改进POT模型及其在边坡安全监测预警中的应用

基于极值理论的BMM(Block Maximum Method)和POT模型是近来分析边坡安全监测资料、评估边坡安全状况的新兴方法之一。相对简便的BMM模型在数据取样时往往忽略区间次极大值,在资料年限较短时样本容量偏小,可能导致所得结果误差较大。本文利用改进的Hill估计方法得到阈值,通过极大似然估计确定广义帕累托分布参数,从而利用超限数据序列来确定测值序列的整体分布,提出了改进POT(Modified Peaks over Threshold)模型,并应用于某边坡工程的安全监测预警指标分析。结果表明,在同一置信水平下利用超限值应用广义帕累托分布拟合得到的预警指标小于利用块极大值应用正态分布得到的预警指标,表明基于超限数据的改进POT模型得到的预警指标更能有效规避极端情况发生的风险,更有利于边坡安全监测和预警。

Modified POT model and its application in early-warning methods for slope safety monitoring

BMM model and POT model which based on extreme value theory are one of the newly-developing methods to assess the safety conditions of slope in recent years. The ignorant of secondary maximum points and the relatively small size of sample in the case of short-time data may lead to a big error in BMM model. A modified POT model was proposed in the paper to get the threshold with improved Hill estimator method and obtain the Pareto parameters with the maximum likelihood estimation so that the whole distribution could be determined. With the analysis of a slope engineering, the early-warning index which used the generalized Pareto distribution with the data exceeding the threshold was less than that using the normal distribution with the block maximum values in the case of same confidence level. It could be drawn from the results that the early-warning index based on modified POT model was more effective in slope safety monitoring, which could be made use of reducing the risk when extreme conditions happened.