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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。
BMM (Block Maximum Method) and POT model based on the extremum theory are one of the emerging methods to analyze the slope safety monitoring data and evaluate the slope safety status recently. The relatively simple BMM model often neglects the interval submaximating in the data sampling. When the data life is short, the sample size is too small, which may result in larger error of the obtained result. In this paper, the improved Hill estimation method is used to get the threshold, and the generalized Pareto distribution parameters are determined by the maximum likelihood estimation, so that the over-limit data sequence is used to determine the whole distribution of the measurement sequence. An improved PTS (Modified Peaks over Threshold) , And applied to the safety monitoring and warning index analysis of a slope project. The results show that the warning index obtained by applying the generalized Pareto distribution fitting with the over-limit value under the same confidence level is smaller than that obtained by applying the normal distribution using the block maximum value, indicating that the improved POT model based on the over-limit data Early warning indicators can effectively avoid the risk of extreme conditions, but also conducive to slope safety monitoring and early warning.