谱表示法模拟空间变化地震动误差分析

发布时间：2018-06-19 11:52

本文选题：误差分析 + 估计　；参考：《华中科技大学》2015年硕士论文

【摘要】：强烈的地震作用会导致大跨度桥梁的损坏甚至倒塌。精确估计大跨度桥梁在强地震作用下的结构响应是桥梁工程中十分重要的必要环节。而通过蒙特卡洛方法进行模拟来产生空间变化地震动时程样本通常是预测大跨度桥梁在地震作用下的响应的前提条件。基于演变功率谱密度(EPSD)模型的谱表示法(SRM)常被用作空间变化地震动时程样本的模拟。然而,目前关于模拟空间变化地震动时程样本的误差分析的研究较为稀缺。为此,本文研究了演变功率谱密度的基本原理与其估计方法以及谱表示法模拟空间变化地震动的误差,具体包含以下两部分内容:第一,研究了演变功率谱密度的估计方法。在滑动窗口滤波法估计演变功率谱密度的基础上,提出了一种新的演变功率谱密度的估计方法,该方法的原理为通过对样本时程统计所得的时变相关函数进行傅立叶变化得到演变功率谱密度的估计值,并通过数值模拟以及对比现有方法充分证明了其有效性。第二,研究了使用谱表示法模拟以服从高斯分布且均值为0的演变非平稳过程向量为模型的空间变化地震动的误差。推导了用于估计模拟样本的演变功率谱密度、时变相关函数和时变标准差的偏度误差和随机误差的解析公式。此外,进一步给出了工程实际中常用的特定情况下估计演变功率谱密度的随机误差的简化解析公式。结果表明,模拟样本的演变功率谱密度、时变相关函数和时变标准差均无偏。其中用于估计演变功率谱密度的随机误差的解析公式退化至平稳过程后的结果与平稳过程的对应解析公式一致。此外,在数值模拟算例中,使用本文提出的解析公式所预测的随机误差与模拟样本的统计随机误差保持一致,证明了本文所提出的用于估计误差的解析公式的正确性。本文还利用这些误差估计解析公式研究了影响模拟样本的随机误差的相关因素。结果表明,同时使用随机振幅和随机相位角的谱表示法会产生较大的随机误差,而增加样本容量以及增加频率分割数可以减小随机误差。最后,通过使用本文所提出的误差估计的解析公式估计青马大桥在上的空间变化地震动的模拟样本关于演变功率谱的随机误差,说明了这些解析公式的使用价值。
[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.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U441.3

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