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Random Dynamic Load Decomposition Technique Based on Orthogonal Basis of Trigonometric Functions

A technology of random dynamics and trigonometric functions, applied in electrical digital data processing, special data processing applications, instruments, etc., can solve the problems of different accuracy and efficiency of Fredholm integral solution, achieve the effect of ensuring decomposition accuracy and improving decomposition efficiency

Active Publication Date: 2017-11-03
SOUTHEAST UNIV
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  • Application Information

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Problems solved by technology

However, when different basis functions are used, the solution accuracy and efficiency of the second kind of Fredholm integral will be quite different

Method used

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  • Random Dynamic Load Decomposition Technique Based on Orthogonal Basis of Trigonometric Functions
  • Random Dynamic Load Decomposition Technique Based on Orthogonal Basis of Trigonometric Functions
  • Random Dynamic Load Decomposition Technique Based on Orthogonal Basis of Trigonometric Functions

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Embodiment Construction

[0034] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments.

[0035] Taking the mean value as zero, the autocovariance as exponential form, the duration as 1s, and the random dynamic load as 1000 time steps as an example, adopt the random dynamic load decomposition technology based on trigonometric function orthogonal basis of the present invention to decompose, including the following steps:

[0036] Step 1: Determine the mean value μ(t) and the autocovariance matrix C(t) of the random dynamic load X(t) 1 ,t 2 ), as shown in formula (9) and formula (10):

[0037] μ(t)=0 (9)

[0038]

[0039] Step 2: Select the trigonometric function h k (t) Solve the second kind of Fredholm integral equation as an orthogonal basis to obtain the eigenvalue λ of the autocovariance matrix i and the eigenvector φ i (t) and the truncation number n of the eigenvalues, the specific steps are as follows:

[0040] 201. T...

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Abstract

The invention discloses a trigonometric function orthogonal basis-based random dynamic load decomposition technology. The technology comprises the following steps of: 1, determining a mean value and an auto-covariance matrix of a random dynamic load; 2, selecting a trigonometric function as orthogonal basis to solve a second type Fredholm integral equation, calculating an eigenvalue and an eigenvector of the auto-covariance matrix, and obtaining a truncation number of the eigenvalue; 3, decomposing the eigenvector of the auto-covariance matrix by adopting the orthogonal basis of the trigonometric function, and calculating a participation factor of the orthogonal factor; and 4, decomposing the random dynamic load on the basis of KL expansion. According to the technology disclosed by the invention, stationary decomposition and non-stationary decomposition can be carried out on the random dynamic load, and the decomposition efficiency can be improved on the basis of ensuring the decomposition precision.

Description

technical field [0001] The invention relates to the technical field of random dynamic load decomposition, in particular to a random dynamic load decomposition technology based on trigonometric function orthogonal basis. Background technique [0002] Engineering structures not only bear deterministic static loads and dynamic loads, but also bear uncertain random dynamic loads, such as atmospheric turbulence, noise, road unevenness, earthquake and wind loads, etc. Random dynamic loads can usually be divided into stationary random loads and non-stationary random loads. Most of the random excitations in engineering are non-stationary excitations, but in order to facilitate calculation and analysis, and also due to the limitations of calculation and analysis methods, non-stationary random excitations are often simplified into stationary random excitations. However, this simplification will affect the subsequent random Dynamic response analysis brings significant errors. [0003...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F19/00
CPCG16Z99/00
Inventor 李彦斌费庆国廖涛吴邵庆张鹏
Owner SOUTHEAST UNIV