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First-order reliability analysis method based on KKT condition and differential evolution algorithm

A technology of differential evolution and analysis method, which is applied in the reliability analysis of differential evolution group intelligent optimization algorithm, the first-order second-order moment method is used to analyze the structural reliability, and in the field of effective reliability analysis model, it can solve the problem that the limit state function constraint loses its effect , Poor accuracy of reliability analysis results, slow convergence and other problems, to achieve the effects of extending validity and versatility, ensuring convergence and stability, and ensuring accuracy

Active Publication Date: 2021-09-03
JINAN UNIVERSITY
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Problems solved by technology

At present, there are swarm intelligent optimization algorithms such as particle swarm optimization for evaluating structural or product reliability problems. These methods are used as global optimization algorithms to avoid the situation of non-convergence, but the penalty function coefficient of the equivalent unconstrained optimization problem increases with the number of iteration steps It grows exponentially. For some cases where the function function changes at a slower speed during the iterative process and strong nonlinear problems, too fast growth may cause the limit state function constraints to lose their effect, resulting in a difference between the equivalent model and the original model. Large deviations, which in turn lead to problems such as poor accuracy of reliability analysis results and slow convergence

Method used

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  • First-order reliability analysis method based on KKT condition and differential evolution algorithm
  • First-order reliability analysis method based on KKT condition and differential evolution algorithm
  • First-order reliability analysis method based on KKT condition and differential evolution algorithm

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Embodiment 1

[0045] figure 1 It is a flow chart of a reliability analysis method based on KKT conditional equivalent reliability analysis model and differential evolution group intelligent optimization algorithm provided by this embodiment, including 7 steps in total. figure 2 It is a flow chart of the differential evolution group intelligent optimization algorithm. The operators in the adaptive mutation operation mechanism are dynamically adaptively adjusted according to the number of consecutive individual successes up to 15 times in the iterative process in the form of a triangular distribution. Embodiment 1 further illustrates the present invention with a 6-dimensional application example.

[0046] Step S1, designate the functional function g(x) of the structure to be analyzed, as follows:

[0047]

[0048] The random variable x of the functional function = [x 1 ,...,x i ,…] and their probability distribution information are as follows:

[0049] Table 1. Embodiment 1 random var...

Embodiment 2

[0058] This embodiment continues to disclose a reliability analysis method based on the equivalent reliability analysis model of the KKT condition and the intelligent optimization algorithm of the differential evolution group. The number of successes reaches 15 dynamic adaptive adjustments. The reliability analysis method includes the following steps:

[0059] Step S1, designate a master-slave two-degree-of-freedom dynamical system structure to be analyzed (such as Figure 4 The functional function g(x) of the shown schematic diagram) is as follows:

[0060]

[0061] g=F s -k s p[E(x s 2 )] 1 / 2

[0062] Among them, ω p =(k p / m p ) 0.5 , ω s =(k s / m s ) 0.5 , ω a =(ω p +ω s ) / 2, ζ a =(ζ p +ζ s ) / 2, v=m s / m p , η=(ω p -ω s ) / ω a , p=3. Random variable x of functional function = [m p , m s ,…] and their probability distribution information are shown in the following table:

[0063] Table 1. Embodiment 2 random variable characteristics

[0064] ...

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Abstract

The invention discloses a first-order reliability analysis method based on a KKT condition and a differential evolution algorithm, and the method comprises the steps of building an equivalent reliability analysis model of which penalty function parameters can be adaptively changed based on the KKT condition, so that the problems that an equivalent reliability analysis model with penalty function parameters in exponential growth is poor in analysis precision and low in calculation efficiency in strong nonlinear problems are solved; using an improved differential evolution optimization algorithm with a self-adaptive crossover operation mechanism for solving an equivalent structural element reliability analysis model, and then calculating the failure probability. When a first-order reliability method is used for evaluating the reliability and safety degree of complex engineering structures in the fields of civil engineering, mechanical engineering, aerospace and the like, the invention has good universality and adaptability, convergence is fast, and precision is high; the new penalty function coefficient determination mode in the equivalent reliability analysis model can avoid the problem of poor reliability analysis result precision caused by the premature local optimum of the most probable failure point search algorithm.

Description

technical field [0001] The present invention relates to the technical field of structural reliability analysis, in particular to the analysis of structural reliability using the first-order second-order moment method based on the swarm intelligence optimization algorithm, and in particular to an equivalent reliability analysis model based on KKT conditions and differential Reliability Analysis Method of Evolutionary Swarm Intelligence Optimization Algorithm. Background technique [0002] Structural reliability design and analysis methods are aimed at evaluating the reliability of normal working ability of structures or products (such as building structures, bridges, power systems, electronic products, etc.) in the fields of civil engineering, mechatronics, and aerospace. The load and so on are the structural function functions of the influencing factors, and the reliability of the structure is quantified on the basis of the functional functions. Compared with the traditiona...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/20G06N3/00G06F111/04G06F111/08G06F119/02
CPCG06F30/20G06N3/006G06F2111/04G06F2111/08G06F2119/02
Inventor 赵卫范宁
Owner JINAN UNIVERSITY
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