming from Modelica models are dealed with by this algorithm implementation. The result shows that for these DAEs, this implementation ensures that the the index reduction methods based on structural index are strictly equivalent to that based on differential index.
语种	中文
学科主题	算法理论
公开日期	2010-06-07
内容类型	学位论文
源URL	[http://124.16.136.157/handle/311060/2332]
专题	软件研究所_并行计算实验室 _学位论文
推荐引用方式 GB/T 7714	饶锴. DAE系统中两类指标约简修正算法的研究与实现[D]. 北京. 中国科学院研究生院. 2010.

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