Method for rapid simulation of non-stationary random course based on characteristic orthogonal decomposition

A random process and simulation method technology, applied in special data processing applications, complex mathematical operations, instruments, etc., can solve problems such as low efficiency

Inactive Publication Date: 2017-10-13
SOUTHWEST JIAOTONG UNIV
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Problems solved by technology

[0006] In view of the above problems, the purpose of the present invention is to provide a non-stationary random process fast simulation method based on characteristic orthogonal decomposition that can effectively solve the problems of application limitations and low efficiency in various current non-stationary simulation methods. The simulated samples are accurate and the simulation efficiency is high

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  • Method for rapid simulation of non-stationary random course based on characteristic orthogonal decomposition
  • Method for rapid simulation of non-stationary random course based on characteristic orthogonal decomposition
  • Method for rapid simulation of non-stationary random course based on characteristic orthogonal decomposition

Examples

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example 1

[0191] Example 1: Simulation accuracy verification

[0192] This example discusses the simulation of a downburst wind field along a tall building. First, the evolution power spectrum and coherence function of the multi-point non-stationary process were estimated based on the measured downburst wind speed data at heights of 0.9, 2.4, 4, 10, 116, 158 and 200 m (No. 1-7). From the characteristics of the coherent function, it is found that it is time-varying, and then the sample generation is performed according to the simulation steps of the above time-varying coherent non-stationary process.

[0193] Figure 1a and Figure 1b The decomposed time-varying spectra H corresponding to points 3 and 5 are shown respectively 33 (f,t) and H 55 The first two order principal coordinates and eigenvectors of (f,t). It can be found that the principal coordinates (time function) corresponding to smaller eigenvalues ​​contain larger energy. Figure 2a and Figure 2b The decomposed spectra...

example 2

[0195] Example 2: Simulation Efficiency Comparison

[0196] The wind field along the deck of a long-span suspension bridge with a main span of 2000 m and a side span of 1000 m is studied. For simplicity, only the wind velocity component perpendicular to the bridge axis is considered. The distance between two adjacent simulation points on the side span and the main span is taken as 10 meters and 20 meters respectively. Therefore, a total of 301 simulation points of the wind field will be simulated. The wind field characteristics are constructed according to the measured typhoon records. As in the previous example, the power spectrum of the typhoon is estimated from the measured data. Then, it is assumed that the self-spectrum of the simulated point in the middle span of the bridge is equal to the typhoon spectrum, and the self-spectrum of each point in the side span is taken as 0.8 times the typhoon spectrum. In addition, the coherence function adopts Davenport's exponential...

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Abstract

The invention discloses a method for rapid simulation of a non-stationary random course based on characteristic orthogonal decomposition. With regard to a multi-point non-stationary course which has arbitrary space distribution and is related to time variation, an EPSD matrix is composed triangularly at first, then POD is used to denote each time-frequency coupled element of the triangular matrix by the sum of products of multiple time functions and multiple frequency functions, and finally an FFT technology is used for rapid simulation; and with regard to a multi-point non-stationary course which has arbitrary space distribution and is related with time invariability, a related matrix is decomposed triangularly at first, then POD is used to denote time-frequency coupled elements of a diagonal matrix composed of auto spectra by the sum of products of multiple time functions and multiple frequency functions and finally a simulation formula is optimized, so that the FFT technology is only used for a few of times for efficient simulation. According to the invention, the POD is used, fitting accuracy is high, and simulated samples are accurate; simulation efficiency is greatly increased through triangular decomposition and optimal use of the FFT technology; and problems existing in current non-stationary simulation methods that applications are limited and efficiency is low can be solved.

Description

technical field [0001] The invention relates to the technical field of random signal simulation, in particular to a fast simulation method for non-stationary random processes based on characteristic orthogonal decomposition. Background technique [0002] Destructive excitations such as earthquakes and transient extreme winds exhibit non-stationary properties and are usually described by non-stationary processes. Monte Carlo simulation (MCS) of non-stationary processes is an important task in structural response analysis when nonlinearity, system randomness, parametric excitations, and certain other stochastic problems are involved. In addition, MCS is a benchmark for evaluating the accuracy of other stochastic methods. [0003] The spectral representation method based on the evolutionary power spectral density function (EPSD Evolutionary Power Spectral Density) is widely used in the simulation of stochastic processes due to its accuracy and simplicity. However, the time-va...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/14G06F17/15
CPCG06F17/142G06F17/156
Inventor 赵宁黄国庆陆成文
Owner SOUTHWEST JIAOTONG UNIV
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