Polynomial Probabilistic Transformation Models And Its Applications In Simulation Of Non-Gaussian Stochastic Processes

When considering structural safety problems,random variables are often non-normally distributed,such as temperature effects,earthquake effects,member resistance,and other random variables do not satisfy the standard normal space.This paper discusses how to deal with and describe the statistical properties of non-normal random distributions in nature,i.e.,to establish the relationship between non-normal target random variables and known normal distributions or other distributions using transformation models,in order to accurately represent the unknown target distributions with certain specific distributions.Based on the current state of research on traditional probability transformation model methods,two new polynomial probability transformation models are proposed in this paper,aiming to improve the flexibility as well as the accuracy of probability distribution models.The proposed polynomial probability transformation models are both flexible and convenient,and can be used in non-intrusive structural reliability analysis methods as well as to describe the non-Gaussian properties of the target distribution in non-Gaussian stochastic process simulations.The main research work of this paper is as follows.(1)A flexible adaptive polynomial transformation model based on skewed normal distribution is proposed.The greatest advantage of the proposed method is that it combines the advantages of skew-normal distribution and polynomial model.The skew-normal distribution is first used to do a preliminary fit to the target distribution,and then the polynomial transformation model is used to fit and calibrate the specified SND distribution again.Because some statistical information of the unknown distribution,such as skewed normal information,is processed and characterized in the initial fitting stage,the problem of limited application of the direct use of the polynomial transformation model can be avoided.At the same time,using the polynomial model to fit the initial SND again can significantly improve the fitting accuracy to the target distribution,especially the tail accuracy which is of interest in structural reliability analysis.(2)Based on the proposed adaptive skew-normal transformation model,a reliability method for reconstructing the LSF distribution is developed for solving reliability problems with small failure probabilities from low to high dimensional random inputs.The results of static and dynamic numerical calculations show that the proposed method can obtain high computational accuracy at low computational cost and outperforms FORM,IS and SS in terms of accuracy and efficiency for reliability analysis of rare events.(3)An improved fifth-order polynomial transformation model is proposed for the simulation of smooth non-Gaussian stochastic processes.The model extends the traditional third-order Hermite polynomial model in the field of stochastic process simulation to the fifth order and introduces the principle of probability weight moment matching to solve the unknown parameters of the polynomial model,which reduces the computational cost of converting Gaussian processes to non-Gaussian processes and obtains higher flexibility and fitting accuracy.At the same time,the inverse transformation relationship between the correlation function of the non-Gaussian process and the intermediate virtual Gaussian process is directly obtained by means of polynomial curve fitting,which decouples the transformation process of the correlation function from time and frequency and reduces the computational cost of the transformation of the correlation function.(4)By studying the non-Gaussian pulsating wind field of a large-span mesh-shell structure and the structural reliability analysis problem,the whole process of numerical simulation from structural load simulation to structural finite element analysis and structural reliability calculation is made for a large structure of actual engineering scale.