灰关联决策与灰生成算子的理论及方法研究
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摘要
公路隧道围岩稳定性分类与失稳预报工作是岩土工程中一门重要的学科.围岩稳定性分析是一个受多因素影响、随时空变异的复杂动态系统,其影响因素的显著特点是数据的多变性、参数的不确定性和数据的不完备性,将灰色系统这一处理少数据,贫信息的理论用在围岩稳定性分析的研究中是合理的.本文主要探讨灰关联决策中指标的选取技术,指标赋权技术,提出灰区间数关联度度量技术,研究灰生成算子属性及其作用下的灰色模型,并应用于围岩稳定性分类与失稳预报工作.
为展示国内外灰色系统理论研究和应用的最新动态,首先本文分别系统综述了灰色关联决策理论、灰生成算子、灰色模型等的最新研究成果以及这些研究成果在应用上的创新并进行了评述.
灰关联决策是灰色系统理论的基础和核心,也是目前灰色关联度应用最广泛的地方.本文首先量化研究基于灰色关联度的多指标决策中指标灵敏度的度量方法,给出度量指标,及其计算方法、属性,探讨了依据指标灵敏度选取多指标决策中合理指标的技术：如果决策指标较多,选取灵敏度较大的指标,剔除灵敏度较小的指标.其次研究灰关联序的稳定性问题：即权重的改变并不导致灰关联序的变化,建立寻求最均匀赋权和最不均匀赋权两类优化模型,采用搜索算法寻求灰关联序的稳定解,对于低维决策问题从几何的角度对赋权进行直观解释.提出了基于哈斯(HASSE)图技术的白化函数未知区间数排序技术,提出了一种新的区间型序列关联度计算方法；同时还研究了赋权哈斯图等技术,论文用实例证实了上述理论和技术的可行性与合理性.
灰生成直接影响灰预测模型的精度,也成为最近研究热点.本章以矩阵分析为主线,在矩阵体系里研究灰序列生成(缓冲算子、累加生成算子)的矩阵表示及其序列的差异信息,讨论灰生成影响灰预测模型精度的因素,推导灰序列生成与GM模型参数和预测值间的量化关系,进而从影响建模的外部机制上探讨灰生成的作用.具体包括经典弱化算子和强化算子的一阶算子、二阶及r阶算子的矩阵形式,任意两个不同阶算子作用下序列的关系及算子的主要属性：线性型、可逆性、压缩性、变换级比、光滑比,及其作用下的灰色GM(1,1)模型的矩阵形式；并研究了三种累加生成算子的凸性：一般的AGO生成,反向AGO生成,广义AGO生成等.
最后使用基于弱化算子的粒子群优化GM(1,1)幂模型实证研究了隧道围岩的位移变化,论文还研究了波动型灰色GM(1,1|tan(κ-т)p,sin(κ-т)p))模型及其在隧道拱顶下沉速率预报上的应用.
The stability classification and geotechnical instability forecasting for the highway tunnel surrounding rock are very important in the geotechnical engineering. Rock stability is a complex dynamic system affected by many factors, and varying with time and space, its distinguishing feature of the impact factors are the variability of the data, parameter uncertainty and incompleteness of the data. Grey system deal with less data, poor information problem, which is agreed with the feature of the surrounding rock. This paper discusses the indicators selection technology based on grey relational grade, indicators weighting technology, proposes grey interval number relational grade,and measurement techniques for the grey number, attributes for grey generating operator and the grey models applied on the rock classification and instability forecasting..
This paper firstly shows the latest research and application developments of the grey system theory in home and abroad, systematicly reviews the grey relational decision-making theory, grey generating operators, grey models.
Grey relational decision-making is the foundation and core of grey relational technology; it is the most widely used grey technology. Firstly, this part quantitative research the index sensitivity measurement methodology for multiple criteria decision making based on grey relational grade, calculation steps, and properties. According to the indicators sensitivity, we get indicators selecting techniques of multiple attribute decision-making: selecting more sensitivity indicators in the decision-making, excluding the smaller sensitivity indicators. Secondly, the stability of grey relational order is studied which means that weights change does not lead to the order change in grey relation order,paper construers two optimization models to seek the most evenness and the most unevenness weights, the search algorithm is used to seek all stability solutions. For low-dimensional decision-making, geometry methodology is used for visual interpretation. Interval number order is proposed on the HASSE diagram technology for whitening function is unknown interval sequencing, a new grey relational grade for interval grey number based HASSE diagram technology is proposed; also giving the weighting methodology based on HASSE diagram technology. Then the case studies confirm the feasibility and reasonableness of the above theory and the technical.
Grey generating operator affects the grey prediction accuracy of the grey model directly, which has become the latest research hotspot. The main line of this section is matrix analysis, including the matrix formulas of grey sequence generation (buffer operators, accumulated generating operators), the sequences differences information expressing, the accuracy factor of the prediction model, the relationship between the grey generation sequences and GM model parameters, the quantitative relationship between the predicted value. Then the paper investigates the role of grey generating from the modeling external mechanism. Matrix forms for buffer operator, including classic weakening and enhancing buffer operator are investigated, including first order, second order, and r-order operator buffer operators, the relationship between any two operators which have different orders, main operator properties:the linearity, reversible, compression, transforms level ratio, smoothness, and the matrix forms for grey GM (1,1) model; and study the convexity for three accumulated generating operator: General AGO generation, reverse AGO generation, generalized AGO generated.
Finally, GM (1,1) power model based on the weakening operator and the particle swarm optimization is used to forecast tunnel surrounding rock displacement; fluctuating grey GM (1,11 tan(κ-т)p,sin(κ-т)p)) model is used to forecast the tunnel vault sinking rate.
为展示国内外灰色系统理论研究和应用的最新动态,首先本文分别系统综述了灰色关联决策理论、灰生成算子、灰色模型等的最新研究成果以及这些研究成果在应用上的创新并进行了评述.
灰关联决策是灰色系统理论的基础和核心,也是目前灰色关联度应用最广泛的地方.本文首先量化研究基于灰色关联度的多指标决策中指标灵敏度的度量方法,给出度量指标,及其计算方法、属性,探讨了依据指标灵敏度选取多指标决策中合理指标的技术：如果决策指标较多,选取灵敏度较大的指标,剔除灵敏度较小的指标.其次研究灰关联序的稳定性问题：即权重的改变并不导致灰关联序的变化,建立寻求最均匀赋权和最不均匀赋权两类优化模型,采用搜索算法寻求灰关联序的稳定解,对于低维决策问题从几何的角度对赋权进行直观解释.提出了基于哈斯(HASSE)图技术的白化函数未知区间数排序技术,提出了一种新的区间型序列关联度计算方法；同时还研究了赋权哈斯图等技术,论文用实例证实了上述理论和技术的可行性与合理性.
灰生成直接影响灰预测模型的精度,也成为最近研究热点.本章以矩阵分析为主线,在矩阵体系里研究灰序列生成(缓冲算子、累加生成算子)的矩阵表示及其序列的差异信息,讨论灰生成影响灰预测模型精度的因素,推导灰序列生成与GM模型参数和预测值间的量化关系,进而从影响建模的外部机制上探讨灰生成的作用.具体包括经典弱化算子和强化算子的一阶算子、二阶及r阶算子的矩阵形式,任意两个不同阶算子作用下序列的关系及算子的主要属性：线性型、可逆性、压缩性、变换级比、光滑比,及其作用下的灰色GM(1,1)模型的矩阵形式；并研究了三种累加生成算子的凸性：一般的AGO生成,反向AGO生成,广义AGO生成等.
最后使用基于弱化算子的粒子群优化GM(1,1)幂模型实证研究了隧道围岩的位移变化,论文还研究了波动型灰色GM(1,1|tan(κ-т)p,sin(κ-т)p))模型及其在隧道拱顶下沉速率预报上的应用.
The stability classification and geotechnical instability forecasting for the highway tunnel surrounding rock are very important in the geotechnical engineering. Rock stability is a complex dynamic system affected by many factors, and varying with time and space, its distinguishing feature of the impact factors are the variability of the data, parameter uncertainty and incompleteness of the data. Grey system deal with less data, poor information problem, which is agreed with the feature of the surrounding rock. This paper discusses the indicators selection technology based on grey relational grade, indicators weighting technology, proposes grey interval number relational grade,and measurement techniques for the grey number, attributes for grey generating operator and the grey models applied on the rock classification and instability forecasting..
This paper firstly shows the latest research and application developments of the grey system theory in home and abroad, systematicly reviews the grey relational decision-making theory, grey generating operators, grey models.
Grey relational decision-making is the foundation and core of grey relational technology; it is the most widely used grey technology. Firstly, this part quantitative research the index sensitivity measurement methodology for multiple criteria decision making based on grey relational grade, calculation steps, and properties. According to the indicators sensitivity, we get indicators selecting techniques of multiple attribute decision-making: selecting more sensitivity indicators in the decision-making, excluding the smaller sensitivity indicators. Secondly, the stability of grey relational order is studied which means that weights change does not lead to the order change in grey relation order,paper construers two optimization models to seek the most evenness and the most unevenness weights, the search algorithm is used to seek all stability solutions. For low-dimensional decision-making, geometry methodology is used for visual interpretation. Interval number order is proposed on the HASSE diagram technology for whitening function is unknown interval sequencing, a new grey relational grade for interval grey number based HASSE diagram technology is proposed; also giving the weighting methodology based on HASSE diagram technology. Then the case studies confirm the feasibility and reasonableness of the above theory and the technical.
Grey generating operator affects the grey prediction accuracy of the grey model directly, which has become the latest research hotspot. The main line of this section is matrix analysis, including the matrix formulas of grey sequence generation (buffer operators, accumulated generating operators), the sequences differences information expressing, the accuracy factor of the prediction model, the relationship between the grey generation sequences and GM model parameters, the quantitative relationship between the predicted value. Then the paper investigates the role of grey generating from the modeling external mechanism. Matrix forms for buffer operator, including classic weakening and enhancing buffer operator are investigated, including first order, second order, and r-order operator buffer operators, the relationship between any two operators which have different orders, main operator properties:the linearity, reversible, compression, transforms level ratio, smoothness, and the matrix forms for grey GM (1,1) model; and study the convexity for three accumulated generating operator: General AGO generation, reverse AGO generation, generalized AGO generated.
Finally, GM (1,1) power model based on the weakening operator and the particle swarm optimization is used to forecast tunnel surrounding rock displacement; fluctuating grey GM (1,11 tan(κ-т)p,sin(κ-т)p)) model is used to forecast the tunnel vault sinking rate.
引文
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