Research On Crack Probability Distribution Model Of Sphere Tank Based On Bayes Theory

Sphere tanks arepressure-bearing special equipment,which arewidely used in the production of petroleum,chemical,machinery,metallurgy,light industry,aviation,aerospace and other industrial field.Due to the ultra high temperature and strong corrosive environment,the crack defects are produced in the sphere tank.The expansion of cracks couldcause safety problems such as leakage and explosion,resulting in fires,air pollution and so on.Therefore,the safety of sphere tanks is vitalto social production activities andhealth of people.It is still difficult to obtain accurate probability of failureby a non-destructivemethod.The crack distribution of sphere tanks is an important input condition for the reliability analysis of spherical tanks.Therefore,based on crack size and number of cracks and Bayes estimation,aprobability distribution model of sphere tank crack is proposed.The posterior estimation for parameters of the model is carried out to simulate the distribution of cracks Bayesian theory is used to comprehensively consider the crack size,crack detection rate,measurement error,crack number and other uncertain factors of the spherical tank by non-destructive methods.The probability and statistical distribution model is constructed,which is suitable for the failure analysis of spherical tanks.In order to obtainthe structural foundation of the spherical tank,the crack position variable is taken into the probability distribution model,under multivariables.Through the MCMC framework,the parameter estimation method and flow of the proposed probability distribution model are established and veridied by Gibbs sampling and M-H algorithm,and verified.Comparing the prior distribution and the posterior distribution of the distribution parameters,it could be observed that the dispersion of the distribution parameters is significantly decreased.the crack size distribution of the spherical tank was statistically analyzed by the in-service test data obtained from the Special Equipment Inspection Institute,including crack size,quantity,position and repair rate.The statistical results show that the lower ring cracks are common produced in various spherical tanks,and the number of cracks accounts for 68.5%,which is the most prone to cracks;most of the cracks are mainly distributed within 10mm,accounting for 67.1% of the total;crack distribution Intensive position,the repair rate is relatively higher,and the repair rate of the lower ring seam is 27.9%.According to the crack statistics of a single spherical tank,owing to the influence of the crack detection rate and the superparameter of the measurement error on the parameter estimation,the parameter sensitivity analysis is also carried out.Combined with the crack position distribution function,the crack position distribution of the spherical tank surface is simulated.Through the theoretical research and analysis,this paper proposes a sphere tank distribution probability distribution model based on Bayes estimation.On the other hand,the process of posterior estimation of model parameters is taken into the model by MCMC method.The distribution of crack position of sphere tank is also simulated by MATLAB.This study provides the necessary input condition for the reliability analysis of sphere tanks,and has certain reference value for engineering practice.