A Method of Correlation Processing and Reliability Calculation of Structural Parameters

Abstract

The present invention provides a kind of structural parameter correlation processing and reliability calculation method based on independent transformation and regression analysis, the steps are as follows: 1, determine the random variable of structure and its sample point or statistical feature parameter and correlation parameter; 2, in step In 1, if the sample points cannot be obtained, it is necessary to generate sample points according to the distribution type of the random variable and the corresponding statistical characteristic parameters; 3. According to the sample points, select the optimal Copula function and calculate the Copula parameters and joint probability density functions between variables; 4 , Deduce the Hermite expansion of the structural response based on the stochastic response surface method; 5. Select the probability collocation point with twice the undetermined coefficient; 6. Use the Rosenblatt transformation and the joint probability density function to convert the collocation point and solve the undetermined coefficient based on the least square method; 7. The reliability of the structure is solved by the step-moment method or the Monte Carlo method; the method of the present invention is scientific, good in manufacturability, and has wide popularization and application 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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