本文選題：Modelica + 建模與仿真��； 參考：《華中科技大學(xué)》2012年碩士論文

【摘要】：應(yīng)用計算機建模和仿真技術(shù)分析產(chǎn)品性能日益得到重視。日趨復(fù)雜的機電產(chǎn)品通常是集機械、電子、液壓、控制等多個不同領(lǐng)域子系統(tǒng)于一體的復(fù)雜大系統(tǒng)，分析優(yōu)化其整體性能必然涉及到多領(lǐng)域建模和仿真。Modelica語言是一種基于方程的陳述式物理建模語言，非常適合現(xiàn)代復(fù)雜多領(lǐng)域工程系統(tǒng)的建模和仿真。陳述式模型的求解仍然是過程式的，Modelica模型內(nèi)在的陳述式平坦化數(shù)學(xué)方程系統(tǒng)首先必須轉(zhuǎn)化為順序求解的方程子集序列，然后生成過程式程序代碼集合提供給求解器執(zhí)行。本文對轉(zhuǎn)化過程中的符號操作技術(shù)做了深入研究。 表達式操作是整個符號操作的基礎(chǔ)�；诜匠痰亩鏄浔硎�，通過規(guī)范轉(zhuǎn)換規(guī)則，實現(xiàn)了書寫形式自由多樣的方程表達式的規(guī)范和簡化，便于提取結(jié)構(gòu)和數(shù)值約束信息；通過自定義函數(shù)內(nèi)聯(lián)，減少方程表達式中函數(shù)調(diào)用次數(shù)，同時還可能避免非線性方程求解，提高了數(shù)值求解效率；通過符號微分和偏微分，支持了DAE系統(tǒng)的微分操作和指標(biāo)約簡,并提出了表達式關(guān)于任意變量的微分方法。 陳述式物理模型映射得到的DAE系統(tǒng)規(guī)模龐大，包含成千上萬個變量和方程，并且不能直接求解。基于方程的二部圖描述，首先，分析了陳述式物理建模的冗余問題，結(jié)合代數(shù)消元方法和DAE系統(tǒng)的特點，通過別名消除有效降低了方程系統(tǒng)的規(guī)模和耦合性；其次，分析了方程系統(tǒng)的結(jié)構(gòu)約束關(guān)系，，研究了方程系統(tǒng)的精簡二部圖描述，提高了空間利用和符號操作效率。
[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.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：TH122;TP391.9

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