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

A technology of differential evolution and analysis method, which applies in-effective reliability analysis model, reliability analysis of differential evolution group intelligent optimization algorithm, and first-order second-order moment method to analyze structural reliability, which can solve slow convergence and reliability analysis Problems such as poor result accuracy and loss of limit state function constraints have achieved the effects of ensuring accuracy, extending validity and versatility, and ensuring convergence and stability.

Active Publication Date: 2022-08-09
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 This is a flow chart of a reliability analysis method based on the KKT conditional equivalent reliability analysis model and the differential evolution group intelligent optimization algorithm provided by this embodiment, and includes 7 steps in total. figure 2 This is the flow chart of the intelligent optimization algorithm of differential evolution swarms. The operators in the adaptive mutation operation mechanism are in the form of triangular distribution in the iterative process, and the number of consecutive successes of individuals reaches 15 dynamic adaptive adjustments. The present embodiment 1 further illustrates the present invention with a 6-dimensional application example.

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

[0047]

[0048] Random variable of function function x = [x 1 ,…,x i ,…] and its probability distribution information as follows:

[0049] Table 1. Random variable characte...

Embodiment 2

[0058] This embodiment continues to disclose a reliability analysis method based on the KKT conditional equivalent reliability analysis model and the differential evolution swarm intelligent optimization algorithm. The operators in the adaptive mutation operation mechanism are in the form of triangular distribution. The number of successful dynamic adaptive adjustments reaches 15 times, and the reliability analysis method includes the following steps:

[0059] Step S1, specify a master-slave two-degree-of-freedom dynamic system structure to be analyzed (such as Figure 4 The functional function g(x) of the schematic diagram shown) 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, ξ a =(ξ p +ζ s ) / 2, v=m s / m p , η=(ω p -ω s ) / ω a , p=3. Random variable x=[m for function function p , m s , …] and its probability distribution information as follows:

...

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Abstract

The invention discloses a first-order reliability analysis method based on KKT conditions and differential evolution algorithm. The method establishes an equivalent reliability analysis model in which penalty function parameters can be adaptively changed based on KKT conditions, so as to improve the performance of penalty function parameters. The exponentially growing equivalent reliability analysis model is used to analyze the problems of poor accuracy and low computational efficiency in strong nonlinear problems; an improved differential evolution optimization algorithm with an adaptive crossover operation mechanism is used to solve the equivalent structural element reliability analysis model, and then calculate the probability of failure. The invention has good versatility and adaptability when using the first-order reliability method to evaluate the reliability and safety of complex engineering structures in the fields of civil engineering, mechanical engineering, aerospace and other fields, and has fast convergence, high precision, and equivalent reliability analysis. The new penalty function coefficient determination method in the model can avoid the problem of the most likely failure point search algorithm falling into the local optimum prematurely, resulting in poor reliability analysis results.

Description

technical field [0001] The invention relates to the technical field of structural reliability analysis, in particular to the analysis of structural reliability using a first-order second moment method based on a swarm intelligence optimization algorithm, in particular to an equivalent reliability analysis model based on KKT conditions and a differential Reliability analysis method of evolutionary swarm intelligent optimization algorithm. Background technique [0002] The structural reliability design and analysis method aims to evaluate the reliability of the 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 is the structural function function of the influencing factors, and the reliability of the structure is quantified on the basis of the function function. Compared with the traditional deterministic analysis method, it ...

Claims

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Application Information

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Patent Type & Authority Patents(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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