空间多点人工地震动幅值收敛性研究EI北大核心CSCD

在空间相关性人工地震动生成中,计算的繁杂和局部场地收敛性与幅值收敛性之间存在的矛盾,是时域合成法中的两大主要问题。为了简化计算,同步实现局部场地及地震动幅值的双重收敛性,在对相位角分布进行深入研究的基础上,构建了空间多点人工地震动幅值收敛因子,并采用虚实分离法来分解功率谱矩阵。结果表明,该方法生成的多点人工地震动计算快速,且幅值稳定收敛。     

与反应谱相容的多点完全非平稳地震动随机过程的快速模拟

为了精确评估结构地震响应的概率特性,地震动随机过程的模拟需要考虑时间变异性(频率和强度非平稳)、空间变异性以及与反应谱的相容性。在经典的多点完全非平稳随机过程的模拟方法中,由于频率与时间变量不可分离,演化功率谱矩阵分解效率较低。为了加快谱矩阵的分解,提出了新Cholesky分解方法。该方法的核心是将演化谱矩阵分离为相位和模矩阵,而模矩阵进一步被转化为与时间不相关的延迟相干矩阵。通过与时间相关的演化谱矩阵相比,延迟相干矩阵仅与频率相关,这样就显著提高了矩阵分解的效率;此外,延迟相干矩阵更适合采用插值技术。最后,将新Cholesky分解方法和插值技术应用到生成与反应谱相容的随机方法中。结果表明:新Cholesky分解与插值能够高效地模拟多点完全非平稳并且与反应谱相容的地震动样本;线性插值与三次样条插值均可达到良好的分辨率,少量的插值点即可满足精度的要求。     

一种考虑局部场地收敛性的多点地震动合成方法

提出一种符合实际地震动传播特点的多点地震动合成方法。目前的非平稳空间相关多点地震动合成方法在局部场地上不具备收敛性，与实际的地震波传播机制相矛盾。通过修正随机相位角，使生成的多点地震动在局部场地上具备收敛性，给出了未知和已知相位差谱统计规律两种情况下非平稳多点地震动的合成方法，进一步提出了基于实际地震记录的空间相关多点地震动合成方法。采用本文方法进行了基于美国Northridge地震和我国集集地震的多点地震动模拟研究，结果表明方法具有良好的局部收敛性，可用于大尺度结构的多点输入分析。     

大跨度结构随机脉动风场的快速模拟方法

针对传统谐波合成法计算量巨大、内存耗费多的缺点,研究了空间各点的分解功率谱密度函数曲线随频率变化的特点。在此基础上,提出采用三次均匀B样条插值方法来拟合分解谱密度函数曲线,引入矩阵Cholesky分解的优化递归算法来加速矩阵分解速度,同时利用FFT技术来减少谐波项合成所需要的时间。经过上述的改进,可以大大提高双索引频率下谐波合成法的计算效率。最后利用两个算例表明,这种方法可以高效、准确地模拟出适合大跨度结构的随机脉动风场。     

基于相干函数矩阵的风场本征正交分解

提出了基于相干函数矩阵的风场本征正交分解(CPOD,Coherency matrix-based POD)。首先推导了基于功率谱函数矩阵的本征正交分解。通过引入功率谱矩阵的预分解,将推导过程中的功率谱矩阵特征值分解改进为相干函数矩阵的特征值分解,得到了CPOD的表达式。对CPOD作频域离散化,得到了基于CPOD的谱表示法随机风场模拟公式。以模拟某18点脉动风速场为算例,对比分析了CPOD与SPT振型的特征并验证了所提模拟算法的有效性。结果表明,CPOD的显式分离特性使得它具有比POD更加明确的物理意义,并适用于风场特征分析。     

与已知场点相关的地震动场模拟研究

提出了一种与已知场点相关地震动场模型。将工程频段(0~25 Hz)分成若干个互不重叠的子段,在每个子频段内将地震动看作面波和体波的叠加;其次在每个子频段内确定影响合成地震动幅值谱的关键因素并将其引入模型中,使每个子频段的合成地震动幅值谱、功率谱和已知幅值谱、功率谱一致;再次由相位差谱频数分布与地震动强度包络的相似性,将决定地震动强度非平稳的关键因素即相位差谱引入到模型中,使合成地震动和已知地震动波形相似;最后,由模型中的频散曲线和距离参数描述不同场点之间的相干性,将合成地震动扩展到地震动场模型。El Centro地震波场点地震动场算例表明,模型不仅可以实现合成地震动场功率谱和已知场点完全一致,而且相干性合理,可以用于工程分析。     

复杂地形场地上多维多点地震动模拟研究

研究了复杂地形场地上多维多点地震动的模拟。将基岩加速度反应谱转换成相应的功率谱,介绍了多土层多维地震波的传播理论和基岩相干函数的选取。利用基岩功率谱与相干函数,给出了复杂地形场地上多维多点地震动的模拟方法。针对一算例进行分析,得到了非同类多土层复杂地形场地上的三个点地震动加速度时程曲线、功率谱以及不同分量的放大函数,通过比较功率谱和相干函数的吻合程度,验证了研究成果的准确性。该研究成果可应用于复杂地形场地上大跨度结构的多维多点地震动的分析。     

一种基于时空瞬时稳定性的方位谱估计方法

针对基于子空间分解的空间方位谱估计方法稳健性问题,提出了一种基于时空瞬时稳定的方位谱估计方法。该方法首先依据空间目标信号时域瞬时稳定性,将协方差矩阵频域求取过程转换为经相参补偿的复域求取,降低空间数据稳定性对协方差矩阵估计的影响;然后依据各子空间输出方位谱峰值索引离散度差异,提取各子空间方位谱加权因子;最后根据加权因子实现对各子空间方位谱加权处理,降低背景噪声对最终合成空间方位谱影响。数值仿真及实测数据处理结果表明,相比子空间分解方法,在不损失空间分辨率情况下,能够有效降低空间数据稳定性对协方差矩阵估计产生的影响,在无目标先验信息情况下,对最低信噪比的需求得到了6 dB以上的降低。     

多点平稳随机载荷识别方法研究

根据矩阵谱分解的思想,提出多点任意相关的随机载荷识别方法.鉴于响应功率谱矩阵和激励功率谱矩阵具有相同的秩且为非负定,首先推导完全相干的功率谱矩阵的识别方法,将任意相干的激励功率谱矩阵进行谱分解成完全相干的功率谱矩阵之和,利用响应信息识别分解后的完全相干功率谱进而完成对激励功率谱的识别.该方法具有较高的识别精度.针对求解逆问题中的适定性进行了讨论,指出病态的原因并运用条件数权重法,该法能在一定程度上减轻病态,提高识别精度.通过实验和仿真验证上述方法的正确性.最后对提高识别精度提出了建议.     

匹配多目标参数的地震动合成方法

地震动合成方法可为结构抗震设计和评估提供人工地震动时程,目前合成方法一般仅满足与目标谱的匹配,只考虑了地震动的频谱和幅值因素,并没有考虑地震动的持时特征.为了合成与目标区域地震动三要素相匹配的地震动时程,提出了一种应用机器学习合成地震动的方法.该方法应用基于数据驱动的主成分分析方法,从目标区域实际地震动数据库中提取用于...     

基于Hermite插值的简化风场模拟

针对传统Deodatis谐波合成法的模拟效率受Cholesky分解次数制约的问题,通过对互谱密度矩阵分解引入Hermite插值,推导了基于Hermite插值的简化风场模拟方法,将传统谐波合成法中的Cholesky分解次数由n×N次缩减为n×2k次（2k < N）,从而大幅度提升了传统谐波合成法的计算效率。以某大跨度三塔悬索桥主梁风场模拟为例,分别基于传统Deodatis法、三次Lagrange插值法、Hermite插值法模拟了时长为4096 s的脉动风速时程,三者在模拟耗时与模拟精度方面的对比表明:Hermite插值法与Lagrange插值法均能显著提高传统谐波合成法的模拟效率;Hermite插值法的模拟效率略低于三次Lagrange插值法,但其对H矩阵的模拟精度明显高出一个层次,因而Hermite插值法在风场模拟中表现更优。采用基于Hermite插值的简化方法,模拟脉动风速的功率谱与相关函数均能与目标值吻合较好,表明所模拟的脉动风速仍具有较高的保真度。在此基础上,通过插值间距的优化分析给出了插值间距的建议取值区间。     

An improved approximation for the spectral representation method in the simulation of spatially varying ground motions

The spectral representation method (SRM), based on the Cholesky decomposition of either cross spectral density matrix or lagged coherency matrix, is widely used in the simulation of spatially varying ground motions. In this study, the SRM, based on the decomposition of lagged coherency matrix, is modified to apply to the common case which the auto spectral densities of simulation points are not the same. When using interpolation approximation approach to improve the efficiency, the SRM based on the decomposition of lagged coherency matrix exhibits much higher accuracy than the SRM based on the decomposition of cross spectral density matrix, because the elements of lower triangular matrix obtained by the Cholesky decomposition of lagged coherency matrix vary slowly with the frequency. Therefore, the SRM, based on the decomposition of lagged coherency matrix, is generally suitable for the combination with the interpolation approximation approach.     

Optimal damper placement for critical excitation

Since earthquake ground motions are very uncertain even with the present knowledge, it is desirable to develop a robust structural design method taking into account these uncertainties. Critical excitation approaches are promising and a new probabilistic critical excitation method is proposed. Different from the conventional critical excitation methods, a stochastic response index is treated as the objective function to be maximized. The energy (area of power spectral density function) and the intensity (magnitude of power spectral density function) are fixed and the critical excitation is found under these restrictions. It is shown that the resonant characteristic of ground motions can be well represented by the proposed critical excitation. An original steepest direction search algorithm due to the present author is applied to the problem of optimal damper placement in structures subjected to the critical excitation. Closed-form expressions of the inverse of the coefficient matrix (tri-diagonal matrix) enable one to compute the transfer function and its derivative with respect to design variables very efficiently. A numerical example of a 6-DOF shear building model is presented to demonstrate the effectiveness and validity of the present method.     

多阻尼比设计反应谱的非平稳地震动场拟合

采用频域调整方法生成与设计反应谱相吻合的地震动,并利用解析迭代方法计算地震动的反应谱,提出了迭代计算的收敛准则。在相关地震动场模拟方法中,将相位差谱的统计模型引入空间相关非平稳地震动场的模拟方法之中,利用快速傅里叶变换技术生成地震动场。将设计反应谱的地震动拟合与非平稳地震动场的合成结合在一起,解决了多阻尼比设计反应谱的非平稳地震动场拟合问题。     

基于输入能量的地震动时程强度包络函数研究

结构随机振动分析和人工合成地震动记录均需要将反应谱转换为功率谱,地震动强度包络函数对转换结果有着重要影响。为合理地确定强度包络函数模型中各参数的取值,依据输入能量谱与傅里叶幅值谱的精确转换关系,建立了由非平稳地震动功率谱计算输入能量谱的方法,并分析了各参数取值对功率谱与能量谱的影响。以匹配设计谱的天然地震动记录样本的平均输入能量谱作为参考依据,通过与设计谱转换得到的输入能量谱进行对比分析,确定了各类场地设计谱转换为功率谱时,强度包络函数模型的各参数取值。通过人工合成地震动记录的输入能量谱分析,验证了各参数取值的合理性。     

New formulation of Cholesky decomposition and applications in stochastic simulation

Monte Carlo simulation plays a significant role in the mechanical and structural analysis due to its versatility and accuracy. Classical spectral representation method is based on the direct decomposition of the power spectral density (PSD) or evolutionary power spectral density (EPSD) matrix through Cholesky decomposition. This direct decomposition of complex matrix usually results in large computational time and storage memory.In this study, a new formulation of the Cholesky decomposition for the EPSD/PSD matrix and corresponding simulation scheme are presented. The key idea to this approach is to separate the phase from the complex EPSD/PSD matrix. The derived real modulus matrix evidently expedites decomposition compared to the direct Cholesky decomposition of the complex EPSD/PSD matrix. In the proposed simulation scheme, the separated phase can be easily assembled. The modulus of EPSD/PSD matrix could be further decomposed into the modulus of coherence matrix (or lagged coherence matrix), which describes the basic coherence structure of stochastic process. The lagged coherence matrix is independence of time and thus remarkably improves the Cholesky decomposition efficiency.The application of the proposed schemes to Gaussian stochastic simulations is presented. Firstly, the previous closed-form wind speed simulation algorithm for equally-spaced locations is extended to a more general situation. Secondly, the proposed approach facilitates the application of interpolation technique in stochastic simulation. The application of interpolation techniques in the wind field simulation is studied as an example.     

脉象采集方法及功率谱分析研究

在对压力脉搏波的分析及中医理论研究基础上,提出了一种多点三维动态压力脉搏波的采集方案,以获得有效的脉象数据用于模拟传统中医诊脉.根据信号功率谱的特点,在数据采集过程中结合了功率谱分析手段动态提取脉象的位置及力度特征,同时通过实验得出脉象变化与压力脉搏波功率谱变化的内在相关性,从而得到一种简单有效的脉象特征分析和提取的实验和研究方法.     

Critical excitation for elastic–plastic structures via statistical equivalent linearization

Since earthquake ground motions and their effects on structural responses are very uncertain even with the present knowledge, it is desirable to develop a robust structural design method taking into account these uncertainties. Critical excitation approaches are promising and a new random critical excitation method for single-degree-of-freedom (SDOF) elastic–plastic structures is proposed. The power (area of power spectral density (PSD) function) and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. In contrast to linear elastic structures, transfer functions and related simple expressions for response evaluation cannot be defined in elastic–plastic structures and difficulties arise in describing the peak responses except elastic–plastic time-history response analysis. Statistical equivalent linearization is utilized to estimate the elastic–plastic stochastic peak responses approximately. The critical excitations are obtained for two examples and compared with the corresponding recorded earthquake ground motions.