多层次系统代理模型的不确定性量化及序列采样方法研究

发布时间：2019-05-18 23:01

【摘要】：随着现代工业的迅速发展,复杂系统的设计通常会涉及众多的决策变量和因素。在传统的“All-In-One(AIO)”求解方法中,对复杂系统中所有的设计变量同时进行优化,导致优化设计模型十分复杂,计算效率非常低。为了减少复杂系统分析和设计过程中的计算复杂度,提高计算效率,并实现复杂系统的并行分析和设计,往往可以将复杂系统按照功能逻辑和物理组成结构分解成若干个相互之间具有层次型关系的子系统(也称为子模型),然后对各个子系统独立地进行分析和设计。对于各个子系统若直接采用计算机仿真技术(如:结构有限元仿真、材料分子动力学仿真),其计算量将非常大,因此工程中普遍使用代理模型(Metamodel)代替子系统真实仿真模型。然而,由于初始采样点数量的限制,代理模型与真实模型之间必然存在代理模型不确定性(Metamodeling Uncertainty),而代理模型不确定性对系统分析和设计有着重要影响。在过去的几十年里,学者们已经研究并提出了很多种代理模型及序列采样方法。但到目前为止,对于多层次复杂系统的设计中代理模型不确定性及提高代理模型精确度(Fidelity)的研究非常有限。围绕这一问题,本论文开展了多层次系统代理模型的不确定性量化及面向多层次系统代理模型的序列采样方法的研究。具体的研究内容和主要创新如下:(1)在多层次复杂系统中,各层子系统的代理模型不确定性将从底层逐层传递到系统顶层的响应中。为了分析多层次复杂系统中各层子系统代理模型的不确定性对系统顶层响应的影响,本论文提出了一种多层次系统代理模型的不确定性量化方法,并推导出了各个子系统代理模型不确定性对系统顶层响应不确定性的解析表达式。(2)为了降低多层次系统代理模型的不确定性量化过程中的计算量,提高计算效率,本文提出了采用数值积分计算代理模型不确定性传递问题的思路,并从计算效率和计算精度两方面对几种常用的数值积分方法在进行对比,最终选取了高斯-埃尔米特积分方法并将其应用在多层次系统代理模型不确定性传递的计算中。(3)现有的序列采样方法大多仅考虑单层代理模型的不确定性及精确度提高策略。然而,这种方法忽略了多层次系统中各层子系统代理模型间的不确定性传递问题,所选取的采样点往往并不能最大程度地提高多层次系统代理模型的精确度。基于这种情况,本文提出了面向多层次系统代理模型的序列采样新方法。该方法综合考虑了各个代理模型的不确定性,选取对整个系统不确定性影响最大的位置采集新的样本点,进而更新系统各层代理模型,直到整个系统的代理模型的精确度达到预定要求。与常规的采样方案对比发现:在新增样本点有限的情况下,本论文提出的方法对新样本点的分配方案更加合理,能最大程度地提高系统代理模型的精确度。
[Abstract]:With the rapid development of modern industry, the design of complex systems usually involves many decision variables and factors. In the traditional "All-In-One (AIO)" method, all the design variables in the complex system are optimized at the same time, which leads to the complexity of the optimization design model and the low computational efficiency. In order to reduce the computational complexity in the process of complex system analysis and design, improve the computational efficiency, and realize the parallel analysis and design of complex system, Often, the complex system can be decomposed into several subsystems (also known as submodels) with hierarchical relationship with each other according to the functional logic and physical composition structure, and then each subsystem can be analyzed and designed independently. If the computer simulation technology is used directly for each subsystem (such as structural finite element simulation, material molecular dynamics simulation), the calculation amount will be very large. Therefore, agent model (Metamodel) is widely used to replace the real simulation model of subsystems in engineering. However, due to the limitation of the number of initial sampling points, there must be agent model uncertainty between the agent model and the real model (Metamodeling Uncertainty), and the uncertainty of the agent model has an important impact on the system analysis and design. In the past few decades, scholars have studied and proposed many proxy models and sequence sampling methods. However, up to now, the research on the uncertainty of agent model and improving the accuracy of agent model (Fidelity) in the design of multi-level complex systems is very limited. Around this problem, this paper studies the uncertainty quantification of multi-level system agent model and the sequence sampling method for multi-level system agent model. The specific research contents and main innovations are as follows: (1) in the multi-level complex system, the uncertainty of the agent model of each layer subsystem will be transferred from the bottom layer to the top level response of the system. In order to analyze the influence of the uncertainty of the agent model of each layer subsystem in the multi-level complex system on the top-level response of the system, a quantitative method of uncertainty of the multi-level system agent model is proposed in this paper. The analytical expression of the uncertainty of each subsystem agent model to the top level response uncertainty of the system is derived. (2) in order to reduce the computational complexity and improve the computational efficiency in the process of uncertainty quantification of the multi-level system agent model, In this paper, the idea of using numerical integration to calculate the uncertainty transfer problem of agency model is put forward, and several commonly used numerical integration methods are compared from two aspects of calculation efficiency and calculation accuracy. Finally, the Gao Si-Hermitian integral method is selected and applied to the calculation of uncertainty transfer of multi-level system agent model. (3) most of the existing sequence sampling methods only consider the uncertainty of single-layer agent model. And the strategy of improving accuracy. However, this method ignores the uncertainty transfer problem between the agent models of each layer subsystem in the multi-level system, and the selected sampling points often can not improve the accuracy of the multi-level system agent model to the greatest extent. Based on this situation, a new sequential sampling method for multi-level system agent model is proposed in this paper. This method takes into account the uncertainty of each agent model, selects the position which has the greatest influence on the uncertainty of the whole system to collect new sample points, and then updates the agent model of each layer of the system. Until the accuracy of the proxy model of the whole system meets the predetermined requirements. Compared with the conventional sampling scheme, it is found that the method proposed in this paper is more reasonable for the allocation of new sample points and can improve the accuracy of the system agent model to the greatest extent when the new sample points are limited.
【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB472

【共引文献】