Research On Probabilistic Uncertainty Correlation Propagation Method For Structures

Uncertainty of structural parameters generally exists in practical engineering problems.These uncertain parameters are not completely independent of each other,and often have correlations.The uncertainty and correlation of structural parameters will cause the uncertainty of the system response.Therefore,the development of an effective and reliable uncertainty propagation method that considers the correlation,and accurately analyzes the uncertainty of the random response is beneficial to improve reliability.The accuracy of the analysis.Based on the Nataf transform and the Copula function,this paper carries out the study of the random uncertainty propagation method considering the correlation,and proposes the multi-level uncertainty propagation method considering the parameter correlation,and applies it to the uncertainty design of the aircraft load.The research content of this article consists of the following parts:(1)In the case of deriving ?-PDF to measure the distribution of random variables,the numerical solution method is used to solve the problem of difficulty in calculating the correlation coefficient in the Nataf transformation process.According to the Nataf transformation,the relationship between the space of related random variables and the independent standard normal space is established.Sampling is carried out in an independent standard normal space,the sample of the relevant random variable is obtained through the Nataf inverse transformation,and then the sample response is obtained by bringing it into the system.The polynomial structure selection technique based on the error reduction ratio is used to expand the system response to a polynomial chaotic expansion,and the optimal Hermite polynomial model is obtained.Using the weighted orthogonal characteristic of the Hermite polynomial when the weight function is a standard normal distribution,the coefficients of the polynomial are analyzed to obtain the moment information of the random response of the system.The probability density function of the random response of the system is obtained by the principle of maximum entropy,and the uncertainty propagation method considering linear correlation is realized.(2)Combining the Copula function and the direct probability integration method,the uncertainty propagation method considering nonlinear correlation is realized.In the case of non-linear correlation between random variables,the Copula function is used to measure the non-linear correlation between variables.Based on the inverse function of the conditional distribution of the Copula function,the point selection method based on the generalized F deviation is improved,so that the selected representative points are distributed in the position with greater probability density.According to the joint probability density function fitted by the Copula function and the Voronoi unit division technique,the concentration probability of the representative point is calculated.Then based on the probability direct integration method,the probability density function of the random response of the system is obtained.(3)In order to solve the uncertainty propagation problem of multiple systems,a multi-level uncertainty propagation method considering the correlation is proposed and applied to the uncertainty design of the aircraft load.The uncertainty analysis problem of aircraft load is simplified to a series of two-level uncertainty propagation problem.The first level adopts the uncertainty propagation method based on Nataf transform and orthogonal polynomial chaotic expansion.Obtain the probability distribution function of the first-level output variable,and get its sample at the same time.Then fit the high-dimensional complexity correlation of the first-level output variables based on the D vine Copula function.In the second-level propagation,samples of the second-level input variables are drawn according to the inverse function of the conditional distribution and the inverse function of the marginal distribution of the Copula function.Then the uncertainty propagation is carried out based on the Monte Carlo simulation method,and the probability density function of the flight load is obtained.