基于支持向量机的主动元建模方法研究
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摘要
随着科学技术的发展及仿真理论的成熟,诸如高层推理、决策支持以及探索性分析等领域的研究对象已经从系统范畴提升到体系范畴,研究问题越来越复杂。由于涉及实体众多、交互关系复杂、不确定性显著,复杂高层决策问题通常具有复杂非线性、多层次多类型及有限时间获取数据有限特性,这些特性使得计算的复杂性和分析的复杂性愈发显著,客观上要求构建简单的低分辨率模型。
近年来,面向高层决策问题的元建模方法研究已成为M&S领域的一个重要研究内容,旨在提高模型的可理解性和可解释性的主动元建模方法一经提出,就立刻成为元建模领域内的研究热点。然而,研究现状的分析表明,包括RAND公司的主动元建模方法和支持向量回归在内的诸多结合先验知识的回归方法,在应对复杂高层决策问题的三类特征:结构复杂性、知识多样性、样本有限性时各具优劣,但无法同时有效应对具有这三类特征的问题,因此研究一种新的主动元建模方法成为M&S领域迫在眉睫的需求。
本文围绕解决“计算的复杂性”和“分析的复杂性”的主题展开研究,提出一种以传统主动元建模思想为核心、以支持向量回归为关键技术的新的主动元建模实现思路基于支持向量机的主动元建模方法。该方法在宏观上保留了传统主动元建模方法对模型结构设计的自顶向下的指导能力,在微观上保留了支持向量回归方法能够逼近任意阶的非线性函数且适于结合多类先验知识的自底向上的机器学习能力,同时克服了这两类方法相应的不足。为此论文对该方法相关的理论问题进行了系统研究与工程实践,具体内容包括:
(1)系统地分析研究了基于支持向量机的主动元建模方法的必要性和可行性,给出其形式化定义;分类并总结了建模所需的各类先验知识,将模型结构设计分为核函数设计和约束设计两个部分,并在此基础上提出了以结构设计、仿真实验、模型生成、评估和确认、模型应用为核心的建模框架。
(2)针对基于支持向量机的主动元建模方法的核函数设计问题展开研究,具体内容包括:1)针对现有核函数“一视同仁”地处理所有输入维度的缺陷以及应用中可能事先已知某些结构型知识的实际情况,提出基于结构型领域知识的核函数构造方法,研究基于直和和张量积构造内涵结构知识的再生核,并给出基于该方法的系统化建模步骤;2)针对现有方法较难处理导数知识的问题以及利用再生核与微分算子之间的相应关系,提出基于非结构型领域知识的核函数构造方法,研究基于微分算子的Green函数的再生核计算方法,包括基于任意m阶微分算子、具有m个互异特征根的微分算子和更简单微分算子等三类情形的计算方法,并给出基于该方法的再生核自适应计算方法;3)针对最优核函数选择(现有文献一般选用高斯核)缺乏指导策略的问题,提出基于静态想定知识的核函数选择方法,通过对仿真问题特征的量化,分析比较高斯核在内的多个核函数,得出高斯核在处理输入维度较高(大于5)且非线性程度较高或输入维度大于10的问题时,其性能不如再生核的结论,并总结出具备一般性的最优核函数选择策略。
(3)针对基于支持向量机的主动元建模方法的约束设计和模型训练展开研究,具体内容包括:针对标准支持向量回归算法面临参数选择困难、应对可变数据集时泛化能力有限、引入和评价先验知识较难等难题,提出了一种基于先验知识的自适应支持向量回归算法,分析了该算法基本框架及流程,并详细论述各个模块的作用和实现过程;考虑多类先验知识在训练过程中的作用和特点,提出了基于确定型约束和随机性约束的两类规划问题设计求解方法,并将改进的遗传算法与支持向量回归进行扩展结合,在宏观上解决了参数选择和知识评价问题,并在分析快速训练算法和精确解增量算法的基础上,提出一种近似增量训练算法。
(4)针对高层决策分析的应用需求,以导弹攻防对抗仿真中蓝方雷达探测系统为应用实例,通过构建雷达发现概率的主动元模型,在宏观上演示了基于支持向量机的主动元建模方法的建模过程,并在微观上验证了基于确定型约束的规划求解方法的有效性;通过构建雷达首次稳定跟踪目标时间的主动元模型,验证了基于随机型约束的规划求解方法的有效性。
论文的主要创新包括:提出了一种基于支持向量机的主动元建模方法,将RAND公司的主动元建模方法和支持向量回归方法有机结合取长补短,完整地给出了该方法形式化定义及建模框架;针对不同应用需求和先验知识类型,提出了三类具体的核函数设计方法;针对参数选择问题、泛化能力问题和知识评价问题,提出一种基于先验知识的自适应支持向量回归算法,它利用改进的遗传算法在宏观上解决参数选择和知识评价问题,同时利用近似增量训练算法,在微观上解决了应对可变训练集的泛化能力问题。
论文的研究属于M&S和机器学习领域的基础性研究,不但丰富和发展了系统建模仿真方法学,对于推动多分辨率建模理论、机器学习、数据挖掘及试验设计理论在复杂高层决策分析中的研究具有重要意义。
The development of simulation theory and technology has made the research ob-jects in some important fields, such as high-level reasoning, decision-making support andexploratory analysis, upgrad from system level to system-of-systems level and becomemore and more complicated. The problems in high-level decision-making usually pos-sess some characters, e.g. complex nonlinearity, multi-levels and multi-types and limiteddata in limited time, since there are numerous entities, complicated interactive relationsand uncertain effect process. These characters make the complex in computation andanalysis more remarkable and require the development of simpler low-resolution models.
Recently, the study on metamodelling for high-level decision-making has become animportant research area. The motivated metamodelling, which primely aims at improv-ing the comprehensibility and interpretability, has exhibited to be the research hotspot.However, the analysis of current relevant research works shows that none of the regres-sion approaches combined with prior knowledge, including the motivated metamodellingin RAND and support vector regression, has the full ability to deal with the problems indecision-making with the main three characters. Thus there are cravings in studying anew motivated metamodelling method for M&S.
This dissertation is focused on solving the”complex in computation”and”complexin analysis”. A new motivated metamodelling method, which combined with classicalmotivated metamodelling and support vector regression, is proposed based on the charac-ters of the problems in decision-making and the analysis results about the existing regres-sion methods. Consequently, this dissertation expands its content in several correlativedirections, including theory of the new method, design methods of kernel function basedon prior knowledge, adaptive regression algorithm, etc. The original works include:
(1) Several key theoretic problems for the motivated metamodelling based on sup-port vector machines have been researched systemically. After analyzing the feasibilityand necessity of the new method, the dissertation presents a formal theoretic framework,classifies and summarizes the prior knowledge systemically. Based on the summary, thestructural design of metamodel is divided into two important parts, i.e. the design of thekernel function and the restrictions, and a new modelling framework, which consists offive sub-frameworks including structural design, simulation experiment, model genera- tion, evaluation and validation, application, is proposed.
(2) The second part is focused on the problem of designing kernel function, whoseworks include: 1) According to the disadvantage of the conventional kernel functions,which perform an equal treatment for all the input dimensions, and the advantage of theaforehand presence of the structural knowledge, a new kernel construction method basedon structural prior knowledge is presented. This method has studied the constructionof reproducing kernel based on direct sum and senor product with prior knowledge andthe systematic modeling process. 2) According to the disadvantage on using derivativeknowledge and the theoretic results on reproducing kernel and differential operator, an-other kernel construction method based on non-structural prior knowledge is proposed.It studied the computation method of reproducing kernel based on the Green’s functionsof three kinds of differential operator, i.e. differential operator with m-order, with m dif-ferent eigenvalues and simpler cases, and presented an automatic, flexible and rigorouscomputation algorithm. 3) According to the lack of theoretic evidence on the so-called”best”kernel of Gaussian kernel, the third kernel construction method based on static sce-nariopriorknowledgeisintroduced. Itfocusesonquantitativelyanalyzingandcomparingseveral kernels, including Gaussian kernel, two new reproducing kernels, and performingthe experiments using multiple criteria and synthetic problems. The results show that thereproducing kernel is an equivalent or even better kernel than RBF for the problems withmore input variables (more than 5, especially more than 10) and higher nonlinearity.
(3) The third part has studied the problems of designing the restrictions and trainingmodel. According to the disadvantages of standard support vector regression training al-gorithm, i.e. disadvantageinparameterselection, limitationinthegeneralizationcapacityon changeable data set, difficult in incorporating and evaluating the prior knowledge, anew regression algorithm, i.e. Adaptive Motivated Support Vector Regression (AMSVR)is presented. Based on the introduction of the function and realization of all the compo-nents in AMSVR, two important components are discussed in detail. Firstly, two kindsof designing and solving approaches of programming problem are presented. Secondly,a new training algorithm, i.e. approximation incremental algorithm that is hybrid withquick training algorithm and accurate incremental algorithm, is proposed.
(4)According to the application requirementin high-leveldecision-making analysis,the theory of this dissertation is demonstrated by an example of motivated metamodelling of radar system in the background of strategy missile breaking through NMD defensesystem simulation.
The main contributions of this dissertation include: a new motivated metamodellingmethod, i.e. motivated metamodelling based support vector machines, which combinedwith the classical motivated metamodelling of RAND and support vector regression, ispresented and the formal conceptual framework and modelling framework are summa-rized. Three different methods for constructing kernel function based on different ap-plication requirement and prior knowledge are proposed. According to the problems, i.e.parameterselection,generalizationabilityandknowledgeevaluation,anewtrainingalgo-rithm, i.e. Adaptive Motivated Support Vector Regression (AMSVR) is presented, whichemploys an improved genetic algorithm to solve the parameter selection and knowledgeevaluation and uses an approximation incremental algorithm to improve the generaliza-tion ability for a changeable experiment data set.
The research topics of this dissertation belong to the fundamental M&S theory andmachine learning categories. Above contributions can advance the system modelling andsimulation methodology, and promote the studies of multi-resolution, machine learning,data mining and experimental design in complex high-level decision-making analysis.
近年来,面向高层决策问题的元建模方法研究已成为M&S领域的一个重要研究内容,旨在提高模型的可理解性和可解释性的主动元建模方法一经提出,就立刻成为元建模领域内的研究热点。然而,研究现状的分析表明,包括RAND公司的主动元建模方法和支持向量回归在内的诸多结合先验知识的回归方法,在应对复杂高层决策问题的三类特征:结构复杂性、知识多样性、样本有限性时各具优劣,但无法同时有效应对具有这三类特征的问题,因此研究一种新的主动元建模方法成为M&S领域迫在眉睫的需求。
本文围绕解决“计算的复杂性”和“分析的复杂性”的主题展开研究,提出一种以传统主动元建模思想为核心、以支持向量回归为关键技术的新的主动元建模实现思路基于支持向量机的主动元建模方法。该方法在宏观上保留了传统主动元建模方法对模型结构设计的自顶向下的指导能力,在微观上保留了支持向量回归方法能够逼近任意阶的非线性函数且适于结合多类先验知识的自底向上的机器学习能力,同时克服了这两类方法相应的不足。为此论文对该方法相关的理论问题进行了系统研究与工程实践,具体内容包括:
(1)系统地分析研究了基于支持向量机的主动元建模方法的必要性和可行性,给出其形式化定义;分类并总结了建模所需的各类先验知识,将模型结构设计分为核函数设计和约束设计两个部分,并在此基础上提出了以结构设计、仿真实验、模型生成、评估和确认、模型应用为核心的建模框架。
(2)针对基于支持向量机的主动元建模方法的核函数设计问题展开研究,具体内容包括:1)针对现有核函数“一视同仁”地处理所有输入维度的缺陷以及应用中可能事先已知某些结构型知识的实际情况,提出基于结构型领域知识的核函数构造方法,研究基于直和和张量积构造内涵结构知识的再生核,并给出基于该方法的系统化建模步骤;2)针对现有方法较难处理导数知识的问题以及利用再生核与微分算子之间的相应关系,提出基于非结构型领域知识的核函数构造方法,研究基于微分算子的Green函数的再生核计算方法,包括基于任意m阶微分算子、具有m个互异特征根的微分算子和更简单微分算子等三类情形的计算方法,并给出基于该方法的再生核自适应计算方法;3)针对最优核函数选择(现有文献一般选用高斯核)缺乏指导策略的问题,提出基于静态想定知识的核函数选择方法,通过对仿真问题特征的量化,分析比较高斯核在内的多个核函数,得出高斯核在处理输入维度较高(大于5)且非线性程度较高或输入维度大于10的问题时,其性能不如再生核的结论,并总结出具备一般性的最优核函数选择策略。
(3)针对基于支持向量机的主动元建模方法的约束设计和模型训练展开研究,具体内容包括:针对标准支持向量回归算法面临参数选择困难、应对可变数据集时泛化能力有限、引入和评价先验知识较难等难题,提出了一种基于先验知识的自适应支持向量回归算法,分析了该算法基本框架及流程,并详细论述各个模块的作用和实现过程;考虑多类先验知识在训练过程中的作用和特点,提出了基于确定型约束和随机性约束的两类规划问题设计求解方法,并将改进的遗传算法与支持向量回归进行扩展结合,在宏观上解决了参数选择和知识评价问题,并在分析快速训练算法和精确解增量算法的基础上,提出一种近似增量训练算法。
(4)针对高层决策分析的应用需求,以导弹攻防对抗仿真中蓝方雷达探测系统为应用实例,通过构建雷达发现概率的主动元模型,在宏观上演示了基于支持向量机的主动元建模方法的建模过程,并在微观上验证了基于确定型约束的规划求解方法的有效性;通过构建雷达首次稳定跟踪目标时间的主动元模型,验证了基于随机型约束的规划求解方法的有效性。
论文的主要创新包括:提出了一种基于支持向量机的主动元建模方法,将RAND公司的主动元建模方法和支持向量回归方法有机结合取长补短,完整地给出了该方法形式化定义及建模框架;针对不同应用需求和先验知识类型,提出了三类具体的核函数设计方法;针对参数选择问题、泛化能力问题和知识评价问题,提出一种基于先验知识的自适应支持向量回归算法,它利用改进的遗传算法在宏观上解决参数选择和知识评价问题,同时利用近似增量训练算法,在微观上解决了应对可变训练集的泛化能力问题。
论文的研究属于M&S和机器学习领域的基础性研究,不但丰富和发展了系统建模仿真方法学,对于推动多分辨率建模理论、机器学习、数据挖掘及试验设计理论在复杂高层决策分析中的研究具有重要意义。
The development of simulation theory and technology has made the research ob-jects in some important fields, such as high-level reasoning, decision-making support andexploratory analysis, upgrad from system level to system-of-systems level and becomemore and more complicated. The problems in high-level decision-making usually pos-sess some characters, e.g. complex nonlinearity, multi-levels and multi-types and limiteddata in limited time, since there are numerous entities, complicated interactive relationsand uncertain effect process. These characters make the complex in computation andanalysis more remarkable and require the development of simpler low-resolution models.
Recently, the study on metamodelling for high-level decision-making has become animportant research area. The motivated metamodelling, which primely aims at improv-ing the comprehensibility and interpretability, has exhibited to be the research hotspot.However, the analysis of current relevant research works shows that none of the regres-sion approaches combined with prior knowledge, including the motivated metamodellingin RAND and support vector regression, has the full ability to deal with the problems indecision-making with the main three characters. Thus there are cravings in studying anew motivated metamodelling method for M&S.
This dissertation is focused on solving the”complex in computation”and”complexin analysis”. A new motivated metamodelling method, which combined with classicalmotivated metamodelling and support vector regression, is proposed based on the charac-ters of the problems in decision-making and the analysis results about the existing regres-sion methods. Consequently, this dissertation expands its content in several correlativedirections, including theory of the new method, design methods of kernel function basedon prior knowledge, adaptive regression algorithm, etc. The original works include:
(1) Several key theoretic problems for the motivated metamodelling based on sup-port vector machines have been researched systemically. After analyzing the feasibilityand necessity of the new method, the dissertation presents a formal theoretic framework,classifies and summarizes the prior knowledge systemically. Based on the summary, thestructural design of metamodel is divided into two important parts, i.e. the design of thekernel function and the restrictions, and a new modelling framework, which consists offive sub-frameworks including structural design, simulation experiment, model genera- tion, evaluation and validation, application, is proposed.
(2) The second part is focused on the problem of designing kernel function, whoseworks include: 1) According to the disadvantage of the conventional kernel functions,which perform an equal treatment for all the input dimensions, and the advantage of theaforehand presence of the structural knowledge, a new kernel construction method basedon structural prior knowledge is presented. This method has studied the constructionof reproducing kernel based on direct sum and senor product with prior knowledge andthe systematic modeling process. 2) According to the disadvantage on using derivativeknowledge and the theoretic results on reproducing kernel and differential operator, an-other kernel construction method based on non-structural prior knowledge is proposed.It studied the computation method of reproducing kernel based on the Green’s functionsof three kinds of differential operator, i.e. differential operator with m-order, with m dif-ferent eigenvalues and simpler cases, and presented an automatic, flexible and rigorouscomputation algorithm. 3) According to the lack of theoretic evidence on the so-called”best”kernel of Gaussian kernel, the third kernel construction method based on static sce-nariopriorknowledgeisintroduced. Itfocusesonquantitativelyanalyzingandcomparingseveral kernels, including Gaussian kernel, two new reproducing kernels, and performingthe experiments using multiple criteria and synthetic problems. The results show that thereproducing kernel is an equivalent or even better kernel than RBF for the problems withmore input variables (more than 5, especially more than 10) and higher nonlinearity.
(3) The third part has studied the problems of designing the restrictions and trainingmodel. According to the disadvantages of standard support vector regression training al-gorithm, i.e. disadvantageinparameterselection, limitationinthegeneralizationcapacityon changeable data set, difficult in incorporating and evaluating the prior knowledge, anew regression algorithm, i.e. Adaptive Motivated Support Vector Regression (AMSVR)is presented. Based on the introduction of the function and realization of all the compo-nents in AMSVR, two important components are discussed in detail. Firstly, two kindsof designing and solving approaches of programming problem are presented. Secondly,a new training algorithm, i.e. approximation incremental algorithm that is hybrid withquick training algorithm and accurate incremental algorithm, is proposed.
(4)According to the application requirementin high-leveldecision-making analysis,the theory of this dissertation is demonstrated by an example of motivated metamodelling of radar system in the background of strategy missile breaking through NMD defensesystem simulation.
The main contributions of this dissertation include: a new motivated metamodellingmethod, i.e. motivated metamodelling based support vector machines, which combinedwith the classical motivated metamodelling of RAND and support vector regression, ispresented and the formal conceptual framework and modelling framework are summa-rized. Three different methods for constructing kernel function based on different ap-plication requirement and prior knowledge are proposed. According to the problems, i.e.parameterselection,generalizationabilityandknowledgeevaluation,anewtrainingalgo-rithm, i.e. Adaptive Motivated Support Vector Regression (AMSVR) is presented, whichemploys an improved genetic algorithm to solve the parameter selection and knowledgeevaluation and uses an approximation incremental algorithm to improve the generaliza-tion ability for a changeable experiment data set.
The research topics of this dissertation belong to the fundamental M&S theory andmachine learning categories. Above contributions can advance the system modelling andsimulation methodology, and promote the studies of multi-resolution, machine learning,data mining and experimental design in complex high-level decision-making analysis.
引文
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