工程系统多领域统一模型编译映射与仿真求解研究
摘要
随着工业实践和科学技术的发展,现代机电产品日趋复杂,通常是由机械、电子、液压、控制等不同领域子系统构成的复杂工程系统。基于多领域统一模型的仿真已经成为支撑复杂工程系统创新设计的新一代CAE技术,该技术的关键在于实现多领域统一模型的编译映射与仿真求解。针对该问题,本文基于多领域统一建模语言Modelica,以构建新一代多领域统一建模与仿真平台为目标,围绕平台构建的关键使能技术,在若干国家863计划项目和国家自然科学基金项目的支持下,对于多领域统一模型编译映射和仿真求解若干关键技术进行了深入研究,主要包括以下几个方面工作：
首先,详细分析了Modelica语义约束并系统归纳了多领域模型映射规则。基于编译原理和Modelica规范,对于Modelica关键语义从语义约束角度进行了详细分析,给出了关键语义的关联语义约束分析表,据此确定了Modelica编译框架；系统归纳了从Modelica层次模型到平坦化混合方程系统的映射规则,并分析了Modelica方程系统的典型特征。
其次,深入研究了高指标微分-代数方程符号指标缩减及其相容初始化问题,并拟定了数值求解流程框架。针对由大规模微分方程、代数方程和离散方程组成的平坦化混合方程系统,介绍了基于下三角块分方法的分析优化策略,着重研究了基于哑导方法的高指标微分-代数方程的符号缩减方法及其相容初始化问题。针对方程系统分析优化得到的有序方程子集序列,分析了混合微分-代数方程系统的连续-离散求解策略,给出了基于数值计算的求解流程框架。
再次,解决了Modelica环境下多体系统建模中的相容性冗余约束符号处理问题。围绕多体建模中产生的相容性冗余约束与Modelica单赋值原则的矛盾问题,首先根据牛顿-欧拉方法推导了基于广义基尔霍夫定律的多体动力学公式,然后将相容性冗余约束分为超定连接冗余约束和自由度重复限制冗余约束。对于前者,分析了冗余约束来源,提出了基于虚拟连接图的冗余约束判定和消除方法。对于后者,针对常见的空间平面闭环机构冗余约束,给出了冗余约束自动判定和消除方法。
最后,实现了多领域统一建模与仿真平台MWorks的编译器和求解器。基于上述研究成果,实现了MWorks的编译器和求解器。简要介绍了MWorks平台的特点、功能以及框架结构,并以几个实际工程应用为例展示了平台的有效性。
With the development of science, technology and engineering practice, modern electromechanical products are increasingly complex and usually become complex engineering systems consisting of a variety of mechanical, electronic, hydraulic and control subsystems. Simulation based on unified multi-domain models has become a new generation of CAE technology supporting innovative design of complex engineering systems. The key of the technology is to achieve compiling and solving of unified multi-domain models. Based on the unified multi-domain modeling language Modelica, in order to build a new generation of unified multi-domain modeling platforms and develop the key enabling technology for the platforms, the paper investigates a number of key technologies in compiling and solving unified multi-domain models. The paper is funded by the National High Technology Research and Development Program of China (863 Program) and the National Natural Science Foundation of China. The main contribution of the paper includes the following.
First, the Modelica semantic constraints the paper analyzes in detail and systematically summarizes the mapping rules of multi-domain models. Based on compiling principles and Modelica standards, the paper analyzes in depth the key Modelica semantics from the perspective of semantic constraints, provides an analysis table of associated semantic constraints of the key semantics and determines the Modelica compiling framework based on it. Further, the paper systematically summarizes the mapping rules from Modelica hierarchy models to flat hybrid equation systems and analyzes typical features of Modelica equations systems.
Second, the paper explores the symbolic index reduction and its consistent initialization in high index differential-algebraic equations (DAEs), and proposes the processing frame of numerical solving. For flat hybrid equation systems consisting of large-scale differential equations, algebraic equations and discrete equations, the paper introduces an analysis approach based on the method of Block Lower Triangular (BLT), focusing on dummy derivative based symbolic reduction and its consistent initialization in high index DAEs. For the ordered equation subset sequences obtained from the analysis of equation systems, the paper analyzes the continuous-discrete solving methods of hybrid differential-algebraic equation systems and presents the processing frame of solving based on numerical computation.
Third, the paper solves the symbol processing problem of consistent residue constraints in multi-body modeling in Modelica. Centered on the contradiction between consistent redundant constraints and the Modelica single assignment rule in multi-body modeling, the paper derives the multi-body dynamics formula based on the general Kirchhoff's law by the Newton-Euler method, and then divides the consistent residue constraints into over-determined connection redundant constraints and repeatedly-constrained degree of freedom redundant constraints. For the former, the paper analyzes the sources of redundant constraints and proposes the determination and elimination of redundant constraints based on virtual connection graphs. For the latter, the paper presents the determination and elimination of redundant constraints in the common mechanisms with planar loops.
Finally, based on the aforementioned findings, the paper achieves the complier and solver of the unified multi-domain modeling and simulation platform MWorks. The paper describes briefly the features, functions and framework of MWorks platform and illustrates the effectiveness of the platform by some practical engineering applications.
首先,详细分析了Modelica语义约束并系统归纳了多领域模型映射规则。基于编译原理和Modelica规范,对于Modelica关键语义从语义约束角度进行了详细分析,给出了关键语义的关联语义约束分析表,据此确定了Modelica编译框架；系统归纳了从Modelica层次模型到平坦化混合方程系统的映射规则,并分析了Modelica方程系统的典型特征。
其次,深入研究了高指标微分-代数方程符号指标缩减及其相容初始化问题,并拟定了数值求解流程框架。针对由大规模微分方程、代数方程和离散方程组成的平坦化混合方程系统,介绍了基于下三角块分方法的分析优化策略,着重研究了基于哑导方法的高指标微分-代数方程的符号缩减方法及其相容初始化问题。针对方程系统分析优化得到的有序方程子集序列,分析了混合微分-代数方程系统的连续-离散求解策略,给出了基于数值计算的求解流程框架。
再次,解决了Modelica环境下多体系统建模中的相容性冗余约束符号处理问题。围绕多体建模中产生的相容性冗余约束与Modelica单赋值原则的矛盾问题,首先根据牛顿-欧拉方法推导了基于广义基尔霍夫定律的多体动力学公式,然后将相容性冗余约束分为超定连接冗余约束和自由度重复限制冗余约束。对于前者,分析了冗余约束来源,提出了基于虚拟连接图的冗余约束判定和消除方法。对于后者,针对常见的空间平面闭环机构冗余约束,给出了冗余约束自动判定和消除方法。
最后,实现了多领域统一建模与仿真平台MWorks的编译器和求解器。基于上述研究成果,实现了MWorks的编译器和求解器。简要介绍了MWorks平台的特点、功能以及框架结构,并以几个实际工程应用为例展示了平台的有效性。
With the development of science, technology and engineering practice, modern electromechanical products are increasingly complex and usually become complex engineering systems consisting of a variety of mechanical, electronic, hydraulic and control subsystems. Simulation based on unified multi-domain models has become a new generation of CAE technology supporting innovative design of complex engineering systems. The key of the technology is to achieve compiling and solving of unified multi-domain models. Based on the unified multi-domain modeling language Modelica, in order to build a new generation of unified multi-domain modeling platforms and develop the key enabling technology for the platforms, the paper investigates a number of key technologies in compiling and solving unified multi-domain models. The paper is funded by the National High Technology Research and Development Program of China (863 Program) and the National Natural Science Foundation of China. The main contribution of the paper includes the following.
First, the Modelica semantic constraints the paper analyzes in detail and systematically summarizes the mapping rules of multi-domain models. Based on compiling principles and Modelica standards, the paper analyzes in depth the key Modelica semantics from the perspective of semantic constraints, provides an analysis table of associated semantic constraints of the key semantics and determines the Modelica compiling framework based on it. Further, the paper systematically summarizes the mapping rules from Modelica hierarchy models to flat hybrid equation systems and analyzes typical features of Modelica equations systems.
Second, the paper explores the symbolic index reduction and its consistent initialization in high index differential-algebraic equations (DAEs), and proposes the processing frame of numerical solving. For flat hybrid equation systems consisting of large-scale differential equations, algebraic equations and discrete equations, the paper introduces an analysis approach based on the method of Block Lower Triangular (BLT), focusing on dummy derivative based symbolic reduction and its consistent initialization in high index DAEs. For the ordered equation subset sequences obtained from the analysis of equation systems, the paper analyzes the continuous-discrete solving methods of hybrid differential-algebraic equation systems and presents the processing frame of solving based on numerical computation.
Third, the paper solves the symbol processing problem of consistent residue constraints in multi-body modeling in Modelica. Centered on the contradiction between consistent redundant constraints and the Modelica single assignment rule in multi-body modeling, the paper derives the multi-body dynamics formula based on the general Kirchhoff's law by the Newton-Euler method, and then divides the consistent residue constraints into over-determined connection redundant constraints and repeatedly-constrained degree of freedom redundant constraints. For the former, the paper analyzes the sources of redundant constraints and proposes the determination and elimination of redundant constraints based on virtual connection graphs. For the latter, the paper presents the determination and elimination of redundant constraints in the common mechanisms with planar loops.
Finally, based on the aforementioned findings, the paper achieves the complier and solver of the unified multi-domain modeling and simulation platform MWorks. The paper describes briefly the features, functions and framework of MWorks platform and illustrates the effectiveness of the platform by some practical engineering applications.
引文
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