Efficient non-stationary random process simulation method

A technology of random process and simulation method, applied in the field of random signal simulation, which can solve the problems of high coincidence between statistical correlation function and objective correlation function, low calculation efficiency and so on.

Inactive Publication Date: 2015-04-15
黄国庆
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Problems solved by technology

[0005] In view of this, the purpose of the present invention is to provide a kind of high-efficiency simulation method of non-stationary stochastic process, propose a kind of spectrum representation simulation method that adopts Fast Fourier Transform (FFT) based on intrinsic orthogonal decomposition (POD), in this method first Perform Cholesky decomposition on the evolved power spectrum matrix, and then use intrinsic orthogonal decomposition (POD) to express the decomposed time-varying spectrum as the sum of the products of several time functions and frequency functions, that is, to decouple the time-varying power spectrum, and finally use FFT Technology improves

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Embodiment 1

[0053] Embodiment 1: specific simulation method

[0054] A non-stationary stochastic process efficient simulation method, the specific steps of the simulation method are as follows:

[0055] 1). Obtain the evolution power spectrum matrix of the non-stationary stochastic process evolution power spectral density EPSD:

[0056] Get zero-mean n-dimensional vector process x(t)=[x 1 (t),x 2 (t),...,x n (t)] T The evolution power spectrum matrix of is shown in the following formula:

[0057] S(ω,t)=[S jk (ω,t)],j,k=1,2,...,n (3)

[0058] The coherence function matrix Γ(ω) satisfies the following formula:

[0059] Γ(ω)=[γ jk (ω)],j,k=1,2,...,n (4)

[0060] where gamma jk (ω) is x j (t) and x k The coherence function between (t), x j (t) and x k The cross-correlation function between (t) is as follows:

[0061] R jk ( t , t + τ ) ...

Embodiment 2

[0099] Example 2: Demonstration of Accuracy

[0100] Decomposition and reconstruction of time-varying spectrum based on POD, without loss of generality, this paper selects an inseparable evolutionary power spectrum for example analysis to verify the accuracy of time-varying spectrum decomposition using POD, and selects representative unilateral power The spectral density function is shown in the following formula (Spanos P D, Kougioumtzoglou I A. Harmonic waves based statistical linearization for response evolutionary power spectrum determination [J]. Probabilistic Engineering Mechanics, 2012, 27 (1): 57-68.):

[0101] S ( f , t ) = 4 π ( f / C ) 2 e - Dt t 2 ...

Embodiment 3

[0104] Embodiment 3: effect analysis

[0105] Simulation example of multi-point non-stationary stochastic process

[0106] In order to better illustrate the superiority of the method proposed in this paper, this paper selects (Li Y, Kareem A.Simulation of multivariate nonstationary random processes by FFT[J].Journal of Engineering Mechanics,1991,117:1037-1058.) The calculation example used is used to simulate the multi-point non-stationary stochastic process, and the calculation results in this paper are compared with the calculation results in the literature. In this example, due to the liquefaction of the soil, there is a sudden change in the power spectral density of the evolution of ground motion after 7s, that is, from a wide-band spectrum to a narrow-band spectrum concentrated in low frequencies.

[0107] Let {x(t)} = [x 1 (t),x 2 (t)] T , and x 1 (t) and x 2 The evolution power spectral density of (t) obeys the following formula:

[0108] S ...

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Abstract

The invention belongs to the field of random signal simulation, in particular to an efficient non-stationary random process simulation method. The simulation method is a spectral representation simulation method adopting fast fourier transform (FFT) based on proper orthogonal decomposition (POD) and comprises the following steps: firstly performing Cholesky decomposition on an evolutionary power spectrum matrix, then representing a decomposed time-varying spectrum as the sum of products of a plurality of time functions and frequency functions by adapting the proper orthogonal decomposition, decoupling a time-varying power spectrum and finally greatly improving the simulation efficiency by utilizing a FFT technology. When the efficient non-stationary random process simulation method is adopted for stimulating a non-stationary random process, the POD precision and the reconstruction precision are high, and the goodness of fit of a statistical correlation function for simulating a sample duration with a target correlation function is high; by the use of the FFT, the simulation speed of a sample is obviously improved; the efficient non-stationary random process simulation method effectively solves the problem of low calculation efficiency caused by the fact that a traditional non-stationary random process simulation method based on spectral representation cannot use the FFT and has the advantages of high efficiency, high precision and high easiness in use.

Description

technical field [0001] The invention belongs to the field of random signal simulation, and in particular relates to a high-efficiency simulation method for a non-stationary random process. Background technique [0002] In engineering practice, excitations such as extreme wind, ground motion and ocean waves all present obvious non-stationary characteristics. These excitations can usually be described as non-stationary random processes with zero mean value, and described by Priestly defined evolutionary power spectrum (EPSD) (Priestley M B. Evolutionary spectrum and non-stationary processes[J]. Journal of Royal Statistical Society, 1965, Series B, 27:204-237.). When using time-domain method to analyze non-stationary random response, the simulation of non-stationary stochastic process based on evolution power spectrum is indispensable. [0003] Due to the accuracy of the method, the simulation of non-stationary stochastic processes based on spectral representation is widely u...

Claims

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Application Information

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IPC IPC(8): G06F9/455
Inventor 黄国庆彭留留苏延文郑海涛
Owner 黄国庆
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