岩爆是一种极易发生在深埋地下工程岩体开挖过程中的一种动力失稳现象，具有突发性、不确定性和强破坏性等特征，开展岩爆烈度分级预测研究已成为一项需要迫切解决的世界性难题。岩爆烈度分级预测是一个典型的多属性有序分割问题，采用属性区间识别理论建立预测模型。根据岩爆的成因及特点，从岩石物理力学性质、岩体完整性和地应力3个方面选取围岩最大切向应力与岩石单轴抗压强度比、岩石单轴抗压强度与抗拉强度比、弹性变形能指数和岩体完整性系数作为岩爆烈度分级预测的评价指标。应用层次分析法和反熵权法分别确定评价指标的主观权重和客观权重，克服了传统熵权法在确定评价指标客观权重时对指标差异度敏感性较大的问题，并在此基础上，提出一种基于离差平方和的最优组合赋权规则，建立了岩爆烈度分级预测的最优组合赋权-属性区间识别模型。以国内外12组典型岩爆工程实例对所建模型进行检验，由于均化系数对模型的预测性能影响较大，为了选取最优的均化系数，使其在区间[0.05,0.95]内变化，步长为0.1，经分析，当均化系数取0.05和0.15时模型的预测准确率最高，达91.7%。将均化系数取0.15时，模型的预测结果与模糊综合评判法、灰评估模型的预测结果以及实际情况进行对比，验证了该模型的可行性与适用性。

Rockburst is a kind of dynamic instability phenomenon that easily occurs in the excavation process of deep underground engineering.It has the characteristics of suddenness,uncertainty and strong destructiveness.The research on the classification and prediction of rockburst intensity has become a worldwide problem that needs urgent solution.Due to the classification and prediction of rockburst intensity is a typical multi attribute ordered segmentation problem,the prediction model is established by using attribute interval recognition theory.Considering the causes of rockburst and its characteristics,the ratio of the maximum tangential stress of surrounding rock to the uniaxial compressive strength of rock,the ratio of the uniaxial compressive strength to the tensile strength of rock,the elastic strain energy index,and the intactness index of rock mass are selected as the evaluation indexes from the aspects of physical and mechanical properties of rock,rock mass integrity and in situ stress.The subjective weight and objective weight of these evaluation indexes are determined by the analytic hierarchy process (AHP) and antientropy weight method respectively,overcoming the problem that the traditional entropy weight method is sensitive to the index difference when determining the objective weight,and based on which,an optimal combined weighting rule on the basis of the sum of squares of deviations is proposed.Further,the optimal combined weighting-attribute interval recognition model for the classification and prediction of rockburst intensity is established.12 groups of typical rockburst engineering cases are chosen to test the proposed model.Since the averaging coefficient has a great influence on the prediction performance of the model,in order to select the optimal averaging coefficient,it is changed within the interval[0.05,0.95] and the step size is 0.1.After the analysis,it is found that when the averaging coefficient is 0.05 and 0.15,the prediction accuracy of the model is the highest,reaching 91.7%.Finally,the prediction result with averaging coefficient being 0.15 is showed and compared with the fuzzy comprehensive evaluation method,the grey evaluation model and the actual situations,which indicates that the proposed model in this paper is feasible and applicable.

1 属性区间识别模型

    1.1 属性测度区间的计算

    1.2 属性测度的计算

    1.3 评价对象等级识别

2 组合赋权

    2.1 层次分析法

    2.2 反熵权法

    2.3 基于离差平方和的最优组合赋权

3 岩爆烈度分级预测模型

    3.1 模型框架

    3.2 评价指标体系的确定

    3.3 原始工程数据及预处理

    3.4 组合权重的确定

    3.5 模型检验

4 结论