基于修正D-S证据理论的锚杆承载力预测方法研究

锚杆极限承载力的准确预测是承载力预测中最重要的部分。传统的方法经常借助于拉拔试验中锚杆系统处于弹塑性阶段的试验数据进行预测，但实际上弹性和弹塑性阶段区分得不太明显，且实际锚杆荷载-位移（P-S）曲线形状多种多样，故使用单一预测模型不能够对锚杆极限承载力破坏值进行准确预测。针对预测锚杆极限承载力破坏值属于不确定问题，引入组合模型思想，借助被广泛使用在多传感器信息融合中的Dempster-Shafer(简称D-S)证据理论融合算法来建立组合预测模型。该方法是将互不相容的基本命题（假定）组成的完备集合表示对某一问题的所有可能答案，并为各命题分配信任程度，使用D-S合并规则计算同一命题下各个证据体共同作用产生的反映融合信息的新证据体的信任程度，分析各命题产生新证据体的信任程度来确定“不确定问题”的答案。通过减少弹性阶段数据使每个参加组合的预测模型产生多个预测值，将每个预测值都视为一个证据体，在同一鉴别框架下，把同类型、不同特征的证据体按照D-S合并规则合并成一个新的证据体，再根据决策规则得到最终的判定结果。将D-S方法与直接求取算术平均值的方法进行对比，结果表明：使用D-S方法得到的预测值较准确；由于预测值受给定初值影响较大，故对原有预测方法进行修正，修正后预测方法的预测效果更好，预测精度更高，适用范围更广。该研究成果可用于矿山、地下工程等施工过程，以及后续质量检测、稳定性评价、岩体强度预测等方面。

A method for predicting bearing capacity of anchor bolt based on modified D-S evidence theory

Predicting the ultimate bearing capacity of anchor bolt is the most important part in the bearing capacity prediction of the anchor bolt. In traditional methods, the elastoplastic stage experimental data are usually from pull-out tests on anchor bolts used to predict bearing capacity. However, in practice, it is not easy to discriminate the elastic stage from elastoplastic stage, and additionally the actual P-S curves usually have various shapes. Thus, the single model is difficult to accurately predict all kinds of anchor bolts ultimate bearing capacity. Since the prediction of ultimate bearing capacity belongs to an uncertain problem, a combined forecasting model is developed with the Dempster-Shafer(D-S) evidence theory fusion algorithm that is widely used in the multi-sensor information fusion. The D-S theory is an efficient method to process uncertain incomplete and vague information in data fusion. The aim of the management of uncertainty in a system is to reach the best approximation. The D-S algorithm firstly employs a complete set consisting incompatible basic hypothesis to represent all possibilities, and assigns the basic possibility of confidence. Then, the D-S combination rules is applied to calculate the confidence of the new evidence body reflecting the combination of information produced by the same proposition with various evidence. Finally, the best approximation of the "uncertainty" will be determined by analyzing the confidence of new evidence body generated by each proposition. This paper, by reducing the elastic phase data, enables each prediction model participating in combination generate many predicted values, and then supposes each predicted value as an evidence, with the same identification framework. Moreover, it combines the evidence with the same type but different characteristics into a new evidence accordance with the D-S combination rules, and obtains the final prediction results according to the decision rules. Comparing the D-S method with traditional arithmetic mean method, the results show that the prediction accuracy using the D-S method is more accurate. As the prediction values are easily influenced by the given initial value, the modified prediction method in this paper shows that the modified method has higher precision. The results can be used for mine construction, underground construction, subsequent quality testing, stability evaluation and rock strength prediction.