Study On Motivated Metamodelling Based On Support Vector Machines

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.