Study On The Theory And Technique For Grey Relation Decision-making And Grey Generating Operator

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(?-?)p,sin(?-?)p)) model is used to forecast the tunnel vault sinking rate.