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High-precision structure reliability analysis method based on three-weighted response surface

An analysis method and reliability technology, applied in manufacturing computing systems, instruments, electrical and digital data processing, etc., can solve problems such as errors, insufficient representativeness of sample points, and errors in calculation results.

Active Publication Date: 2020-06-19
BEIHANG UNIV
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Problems solved by technology

[0005] At present, there are the following problems in the research of weighted response surface method: (1) The sample points of weighted regression processing are not representative enough, and the selection strategy of sample points can be optimized and improved; (2) The calculation results may be caused by unreasonable interpolation coefficients. Large errors, or even wrong results; (3) After fitting the limit state function, there is a certain error in the solution using the traditional first-order second-order moment, and it can be considered to be mixed with other methods

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  • High-precision structure reliability analysis method based on three-weighted response surface
  • High-precision structure reliability analysis method based on three-weighted response surface
  • High-precision structure reliability analysis method based on three-weighted response surface

Examples

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example 1

[0069] Example 1 : The limit state equation of a structure is as follows:

[0070] g=exp(1+x 1 -x 2 )+exp(5-5x 1 -x 2 )-1=0

[0071] where x 1 and x 2 All obey the standard normal distribution, x 1 ~N(0,1),x 2 ~N(0,1).

[0072] Step 1: In this example, the random variable is x 1 and x 2 , the distribution type and parameters have been given, satisfy the normal distribution and are independent of each other, so normalization and variable conversion are not required.

[0073] The response surface function is

[0074] In the formula: b=(b 1 ,b 2 ,...,b 2n+1 ) T is the undetermined coefficient of the response surface function that needs to be determined by the sample points;

[0075] Step 2: Use the classical response surface method to perform the first iterative calculation to obtain the sampling center point x (1) =(3.8041,0.0013) T and reliability index β (1) =2.7515.

[0076] Step 3: Use the Bucher method to select the initial sample points for the next...

example 2

[0099]The calculation diagram of a cantilever beam with a rectangular section is shown in image 3 . The allowable maximum displacement of the right end of the cantilever beam is l is the span of the beam, and the limit state equation of the deflection at the free end of the cantilever beam is:

[0100]

[0101] In the formula, ω represents the uniform load density per unit area, which is a random variable; b is the section width; l is the span of the beam, l=6m; E is the elastic modulus of the material, E=2.6×10 4 MPa; I is the section moment of inertia, where h represents the section height and is a random variable. The random variables are independent of each other.

[0102] The sorted limit state equation can be written in the following form:

[0103]

[0104] where x 1 Denotes the load density ω, x 2 Indicates the height h of the cantilever beam. These two random variables are normal distributions independent of each other, and their statistical distributio...

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Abstract

The invention provides a high-precision structural reliability analysis method based on a three-weighted response surface. The method comprises the following steps: 1, determining a random variable and a response surface function form; 2, a classical response surface method is adopted for the first iteration; 3, in subsequent iteration, selecting an initial sample point by adopting a Bucher method, and calculating a true value of a limit state function; 4, selecting a newly added final sample point in the iteration by adopting a continuous interpolation method, and calculating a true value ofa limit state function of the final sample point; 5, constructing a regression matrix; 6, constructing a weight matrix; 7, solving an undetermined coefficient in the undetermined response surface function by using a weighted least square method; 8, calculating reliability indexes, checking calculation points and limit state function values of the checking calculation points by adopting an important sampling method; 9, calculating a new sampling center by adopting an interpolation method; tenthly, repeating the third step to the ninth step until the difference between the reliability indexes obtained through two times of iterative computation meets the precision requirement; the method is scientific and good in manufacturability and has wide application and popularization value.

Description

technical field [0001] The invention relates to a high-precision structural reliability analysis method based on a three-weighted response surface, and belongs to the technical field of structural reliability analysis. Background technique [0002] Structural reliability analysis is an important tool to study whether the structural design of the product meets the requirements of safety, reliability, economy and durability, and the safety of the product in operation. [0003] Structural reliability analysis generally has methods such as first-order second-order moment method, second-order second-order moment method, Monte Carlo method, and response surface method. For structural reliability analysis, the limit state function is implicit in most cases, and analytical methods such as the first-order second-order moment method and the second-order second-order moment method are no longer applicable. Although the Monte Carlo method can obtain an exact solution when the limit sta...

Claims

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Application Information

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IPC IPC(8): G06F30/10G06F119/02
CPCY02P90/30
Inventor 张建国吴洁叶楠
Owner BEIHANG UNIV
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