Structural parameter correlation processing and reliability calculation method

Abstract

The invention provides a structural parameter correlation processing and reliability calculation method based on independent transformation and regression analysis. The method comprises the followingsteps: 1, determining random variables of a structure and sample points thereof or statistical characteristic parameters and correlation parameters; 2, in the step 1, if the sample points cannot be obtained, the sample points need to be generated according to the random variable distribution types and the corresponding statistical characteristic parameters; 3, selecting an optimal Copula functionaccording to the sample points and calculating Copula parameters and a joint probability density function between variables; 4, deducing a Hermite expansion formula of the structural response based ona random response surface method; 5, selecting a probability distribution point of which the undetermined coefficient is twice; 6, converting the collocation points by using Rosenblatt transform anda joint probability density function, and solving an undetermined coefficient based on a least square method; 7, solving the reliability of the structure by using a moment method or a Monte Carlo method. The method is scientific and good in manufacturability and has wide application and popularization value.

Description

technical field [0001] The invention provides a structural parameter correlation processing and reliability calculation method, which relates to a structural parameter correlation processing and reliability calculation method based on independent transformation and regression analysis, and belongs to the field of structural reliability calculation. Background technique [0002] In the first aspect, at present, the structural reliability analysis method is mainly based on the probabilistic method. The probabilistic method is based on the traditional stress intensity interference model, and many classic methods have been derived, such as the first order second moment method (First Order Second Moment, FOSM) , Second Order Second Moment (SOSM), JC method, Monte Carlo Method (MCM), etc. These methods generally rely on the statistical properties of random variables. It is worth noting that most of them It is assumed that the random variables are independent of each other and have...

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Problems solved by technology

[0004] The second aspect, in most of the current structural reliability modeling and analysis methods, the functional function is usually unknown, which brings difficulties to the structural reliability analysis, and different surrogate model methods can be used under different conditions and environments Fitting functional functions, so proxy model methods are often used to deal with the problem of implicit functional functions

[0010] From the analysis, we know that the above formula can be approximated to L 2 For any element in the space, the higher the expansion order, the smaller the approximation error, which theoretically ensures that the response surface function based on the Hermite chaotic polynomial can guarantee convergence in the sense of probability, while the traditional two Sub-polynomial response surface methods cannot achieve this

In addition, the traditional method for solving the undetermined coefficients of the random response surface method is the probability collocation method. Generally speaking, the number of collocation points that can be selected is far greater than the number of undetermined coefficients. For example, the number of random variables is n=5 , for the third-order Hermite chaotic polynomial, the number of optional matching points is M=(3+2) 5 =31, the number of undetermined coefficients is N=(5+3)! / (5! 3!)=56, and the selection of collocation points will directly affect the solution accuracy of the undetermined coefficients. In theory, the more collocation points are selected, the better the solution of the coefficients is, but too many collocation points are selected to solve the undetermined coefficients It will consume a lot of resources. Some studies suggest to select collocation points twice the coefficients of Hermite chaotic polynomials to solve the coefficients, so as to balance the influence of collocation points on the calculation results. However, the disadvantage of this method is that the selected collocation points may be linearly related, which not only cannot Improve the accuracy of calculations, but also waste computing resources

Some studies suggest that the principle of point selection is that the selected points can make the Hermite coefficient matrix row full rank. The disadvantage of this method is that it cannot balance the error caused by some points to the calculation results.

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