多学科模糊满意协同优化方法及其应用
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摘要
在国家自然科学基金和国家863高技术发展计划的资助下,本文研究了多学科模糊满意协同优化方法,主要包括：多学科协同优化(CO)分学科(子系统)建模方法、模糊满意协同优化方法、基于全局共享变量近似子空间的协同优化方法,并将其应用于全断面岩石掘进机刀具布局优化设计中。该问题在理论研究中属于多学科设计优化方法(MDO)；在机械设计中属于复杂布局方案设计；在人工智能领域中属于人机结合问题,具有重要的理论和工程应用价值。
提出了基于全局共享变量近似子空间的协同优化方法,对于学科级共享变量的可行域以超切平面法来近似,当系统级共享设计变量达到了一致性要求,系统级才进行解耦操作,在一定程度上降低学科级的分析次数,具有很好的计算精度和计算稳定性,可以有效地解决TBM刀具布局优化设计这类涉及共享变量多,耦合变量相对较少的优化设计问题。
为了能在协同优化中嵌入模糊因素与领域专家的知识和经验,本文给出了模糊满意协同优化模型及算法,在学科级分析模块中增加了极角模糊规则和模糊约束最优截集水平分析。从TBM刀具布局优化设计问题的应用效果来看,有效地解决了刀具布局协同优化设计中模糊推理、模糊约束的处理问题。
针对TBM刀盘布置设计中具有布局计算复杂,优化器负载重、学科领域内容交叉的特点,提出了按MDO的学科分级优化的思想,利用协同优化方法,将刀盘最优布置模型分成了两层,共包括1个系统级和4个子系统(学科)级：刀盘几何学计算子系统、刀盘力学计算子系统、刀盘质心计算子系统和破岩量计算子系统,各子系统级采用并行优化器处理,以降低问题的求解规模,提高刀具布局寻优的效率。
全文的主要工作内容包括：
(1)讨论了并行子空间优化、协同优化和两级集成系统三种多学科优化方法的特点和应用,并根据系统工程学原理和TBM盘刀布置问题的特点,提出利用多学科协同优化方法来解决TBM刀具布局优化这类复杂问题的思想。
(2)提出了多学科协同优化分学科优化策略、建模方法和盘刀布置方案系统级调整机制。分析了标准协同优化计算困难的原因,在此基础上提出了一种改良的协同优化方法——基于全局共享变量近似子空间协同优化。并通过实例验证该方法在求解复杂工程布局问题的可行性和有效性。
(3)提出模糊协同优化模型及算法,主要包括两类模型——对称和非对称模糊协同优化模型,前者将截集水平作为学科级的共享变量来处理,它比较适合于约束条件和优化目标具有同等重要程度的情况；后者将截集水平嵌入到学科级中,由学科级分析模块来处理,比较适合于对约束条件和优化目标具有不同的重视度情况。
(4)将本文提出的方法,应用到TBM掘进机刀具布局优化的工程实例中,具体方法包括：非对称模糊满意协同优化模型、学科级分析模块中极角模糊规则、模糊约束的最优截集水平、学科级模糊推理、极角模糊推理约束条件的构建等。
本文以全断面岩石掘进机刀具布局设计为应用背景,根据MDO及模糊理论与方法,给出了多学科模糊满意协同优化方法,并在该方法中应用了近似和解耦协调机制、模糊优化、模糊推理等相关理论,具有一定的工程实用价值,本文工作期望有助于推动一类复杂工程布局优化设计理论研究的进展。
Supported by National Natural Science Foundation of China and National Hi-Tech Research and Development Program (863Program) of China, this research studies multidisciplinary collaborative satisficing design method, which mainly includes the method modeled by the discipline (subsystem) using multidisciplinary collaborative optimization(CO), the fuzzy satisficing collaborative optimization method, the collaborative optimization method based on the global shared variables approximation subspace. The indicated method is finally used at the cutter layout design of Full Face Rock Tunnel Boring Machine(TBM). The aforementioned studies belong to the method of multidisciplinary design optimization (MDO) in theory, the complex layout scheme design in mechanics design, and the human-computer cooperative problem in artificial intelligence, which is of the important theory and application value.
This study proposes a collaborative optimization method based on the global shared variables approximation subspace. The super tangent plane method is used to approximate the feasible domain of each discipline level's shared variable. When shared design variables at the system level satisfy the consistency constraints, system level is to decouple the auxiliary variables in certain to reduce the analysis times of discipline level, and may obtain good accuracy and stability of computation. This method may efficiently solve this kind of problem, such as cutter layout design, which contains lots of shared variables and relatively few auxiliary variables.
For cutter layout design problem of TBM involves fuzzy factors and expertise's experience, a fuzzy satisficing collaborative optimization model and algorithm are presented. This model increases the analysis for fuzzy rules of the polar angle and optimal cut set level of fuzzy constrained at the discipline level, which may solve effectively multidisciplinary design problems of fuzzy constraint and fuzzy reasoning problem in cutter layout design.
Considering the computational complexity, heavy load of the optimizer, multidisciplinary contents involved in TBM cutter layout design, and this dissertation indicates an optimization method classified by discipline of MDO. In accordance with collaborative optimization idea, the cutter optimal layout model is divided into two layers, including one system and four subsystems (disciplines) level, that is, cutterhead geometry subsystem, cutter dynamics subsystem, cutterhead center of mass subsystem and rock breaking volume subsystem. The subsystem level uses parallel optimizer, which reduces the scale of solving, and improves the efficiency of cutterhead layout optimization.
The main contents of this dissertation are as follows:
(1) This study reviews the layout design and development of multidisciplinary design optimization, discusses concurrent subspace optimization, collaborative optimization and Bi—level integration system synthesis optimization methods and the characteristics of their respective application. According to the idea of system engineering, multidisciplinary collaborative optimization method is proposed to solve the cutterhead layout optimization of this kind of complicated problem.
(2) This dissertation presents a optimization strategy of disciplines, modeling method and adjustment mechanism of cutterhead layout scheme at system level.Through the analysis of the computational difficulties reason for standard collaborative optimization algorithm, this study puts forward an improved CO method:Based on global shared variables approximation subspace collaborative optimization. An example is used to test and verify that this method is feasible and effective.
(3) Fuzzy collaborative optimization model and algorithm are presented, including two main kinds of model, that is, symmetric and asymmetric fuzzy collaborative optimization model. The former takes cut set level as the discipline level's shared variables, and it is more suited to the condition of the constraints and objectives with equal importance degree; The latter embeds cut set level into the discipline level, and it is processed by level analysis module, which is more suited to the condition of constraints and objectives with different importance degree.
(4) The methods introduce by the above sections are applied to the cutter layout design optimization of TBM, such as the selection of asymmetric fuzzy satisficing collaborative optimization model, optimal cut set level of the polar angle of fuzzy rules and fuzzy constrained at the discipline level analysis module, fuzzy reasoning, the construction of the polar angle of fuzzy constraints, interactive preference optimization design at system level.
Based on cutter layout design problem of full face rock tunnel boring machine, the study gives the multidisciplinary fuzzy and satisficing collaborative optimization method combined with human-computer interaction,which uses the approximation and decoupling coordination mechanism, fuzzy optimization, fuzzy reasoning theory. The research has a certain engineering application value, and contributes to the research progress of layout MDO problem.
提出了基于全局共享变量近似子空间的协同优化方法,对于学科级共享变量的可行域以超切平面法来近似,当系统级共享设计变量达到了一致性要求,系统级才进行解耦操作,在一定程度上降低学科级的分析次数,具有很好的计算精度和计算稳定性,可以有效地解决TBM刀具布局优化设计这类涉及共享变量多,耦合变量相对较少的优化设计问题。
为了能在协同优化中嵌入模糊因素与领域专家的知识和经验,本文给出了模糊满意协同优化模型及算法,在学科级分析模块中增加了极角模糊规则和模糊约束最优截集水平分析。从TBM刀具布局优化设计问题的应用效果来看,有效地解决了刀具布局协同优化设计中模糊推理、模糊约束的处理问题。
针对TBM刀盘布置设计中具有布局计算复杂,优化器负载重、学科领域内容交叉的特点,提出了按MDO的学科分级优化的思想,利用协同优化方法,将刀盘最优布置模型分成了两层,共包括1个系统级和4个子系统(学科)级：刀盘几何学计算子系统、刀盘力学计算子系统、刀盘质心计算子系统和破岩量计算子系统,各子系统级采用并行优化器处理,以降低问题的求解规模,提高刀具布局寻优的效率。
全文的主要工作内容包括：
(1)讨论了并行子空间优化、协同优化和两级集成系统三种多学科优化方法的特点和应用,并根据系统工程学原理和TBM盘刀布置问题的特点,提出利用多学科协同优化方法来解决TBM刀具布局优化这类复杂问题的思想。
(2)提出了多学科协同优化分学科优化策略、建模方法和盘刀布置方案系统级调整机制。分析了标准协同优化计算困难的原因,在此基础上提出了一种改良的协同优化方法——基于全局共享变量近似子空间协同优化。并通过实例验证该方法在求解复杂工程布局问题的可行性和有效性。
(3)提出模糊协同优化模型及算法,主要包括两类模型——对称和非对称模糊协同优化模型,前者将截集水平作为学科级的共享变量来处理,它比较适合于约束条件和优化目标具有同等重要程度的情况；后者将截集水平嵌入到学科级中,由学科级分析模块来处理,比较适合于对约束条件和优化目标具有不同的重视度情况。
(4)将本文提出的方法,应用到TBM掘进机刀具布局优化的工程实例中,具体方法包括：非对称模糊满意协同优化模型、学科级分析模块中极角模糊规则、模糊约束的最优截集水平、学科级模糊推理、极角模糊推理约束条件的构建等。
本文以全断面岩石掘进机刀具布局设计为应用背景,根据MDO及模糊理论与方法,给出了多学科模糊满意协同优化方法,并在该方法中应用了近似和解耦协调机制、模糊优化、模糊推理等相关理论,具有一定的工程实用价值,本文工作期望有助于推动一类复杂工程布局优化设计理论研究的进展。
Supported by National Natural Science Foundation of China and National Hi-Tech Research and Development Program (863Program) of China, this research studies multidisciplinary collaborative satisficing design method, which mainly includes the method modeled by the discipline (subsystem) using multidisciplinary collaborative optimization(CO), the fuzzy satisficing collaborative optimization method, the collaborative optimization method based on the global shared variables approximation subspace. The indicated method is finally used at the cutter layout design of Full Face Rock Tunnel Boring Machine(TBM). The aforementioned studies belong to the method of multidisciplinary design optimization (MDO) in theory, the complex layout scheme design in mechanics design, and the human-computer cooperative problem in artificial intelligence, which is of the important theory and application value.
This study proposes a collaborative optimization method based on the global shared variables approximation subspace. The super tangent plane method is used to approximate the feasible domain of each discipline level's shared variable. When shared design variables at the system level satisfy the consistency constraints, system level is to decouple the auxiliary variables in certain to reduce the analysis times of discipline level, and may obtain good accuracy and stability of computation. This method may efficiently solve this kind of problem, such as cutter layout design, which contains lots of shared variables and relatively few auxiliary variables.
For cutter layout design problem of TBM involves fuzzy factors and expertise's experience, a fuzzy satisficing collaborative optimization model and algorithm are presented. This model increases the analysis for fuzzy rules of the polar angle and optimal cut set level of fuzzy constrained at the discipline level, which may solve effectively multidisciplinary design problems of fuzzy constraint and fuzzy reasoning problem in cutter layout design.
Considering the computational complexity, heavy load of the optimizer, multidisciplinary contents involved in TBM cutter layout design, and this dissertation indicates an optimization method classified by discipline of MDO. In accordance with collaborative optimization idea, the cutter optimal layout model is divided into two layers, including one system and four subsystems (disciplines) level, that is, cutterhead geometry subsystem, cutter dynamics subsystem, cutterhead center of mass subsystem and rock breaking volume subsystem. The subsystem level uses parallel optimizer, which reduces the scale of solving, and improves the efficiency of cutterhead layout optimization.
The main contents of this dissertation are as follows:
(1) This study reviews the layout design and development of multidisciplinary design optimization, discusses concurrent subspace optimization, collaborative optimization and Bi—level integration system synthesis optimization methods and the characteristics of their respective application. According to the idea of system engineering, multidisciplinary collaborative optimization method is proposed to solve the cutterhead layout optimization of this kind of complicated problem.
(2) This dissertation presents a optimization strategy of disciplines, modeling method and adjustment mechanism of cutterhead layout scheme at system level.Through the analysis of the computational difficulties reason for standard collaborative optimization algorithm, this study puts forward an improved CO method:Based on global shared variables approximation subspace collaborative optimization. An example is used to test and verify that this method is feasible and effective.
(3) Fuzzy collaborative optimization model and algorithm are presented, including two main kinds of model, that is, symmetric and asymmetric fuzzy collaborative optimization model. The former takes cut set level as the discipline level's shared variables, and it is more suited to the condition of the constraints and objectives with equal importance degree; The latter embeds cut set level into the discipline level, and it is processed by level analysis module, which is more suited to the condition of constraints and objectives with different importance degree.
(4) The methods introduce by the above sections are applied to the cutter layout design optimization of TBM, such as the selection of asymmetric fuzzy satisficing collaborative optimization model, optimal cut set level of the polar angle of fuzzy rules and fuzzy constrained at the discipline level analysis module, fuzzy reasoning, the construction of the polar angle of fuzzy constraints, interactive preference optimization design at system level.
Based on cutter layout design problem of full face rock tunnel boring machine, the study gives the multidisciplinary fuzzy and satisficing collaborative optimization method combined with human-computer interaction,which uses the approximation and decoupling coordination mechanism, fuzzy optimization, fuzzy reasoning theory. The research has a certain engineering application value, and contributes to the research progress of layout MDO problem.
引文
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