本文選題：誤差分析 + 估計�。� 參考：《華中科技大學》2015年碩士論文

【摘要】：強烈的地震作用會導致大跨度橋梁的損壞甚至倒塌。精確估計大跨度橋梁在強地震作用下的結構響應是橋梁工程中十分重要的必要環(huán)節(jié)。而通過蒙特卡洛方法進行模擬來產生空間變化地震動時程樣本通常是預測大跨度橋梁在地震作用下的響應的前提條件�；谘葑児β首V密度(EPSD)模型的譜表示法(SRM)常被用作空間變化地震動時程樣本的模擬。然而,目前關于模擬空間變化地震動時程樣本的誤差分析的研究較為稀缺。為此,本文研究了演變功率譜密度的基本原理與其估計方法以及譜表示法模擬空間變化地震動的誤差,具體包含以下兩部分內容:第一,研究了演變功率譜密度的估計方法。在滑動窗口濾波法估計演變功率譜密度的基礎上,提出了一種新的演變功率譜密度的估計方法,該方法的原理為通過對樣本時程統(tǒng)計所得的時變相關函數(shù)進行傅立葉變化得到演變功率譜密度的估計值,并通過數(shù)值模擬以及對比現(xiàn)有方法充分證明了其有效性。第二,研究了使用譜表示法模擬以服從高斯分布且均值為0的演變非平穩(wěn)過程向量為模型的空間變化地震動的誤差。推導了用于估計模擬樣本的演變功率譜密度、時變相關函數(shù)和時變標準差的偏度誤差和隨機誤差的解析公式。此外,進一步給出了工程實際中常用的特定情況下估計演變功率譜密度的隨機誤差的簡化解析公式。結果表明,模擬樣本的演變功率譜密度、時變相關函數(shù)和時變標準差均無偏。其中用于估計演變功率譜密度的隨機誤差的解析公式退化至平穩(wěn)過程后的結果與平穩(wěn)過程的對應解析公式一致。此外,在數(shù)值模擬算例中,使用本文提出的解析公式所預測的隨機誤差與模擬樣本的統(tǒng)計隨機誤差保持一致,證明了本文所提出的用于估計誤差的解析公式的正確性。本文還利用這些誤差估計解析公式研究了影響模擬樣本的隨機誤差的相關因素。結果表明,同時使用隨機振幅和隨機相位角的譜表示法會產生較大的隨機誤差,而增加樣本容量以及增加頻率分割數(shù)可以減小隨機誤差。最后,通過使用本文所提出的誤差估計的解析公式估計青馬大橋在上的空間變化地震動的模擬樣本關于演變功率譜的隨機誤差,說明了這些解析公式的使用價值。
[Abstract]:Strong seismic action can cause damage or even collapse of long-span bridges. It is an important necessary link in bridge engineering to accurately estimate the structural response of long-span bridges under strong earthquake action. The spectral representation method (SRM) based on the evolutionary power spectral density (EPSD) model is often used as a simulation of the time history samples of the spatial variation ground motion. However, the research on the error analysis of the time history samples for the simulated spatial variation of ground motion is scarce. With its estimation method and the spectral representation method to simulate the spatial variation of ground motion, the following two parts are included. Firstly, the estimation method of the evolutionary power spectral density is studied. On the basis of the estimation of the evolutionary power spectral density by the sliding window filtering method, a new estimation method of the evolutionary power spectral density is proposed. The original method is the original method. The estimation of the evolution of the power spectral density is obtained by changing the time-varying correlation function obtained by the sample time history statistics. The validity of the power spectral density is proved by numerical simulation and comparing with the existing methods. Second, the evolution of the nonstationary process vector, which is modeled by the spectral representation method, is subject to the Gauss distribution and the mean value is 0. Second For the error of the spatial variation of ground motion of the model, an analytical formula for estimating the evolutionary power spectral density, the time-varying correlation function and the bias error and the random error of the time-varying standard difference is derived for the estimation of the simulated sample. Furthermore, the simplification of the random error of the estimated power spectral density in the engineering practice is further given. The analytical formula shows that the evolutionary power spectral density of the simulated sample, the time-varying correlation function and the time variation standard difference are all unbiased. The analytic formula for estimating the random error of the evolutionary power spectral density is degenerated to the corresponding analytic formula of the stationary process and the corresponding analytic formula of the stationary process. In addition, in the numerical simulation example, this paper is used in this paper. The stochastic error predicted by the proposed analytic formula is consistent with the statistical random error of the simulated sample, which proves the correctness of the analytical formula used to estimate the error. The spectral representation of the amplitude and the random phase angle can produce large random errors, while increasing the sample size and increasing the frequency division number can reduce the random error. Finally, by using the analytical formula of the error estimation proposed in this paper, the simulation samples of the spatial variation of the space motion of the Tsing Ma Bridge on the evolution of the power spectrum are estimated. Random errors illustrate the value of these analytical formulas.
【學位授予單位】：華中科技大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：U441.3

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本文編號：2039791