Fourier frequency prediction of blasting vibration based on the probability theory

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (12) : 46-54.

DENG Bingjie1,2,3，WANG Linfeng1,4,5，LI Zhen1,3，LI Lingang1,4，MO Qu4,5

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Abstract

Taking the Fourier Principal Frequency as the research object, on the basis of summarizing the research status of the prediction of the principal frequency, a basic formula prediction model of the Fourier principal frequency was put forward, and the method of solving the parameters of the prediction model was given.This paper pointed out the deficiency of using the Regression Coefficient (R2)as the criterion for predicting the relative merits and demerits, and put forward that residual square sum(RSS) should be used as the criterion for predicting the relative merits and demerits.Based on the field data, the prediction results of six prediction models, which are Zhang Liguo’s formula, Meng Haili’s formula, and the basic formula proposed by this paper, the formula based on the spherical wave theory and the cylindrical wave theory proposed by Lu Wenbo, and Ye Hongyu formula, were compared.the measured data show that the RSS predicted by the basic formula presented in this paper is the smallest.Considering the randomness of blasting vibration, based on the basic formula prediction model proposed in this paper, the normal distribution theory was introduced to modify the main vibration frequency prediction model.On the basis of defining the relative error of the main frequency (REMVF), the distribution model of Fourier Principal Frequency about the detonation center distance (R) and the single maximum charge quantity (Q) was obtained, and the accuracy of the distribution model was verified by using the “3σ criterion”.According to the basic idea of “small probability event”, the confidence of both sides should be 95% is suggested.Then the possible range of Fourier Principal Frequency can be determined by the blasting parameters.

Key words

blasting vibration / Fourier principal frequency / principal frequency prediction mode / normal distribution / bilateral confidence level

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DENG Bingjie1,2,3，WANG Linfeng1,4,5，LI Zhen1,3，LI Lingang1,4，MO Qu4,5. Fourier frequency prediction of blasting vibration based on the probability theory[J]. Journal of Vibration and Shock, 2021, 40(12): 46-54

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