Transcendental Probability Analysis Of Wiener Process Based On Monte Carlo Simulation

It is very difficult to solve the transcendental probability of Wiener process analytically.Therefore,based on the Monte Carlo simulation method,this paper studies the Wiener process beyond the security limit,including the first transcendence problem and the multiple transcendence problem.Monte Carlo simulation method makes use of high speed electronic computer to carry out a large number of repeated random sampling simulations by programming,which simplifies complex problems and obtains high precision probability solutions.Monte Carlo simulation method provides a reliable test method for the reliability analysis results of practical engineering products.This method is also often used to verify the analytical solutions derived from the theoretical derivation.In this paper,the basic theory of Monte Carlo simulation method is introduced,and the generating methods of random numbers and several important sampling methods are summarized.Then,based on the characteristics of incremental Wiener process from normal distribution,a simulation program of Wiener process sample function is developed,and a large number of sample curves of Wiener process are simulated.Based on the simulation program,the failure probability calculation code,the limit value code and the condition judgment statement are added,and the first super-probability calculation program of the Wiener process based on Monte Carlo simulation method is developed.By calculating the failure probability of concrete structure within 100 years,the correctness of the analytical formula for the first superprobability of Wiener process is verified.Finally,the multiple transcendence problem of Wiener process is analyzed.10000 groups of Wiener process sample functions are obtained by simulation,and the crossing times of each sample function are counted,and then the crossing number data are fitted and analyzed.The probability distribution of the passing times of Wiener process is obtained.This method can simulate the Wiener process with different statistical parameters.By knowing the variance,the limit value and the time interval,the first superprobability can be calculated automatically by the computer.The accuracy of the calculation is high enough to approach the true value.Therefore,the transcendental probability analysis of Wiener process based on Monte Carlo simulation method and its simulation program are of practical value.