Random Dynamic Load Decomposition Technique Based on Orthogonal Basis of Piecewise Constant Functions
A stochastic dynamic, orthogonal basis technology, applied in the direction of electrical digital data processing, special data processing applications, instruments, etc., can solve the problems of autocovariance function with negative eigenvalues and infinity, so as to ensure the decomposition accuracy and improve The effect of decomposition efficiency
Active Publication Date: 2017-11-03
SOUTHEAST UNIV
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If the selected basis function is inappropriate, there may be cases where the eigenvalues of the autocovariance function are negative or infinite
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[0031] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments.
[0032] Taking the random dynamic load with zero mean and Bezier form as an example, the number of load steps is 1000, and the load duration is 1s. Adopt the random dynamic load decomposition technology decomposition based on piecewise constant function orthogonal basis of the present invention, comprise the following steps:
[0033] 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 (8) and formula (9):
[0034] μ(t)=0 (8)
[0035]
[0036] Among them, J 0 Represents a Bessel function of the first kind of order 0;
[0037] Step 2: Select the piecewise constant function h k (t) Solving the Fredholm integral equation of the second type as an orthogonal basis to obtain the eigenvalues and eigenvectors of the autocovariance matrix and the truncation numb...
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This invention discloses a decomposition technique of random dynamic load based on orthogonal basis of piecewise constant function. The decomposition technique comprises the following steps: 1, determining an average value and an auto-covariance matrix of the random dynamic load; 2, selecting the piecewise constant function as the orthogonal basis to solve second kind Fredholm equation, calculating a characteristic value and a characteristic vector of the auto-covariance matrix and acquiring the truncation number of the characteristic value; 3, decomposing the characteristic vector of the auto-covariance matrix through using the orthogonal basis of piecewise constant function, and calculating participation factors of the orthogonal basis; 4, and decomposing the random dynamic load based on KL expansion. By adoption of the method, steady and unsteady random dynamic loads can be decomposed; and the method can improve the decomposition efficiency 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 a piecewise constant function orthogonal basis. Background technique [0002] Random dynamic loads are common loads in engineering structures, such as wind loads, earthquakes, atmospheric turbulence, aerodynamic noise, engine noise, etc. At the same time, most of the random dynamic loads in engineering are non-stationary, but in order to facilitate calculation and analysis, and because of the limitations of non-stationary random dynamic response analysis methods, non-stationary random dynamic loads are often simplified into stationary random dynamic loads. The simplification of the method will bring non-negligible errors to the subsequent random motion response prediction. [0003] At present, in order to facilitate random dynamic response analysis, especially non-stationary random dynamic response...
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IPC IPC(8): G06F19/00
CPCG16Z99/00
Inventor 李彦斌费庆国廖涛吴邵庆陈强
Owner SOUTHEAST UNIV