Assessment Of Earthquake Casualties Based On Chebyshev Inequality

The assessment of casualties of earthquake victims is an important reference basis for carrying out seismic fortification work before the earthquake and emergency rescue work after the earthquake.As an important part of earthquake risk assessment,it is of great significance to carry out earthquake casualties assessment.According to the summary of the current situation of earthquake casualty assessment methods,the current assessment methods for earthquake casualties are divided into two categories on the basis of the expression of their assessment results,including the expected value of earthquake casualties and the results of the probability-based casualty assessment of earthquakes.However,the above two categories can not fully describe the uncertainty of earthquake damage loss assessment in the expression of results.Based on the strong uncertainty of the actual damage performance of buildings in the earthquake,the former can only give the evaluation result of the expected value of earthquake casualties,which is very insufficient in the description of the uncertainty of casualties by a single expected value evaluation result.Although the latter can give a certain uncertainty probability evaluation result for earthquake casualties,But it often reflects not the main factor of building damage.Therefore,the limitation of variation range of uncertainty of building structure of earthquake damage that is completed by the use of Chebyshev inequality,and gives the variation function of the seismic casualty assessment results.The Monte Carlo method is used to simulate the casualties of earthquake victims,and the casualty function obtained by the empirical method is compared and analyzed,so as to give the corrective relations of the related parameters of the casualty function.The convolution theory is used to solve the joint probability distribution of various building structures under different earthquakes,so as to give the earthquake casualties function of the region and the city.At the same time,the applicability of the evaluation method is compared and analyzed with an example.The paper mainly completed the following tasks:1.The limitation of variation range of uncertainty of building structure of earthquake damage that is completed by the use of Chebyshev inequality and on the basis of the vulnerability of building structure combines with the occupancy rate and the casualty rate of building structure with different damage degrees to obtain the maximum and minimum casualties.Then,the average value of the maximum and minimum values of casualties is taken as the mean value through the empirical method,and the standard deviation is obtained on the premise that the difference between the normal distribution function and the mean value is 3 times to form a confidence interval of about 99.7%,thereby showing the probability density function of earthquake casualties.2.Monte Carlo method is used to simulate the casualties caused by earthquakes to get the probability density function of earthquake casualties,which is compared with the earthquake casualties obtained by the empirical method to reveal the modified relationship of the relevant parameters of the probability density function of earthquake casualties based on the empirical method.3.Based on the convolution theory,the joint probability density distribution of earthquake casualties of various structural types is calculated.The log-normal probability density function of earthquake casualties in a region or city is given.The applicability of the method is compared and analyzed with an example.