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耦合拐点偏移修正的Boltzmann函数预计模型及其参数反演方法

Boltzmann function prediction model coupled with the correction of inflection point offset and its parameter inversion method

  • 摘要: 针对常规概率积分法应用于矿山开采沉陷预计的不足,为了进一步提高沉陷预计的准确性和可靠性,开展了耦合拐点偏移修正的Boltzmann函数预计模型及其参数反演方法研究。基于Boltzmann函数,通过探讨拐点偏移修正方法,构建了耦合拐点偏移修正的Boltzmann函数预计模型;为了准确可靠地求取模型参数,引入FWA (Fireworks Algorithm),提出了耦合拐点偏移修正的Boltzmann函数模型参数反演方法(BFWA-MSPP)。仿真试验结果表明,BFWA-MSPP反演参数的平均相对误差约为2.1%,平均中误差为2.3,预计拟合下沉和水平移动误差为-11.6~5.7 mm,中误差为±6.1 mm;另外,抗差试验表明,在观测值中加入大量的随机误差和粗差后,BFWA-MSPP能够较为准确地反演模型参数,在一定程度上削弱了观测误差的影响。将BFWAMSPP和PIM-MSPP (基于概率积分法模型的求参方法)分别应用在顾桥煤矿1414(1)工作面,预计拟合下沉和水平移动中误差分别为±83 mm和±108 mm,BFWA-MSPP求参结果为:q=1.07,tan β=1.91,b=0.41,θ=88.32°,S1=-18.89 m,S2=14.74 m,S3=48.89 m,S4=64.42 m。

     

    Abstract: In order to further improve the accuracy and reliability of mining subsidence prediction,a Boltzmann function prediction model coupled with the correction of inflection point offset and its parameter inversion method were carried out. Based on Boltzmann function,a Boltzmann function prediction model coupled with the correction of inflection point offset was constructed by discussing the correction method of inflection point offset. In order to obtain the model parameters accurately and reliably,the FWA was introduced,a parameter inversion method of Boltzmann function prediction model coupled with the correction of inflection point offset (BFWA-MSPP) was proposed. The results of the simulation experiment show that the average relative error of thesolved parameters by BFWA-MSPP was approximately 2.1%,with 2.3 of average RMSE of the solved parameters,and the error of the fitting subsidence and horizontal movement were between -11.6~5.7 mm,with ±6.1 mmof average RMSE. In addition,after adding a large number of random errors and gross errors to the observations,BFWA-MSPP can inverted model parameters more accurately,which weaken the influence of observation errors to a certain extent. The BFWA-MSPP and PIM-MSPP were applied to the inversion prediction parametersof the 1414(1) working face of Guqiao Coal Mine respectively. The RMSE of fitting the subsidence andhorizontal movement were ±83 mm and ±108 mm,respectively,and the result of the solved parameters by BFWAMSPP was as follow:q=1.07,tan β=1.91,b=0.41,θ=88.32°,S1=-18.89 m,S2=14.74 m,S3=48.89 m,S4=64.42 m.

     

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