多领域陈述式模型的符号操作技术研究

发布时间：2018-05-01 06:21

本文选题：Modelica + 建模与仿真　；参考：《华中科技大学》2012年硕士论文

【摘要】：应用计算机建模和仿真技术分析产品性能日益得到重视。日趋复杂的机电产品通常是集机械、电子、液压、控制等多个不同领域子系统于一体的复杂大系统，分析优化其整体性能必然涉及到多领域建模和仿真。Modelica语言是一种基于方程的陈述式物理建模语言，非常适合现代复杂多领域工程系统的建模和仿真。陈述式模型的求解仍然是过程式的，Modelica模型内在的陈述式平坦化数学方程系统首先必须转化为顺序求解的方程子集序列，然后生成过程式程序代码集合提供给求解器执行。本文对转化过程中的符号操作技术做了深入研究。表达式操作是整个符号操作的基础。基于方程的二叉树表示，通过规范转换规则，实现了书写形式自由多样的方程表达式的规范和简化，便于提取结构和数值约束信息；通过自定义函数内联，减少方程表达式中函数调用次数，同时还可能避免非线性方程求解，提高了数值求解效率；通过符号微分和偏微分，支持了DAE系统的微分操作和指标约简,并提出了表达式关于任意变量的微分方法。陈述式物理模型映射得到的DAE系统规模庞大，包含成千上万个变量和方程，并且不能直接求解。基于方程的二部图描述，首先，分析了陈述式物理建模的冗余问题，结合代数消元方法和DAE系统的特点，通过别名消除有效降低了方程系统的规模和耦合性；其次，分析了方程系统的结构约束关系，，研究了方程系统的精简二部图描述，提高了空间利用和符号操作效率。
[Abstract]:Application of computer modeling and simulation technology to analyze product performance has been paid more and more attention. Increasingly complex mechanical and electrical products are usually a large complex system that integrates mechanical, electronic, hydraulic, control and other subsystems in different fields. Analysis and optimization of its overall performance must involve multi-domain modeling and simulation .Modelica is a declarative physical modeling language based on equations, which is very suitable for modeling and simulation of modern complex multi-domain engineering systems. The solution of the declarative model is still the process model, the inherent declarative flattening mathematical equation system must be transformed into the sequentially solved subset sequence of equations, and then generate the procedural program code set to be supplied to the solver for execution. In this paper, the symbol operation technology in the process of transformation has been deeply studied. Expression operation is the basis of the whole symbol operation. Based on the binary tree representation of equations, the canonical and simplified expression of equations with various forms is realized by canonical transformation rules, which is convenient to extract the information of structure and numerical constraints, and inline by custom functions. The efficiency of numerical solution is improved by reducing the number of function calls in the equation expression and avoiding the solving of nonlinear equations. The differential operation and index reduction of DAE system are supported by symbolic differential and partial differential. A differential method for the expression of arbitrary variables is proposed. The DAE system derived from the mapping of declarative physical models has a large scale, including thousands of variables and equations, and can not be solved directly. Based on the bipartite graph description of equations, firstly, the redundancy problem of declarative physical modeling is analyzed. Combining with the characteristics of algebraic elimination method and DAE system, the scale and coupling of the equation system are effectively reduced by removing aliases. The structure constraint relation of the equation system is analyzed, the simplified bipartite graph description of the equation system is studied, and the efficiency of space utilization and symbolic operation is improved.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH122;TP391.9

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