基于Modelica模型的参数优化及推理求解研究
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摘要
产品设计是一个工程分析和优化决策的过程,其中优化是目的,仿真是优化的手段,建模是仿真和优化的基础。本文主要研究Modelica仿真模型的参数优化方法及推理求解等问题。
针对参数优化中参数变动后重复仿真的效率问题,研究了一种分治求解策略,即在仿真模型规模分解基础上建立耦合块依赖图和序列表,对各耦合块建立相应的求解块,通过遍历耦合块序列表并调用相应求解块,便可获得仿真模型的数值解。考虑到参数变动下的重复仿真,对耦合块依赖图进行分层处理,生成对应于变动参数集的变动子图;通过施加虚根节点将变动子图转化成最小求解树结构。因此,对变动参数集的不同参数值进行重复仿真只需层次遍历最小求解树,再调用相应的求解块即可。该方法可一定程度上提高复杂模型的多次仿真求解效率。
在分析多领域物理系统仿真优化特点的基础上,研究了Modelica参数优化建模的关键问题,以及多领域优化模型的寻优策略和模型参数实验技术。基于模型的编译信息实现多实例、多目标启发式仿真优化建模;并利用Modelica语言的结构化注解特征研究了仿真优化模型的混合表达,实现了优化信息的可重用性和继承性。在优化算法中引入拟梯度、复步微分和自动微分三种数值方法以提高敏度计算效率和精度。
在相对差分概念的基础上研究了一种新的通用的混合离散非线性优化方法。详细阐述了该方法的基本原理、思想和算法描述。该方法的特点是迭代中间设计点均是可行离散点,无需邻域查点和圆整,并且可避免收敛于伪极值点,和现有方法相比具有较强的稳健性和通用性。
利用支配关系的定义证明Pareto适应度函数判断非支配点的有效性,并在此基础上结合序列近似模型技术和启发式搜索算法研究了两种基于Pareto解集的多目标优化方法。这两种方法均可很大程度上有助于降低精确分析次数。对于Pareto边界为凸、非凸、非连续的多目标优化问题,该方法均能取得较好的Pareto解集。
利用Modelica语言的结构化注解机制表达设计知识,从而实现基于知识的建模。根据部件知识之间的依赖关系确定推理求解顺序。通过知识模型的推理求解得到确定的仿真模型结构和确定的模型参数。为了便于领域库模型的搜索和应用,研究了面向模型搜索的实例推理技术,针对最近邻实例检索中实例属性相似度和权重的计算问题,给出区间值属性相似度的计算模型,并将各种属性类型的相似度计算方法统一起来。研究了基于相似度信息的客观赋权方法,以组合权重计算实例相似度。
Product design is a process of analysis and optimization, where optimization is the goal, simulation is a means of optimization, simulation and modeling is the basis of optimization. Some Problems about parameter optimization and inference solving for simulation models based on Modelica are studied in this dissertation.
For the efficiency of repetitious simulation after parameters tuning, a kind of subdivision solving strategy is put forward: Based on the scale decomposing of the simulation model, a coupling blocks dependency graph and sequential list are built. As for all coupling blocks, their corresponding solving blocks. Then numerical solution of the simulation model can be achieved through traversing the coupling sequential list and simultaneously calling the corresponding solving blocks. Considering the efficiency of repetitious simulation after parameters varying, the altering sub-graph of the altering parameters set is built after hierarchically processing the coupling blocks graph. And the sub-graph is converted into a minimum solving tree by adding a virtual root node. In this way, carrying out repetitious simulation with different parameters values only need traverse widely the minimum solving tree of the altering parameters set and simultaneously calling corresponding solving blocks. This method of the paper could greatly improve the efficiency of repetitious simulation of complex model.
After analyzing the characters of simulation and optimization for multi-domain physical systems, some key technologies based on Modelica model, such as design optimization modeling, optimization strategies and parameters design, are presented. Firstly, a heuristic method is presented to setup optimization models based on the compiler information of simulation models. Then, based on the structure annotation feature, optimization models are embedded in simulation models to form a hybrid representation, through which the optimization information becomes reusable and inheritable. To enhancing accuracy and efficiency of evaluating gradient in optimization, three numerical methods: quasi-gradient, complex-step derivative and automatic differentiation, are presented.
A new mixed discrete nonlinear optimization method is put forward based on the concept of relative difference. The basic principle, idea and algorithm of the method are elaborated. Compared to existing algorithms, the method is more robust and versatile, and it has many advantages, such as: All the middle iterative design points are feasible discrete points. No neighborhood enumeration and roundness are needed, and it can avoid convergence in the pseudo-extreme point.
The concept of Pareto fitness function is introduced, and the effectiveness of it to identify non-dominated point is proved by using the definition of domination. Two Pareto multi-objective optimization methods are put forward by combined the sequence approximate model technology and heuristic search algorithm. Research shows that these two methods can largely reduce the number of precision analysis. And for the multi-objective optimization problems with convex, non-convex or non-consecutive Pareto frontier, better Pareto points of which can be identified by both the methods.
To implement knowledge-based modeling, a knowledge representation method is studied based on the structure annotation mechanism. The inference order is determined by the knowledge dependent relationship between model parts. Model structure and parameters are determined through reasoning of knowledge model. In order to facilitate the application of domain library, case-based reasoning (CBR) technology is implemented for model search. Two key technologies about similarity measuring and weights assigning in CBR are studied. A similarity computation model between range properties is introduced. This model unifies the computation methods of other types of properties. To assign weights, proposing an objective method based on the deviation information of similarity values among properties. Objective and subjective weights are combined to form synthesis weights.
针对参数优化中参数变动后重复仿真的效率问题,研究了一种分治求解策略,即在仿真模型规模分解基础上建立耦合块依赖图和序列表,对各耦合块建立相应的求解块,通过遍历耦合块序列表并调用相应求解块,便可获得仿真模型的数值解。考虑到参数变动下的重复仿真,对耦合块依赖图进行分层处理,生成对应于变动参数集的变动子图;通过施加虚根节点将变动子图转化成最小求解树结构。因此,对变动参数集的不同参数值进行重复仿真只需层次遍历最小求解树,再调用相应的求解块即可。该方法可一定程度上提高复杂模型的多次仿真求解效率。
在分析多领域物理系统仿真优化特点的基础上,研究了Modelica参数优化建模的关键问题,以及多领域优化模型的寻优策略和模型参数实验技术。基于模型的编译信息实现多实例、多目标启发式仿真优化建模;并利用Modelica语言的结构化注解特征研究了仿真优化模型的混合表达,实现了优化信息的可重用性和继承性。在优化算法中引入拟梯度、复步微分和自动微分三种数值方法以提高敏度计算效率和精度。
在相对差分概念的基础上研究了一种新的通用的混合离散非线性优化方法。详细阐述了该方法的基本原理、思想和算法描述。该方法的特点是迭代中间设计点均是可行离散点,无需邻域查点和圆整,并且可避免收敛于伪极值点,和现有方法相比具有较强的稳健性和通用性。
利用支配关系的定义证明Pareto适应度函数判断非支配点的有效性,并在此基础上结合序列近似模型技术和启发式搜索算法研究了两种基于Pareto解集的多目标优化方法。这两种方法均可很大程度上有助于降低精确分析次数。对于Pareto边界为凸、非凸、非连续的多目标优化问题,该方法均能取得较好的Pareto解集。
利用Modelica语言的结构化注解机制表达设计知识,从而实现基于知识的建模。根据部件知识之间的依赖关系确定推理求解顺序。通过知识模型的推理求解得到确定的仿真模型结构和确定的模型参数。为了便于领域库模型的搜索和应用,研究了面向模型搜索的实例推理技术,针对最近邻实例检索中实例属性相似度和权重的计算问题,给出区间值属性相似度的计算模型,并将各种属性类型的相似度计算方法统一起来。研究了基于相似度信息的客观赋权方法,以组合权重计算实例相似度。
Product design is a process of analysis and optimization, where optimization is the goal, simulation is a means of optimization, simulation and modeling is the basis of optimization. Some Problems about parameter optimization and inference solving for simulation models based on Modelica are studied in this dissertation.
For the efficiency of repetitious simulation after parameters tuning, a kind of subdivision solving strategy is put forward: Based on the scale decomposing of the simulation model, a coupling blocks dependency graph and sequential list are built. As for all coupling blocks, their corresponding solving blocks. Then numerical solution of the simulation model can be achieved through traversing the coupling sequential list and simultaneously calling the corresponding solving blocks. Considering the efficiency of repetitious simulation after parameters varying, the altering sub-graph of the altering parameters set is built after hierarchically processing the coupling blocks graph. And the sub-graph is converted into a minimum solving tree by adding a virtual root node. In this way, carrying out repetitious simulation with different parameters values only need traverse widely the minimum solving tree of the altering parameters set and simultaneously calling corresponding solving blocks. This method of the paper could greatly improve the efficiency of repetitious simulation of complex model.
After analyzing the characters of simulation and optimization for multi-domain physical systems, some key technologies based on Modelica model, such as design optimization modeling, optimization strategies and parameters design, are presented. Firstly, a heuristic method is presented to setup optimization models based on the compiler information of simulation models. Then, based on the structure annotation feature, optimization models are embedded in simulation models to form a hybrid representation, through which the optimization information becomes reusable and inheritable. To enhancing accuracy and efficiency of evaluating gradient in optimization, three numerical methods: quasi-gradient, complex-step derivative and automatic differentiation, are presented.
A new mixed discrete nonlinear optimization method is put forward based on the concept of relative difference. The basic principle, idea and algorithm of the method are elaborated. Compared to existing algorithms, the method is more robust and versatile, and it has many advantages, such as: All the middle iterative design points are feasible discrete points. No neighborhood enumeration and roundness are needed, and it can avoid convergence in the pseudo-extreme point.
The concept of Pareto fitness function is introduced, and the effectiveness of it to identify non-dominated point is proved by using the definition of domination. Two Pareto multi-objective optimization methods are put forward by combined the sequence approximate model technology and heuristic search algorithm. Research shows that these two methods can largely reduce the number of precision analysis. And for the multi-objective optimization problems with convex, non-convex or non-consecutive Pareto frontier, better Pareto points of which can be identified by both the methods.
To implement knowledge-based modeling, a knowledge representation method is studied based on the structure annotation mechanism. The inference order is determined by the knowledge dependent relationship between model parts. Model structure and parameters are determined through reasoning of knowledge model. In order to facilitate the application of domain library, case-based reasoning (CBR) technology is implemented for model search. Two key technologies about similarity measuring and weights assigning in CBR are studied. A similarity computation model between range properties is introduced. This model unifies the computation methods of other types of properties. To assign weights, proposing an objective method based on the deviation information of similarity values among properties. Objective and subjective weights are combined to form synthesis weights.
引文
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