【作者】 曾波；

【导师】 刘思峰；

【作者基本信息】 南京航空航天大学 ， 系统工程， 2012， 博士

【摘要】 灰色系统理论是研究和解决现实世界不确定性问题主要方法之一，灰色预测建模技术是灰色系统理论的重要组成部分，经过近30年的发展，灰色预测建模技术取得了可喜的研究成果，但作为一门新兴横断学科，其理论体系还有待于进一步丰富和完善。本文从建模思想的创新、建模对象的拓展、建模方法的改进、建模序列的优化等方面对灰色预测建模技术进行了深入研究，其主要成果包括以下几个方面。（1）基于区间灰数及其白化权函数所围成图形的几何重心，研究了区间灰数“核”的计算新方法，有效解决了传统方法仅能在“对称型”白化权函数条件下计算区间灰数“核”的不足，从而能够对基于“非对称型”三角形或梯形白化权函数的区间灰数“核”进行计算；另外，本文还通过面积法对传统区间灰数“灰度”的测度方法进行了拓展，拓展后的测度方法能够对各种白化权函数的区间灰数“灰度”进行计算。（2）针对既有灰色预测模型的建模对象仅局限于实数序列，尚难以构建面向区间灰数序列预测模型的缺陷，本文在区间灰数白化权函数未知及已知两种情况下，深入研究了基于区间灰数序列的灰色预测模型建模方法，详细探究了模型的建模思路、推导过程及建模步骤，从而将灰色预测模型的建模对象从实数序列延伸至区间灰数序列，丰富并完善了灰色预测模型的理论体系。（3）离散灰数是灰信息的一种重要表现形式，研究基于离散灰数序列的灰色预测模型具有重要价值。本文提出了标准离散灰数和灰单元格两个概念，按照离散灰数取值分布信息未知及已知两种情况，研究了基于离散灰数序列的灰色预测模型建模方法，详细讨论了模型的推导过程及建模步骤，从而将灰色预测模型的建模对象从实数序列延伸至离散灰数序列，拓展了灰色预测模型的应用范围。（4）传统灰色预测建模技术通过对满足灰指数规律的累加生成序列建立指数模型来实现对未知世界的预测；然而，当建模序列本身已具有近似非齐次指数特征时，累加生成反而会破坏建模序列的这种特征。本文通过近似非齐次指数增长序列的齐次性转换以及省略累加生成直接建模的方法，构建了基于近似非齐次指数增长序列的两类不同灰色预测模型，从而增强了灰色模型对此类特殊序列的预测能力。（5）针对振荡序列灰色预测模型的构建，已有的灰色波形预测建模技术不仅需要的数据量大，而且对超出已有数据取值范围的情况无能为力。本文通过构建序列的平滑算法以压缩振荡序列的振幅，提高建模序列的光滑度，从而构建适用于振荡序列的灰色预测模型，以提高灰色预测模型对振荡序列的模拟及预测精度。更多还原

【Abstract】 Grey system theory is one of the major methods for studying and solving uncertain problems of thepresent world, and modeling technologies of grey prediction is an important component of greysystem theory, undergoing30years’ development, it has obtained many encouraging researchachievements. However, as an emerging cross-discipline, its theory system is still expected to befurther enriched and perfected, based on this, the paper in-depth studied grey prediction modelingtechnologies from modeling thought innovation, modeling object expansion, modeling methodimprovement, modeling sequences optimization, etc, and the main achievements of this paper are asfollowing.⑴Based on the centre of geometric gravity encircled by interval grey number and whitenizationweight function,the new calculation method for the “kernel” of interval grey number is presented,which effectively figures out the deficiency of the traditional method that only can be used tocalculate the “kernel” of interval grey number on the condition of symmetric form Whitenizationweight function, in this way,the kernel of interval grey number of unsymmetricform triangle andtrapezoid Whitenization weight function can be calculated. Apart from this, the paper also expandsthe traditional measure methods for degree of grey of interval grey by acreage method, which can beused to calculate degree of grey of interval grey of a variety of whitenization weight function⑵With the limitations of current existing grey prediction models whose modeling objects areonly based on real number sequences and cannot build models for interval grey number sequence, thispaper in-depth researched the grey prediction modeling methods of interval and discussed detailedlythe modeling thought, derivation process and modeling steps. Consequently, the modeling objects ofgrey predction models extend to interval grey number sequence from real number sequence, and itenriches and perfects the theory system of grey prediction models.⑶Discrete grey number is an important manifestation of grey information, and it has a veryimportant significance to study a grey prediction model based on the sequence of discrete greynumber. This paper puts forward two concepts: standard discrete grey numbers and grey unit cells,and study the modeling methods of grey prediction model based on discrete grey number sequenceaccording to the case of the value distribution information of discrete grey number is known orunknown, introduces detailedly derivation process and modeling steps. Consequently, the modelingobjects of grey prediction models extend to discrete grey number sequence from real numbersequence and it expands the applied scope of grey prediction models.⑷Traditional grey prediction technologies establish exponent models based on accumulating generation sequence which satisfies the law of quasi-exponent, and accomplish predictions of theunknown world. However, when modeling sequence has alrealy the characteristic of approximatenonhomogeneous index, the procedure of accumulating generation maybe destroy this feature. Thispaper converts an approximate nonhomogeneous exponential growth sequence into a homogeneousone and a direct modeling method that omits the procedure of accumulating generation, through those,two different grey prediction models are built, and it enhances the prediction ability of grey models dowith such kind of specific sequences.⑸with oscillation sequence grey model’s build, the existing modeling technology of greywaveform prediction not only needs large amount of data but also cannot do such situation of beyondexisting data value range. This paper builds a smooth algorithm of oscillation sequence to compressits amplitude, and enhance the degree of smoothness of modeling sequence, after this, we canestablish a grey prediction model which is suitable for oscillation sequence, and it can improve thesimulation and forecast accuracy of grey prediction model of oscillation sequence.更多还原