Quick algorithms for computing either displacement,velocity or acceleration of an oscillator

Accurate and efficient algorithms are derived for computing any desired response quantity of a single-degree-of-freedom linear oscillator subjected to an arbitrary forcing function. These algorithms are based on linear interpolation of the excitation between discrete points sampled uniformly in time. In the special case of the undamped oscillator, the displacement algorithm is equivalent to a previously published algorithm for this situation which was derived using a finite element approach. However, contrary to the claim made by the authors of this latter algorithm, it does not give an exact solution of the equation of undamped motion for an arbitrary forcing function.     

Disaggregation-based response weighting scheme for seismic risk assessment of structures

The results of seismic hazard disaggregation can be used to assign relative weights to a given ground motion record based on its corresponding magnitude, distance and deviation from the ground motion prediction model (epsilon) in order to make probability-based seismic assessments using non-linear dynamic analysis. In this paper, the implications of using the weighted ground motion records are investigated in terms of the mean annual frequency of exceedance of the critical component-based demand to capacity ratio in an existing reinforced concrete structure using both the peak ground acceleration and the first-mode spectral acceleration as intensity measures. It is demonstrated how site-specific seismic hazard disaggregation can be used in order to obtain the conditional probability distribution for a relevant ground motion characteristic given the chosen intensity measure. Distinguished by the amount of structural analysis required, two alternative non-linear dynamic analysis procedures, namely the cloud and the stripes method are implemented. The weighted cloud and the weighted stripes methods are then introduced as analysis procedures which modify the structural response to the selected ground motion records by employing the information provided from the seismic hazard analysis. It is demonstrated that the resulting annual frequencies based on weighted records are comparable to those obtained by using vector-valued intensity measures, while requiring less computational effort.     

A FE–BE method for dynamic analysis of dam–foundation–reservoir systems in the time domain

By coupling FEM and BEM, a numerical method was developed for dynamic response analyses of dam–foundation–reservoir systems in the time domain. During formulation, the weighted residual procedure was applied to the coupling of several equations of motion for solid and fluid in the FE and BE regions, and an algorithm similar to the Newmark beta procedure was finally obtained. The algorithm is advantageous in that it takes into account all the effects of dam–foundation, dam–reservoir and reservoir–foundation interactions, as well as of the absorption of both elastodynamic and hydrodynamic waves at the boundaries of the foundation and the reservoir. To demonstrate the validity of the present method, the impulsive response of a dam–foundation–reservoir system was calculated using the algorithm, and showed a good agreement with the existing results obtained by other researchers.     

基于加权一致性的蚁群算法在断层检测中的应用

突出地震数据振幅空间不连续性的断层增强属性体是断层自动解释的基础,而如何压制噪声、地层残余响应、角度不整合接触等伪断层的影响是断层自动检测的关键问题之一.在指纹图像边缘检测处理中,一致性是对指示局部方向场信息各向异性强度的一个度量,本文将其作为一种新的断层增强属性引入到地震数据处理中.为了更有效地压制噪声,本文通过对一致性进行加权处理,再结合蚁群算法,提出了新的断层自动检测方法——基于加权一致性的蚁群算法.理论地震模型和实际地震数据的处理结果表明,对于相同的断层检测过程,对比常规的基于方差属性的蚁群算法和基于C3相干属性的蚁群算法,本文所提方法不仅更有效地压制了噪声和地层残余响应产生的伪断层信息,而且更完整地展现了断层的延伸长度,同时具有更高的稳定性和计算效率.     

地震动强度非平稳特性参数与结构响应之间的近似定量关系分析

本文在对实际地震加速度记录统计分析的基础上,给出了能够合理描述地震动强度非平稳特性的参数及其取值范围;然后引入实验设计方法,建立了适合于地震动强度非平稳特性参数分析的实验设计算法,用来分析地震动强度非平稳特性参数的变化对结构响应的影响;最后通过与近似技术相结合,建立了地震动强度非平稳特性参数与结构响应之间的近似定量关系模型.结果表明,本文提出的实验设计方法适合于对地震动强度非平稳特性参数进行分析,该方法在有效地减小计算量的同时,获得了结构响应与参数变化之间的对应关系.基于实验设计方法进行的特性参数方差分析结果表明:地震动的稳态持时对结构地震响应的影响比较显著;对于周期较小的结构,特性参数之间的交互作用对结构地震响应的影响显著,但当周期大于1 s时,则不显著.本文建立的近似定量关系模型能够较好地反映不同特性参数、不同周期结构动力响应之间的联系,为工程实践中基于结构特性合理设置地震动特性参数、合成或挑选地震加速度时程提供理论依据.      

An unconditionally stable time-stepping procedure with algorithmic damping: a weighted integral approach using two general weight functions

An accurate algorithm for the integration of the equations of motion arising in structural dynamics is presented. The algorithm is an unconditionally stable single-step implicit algorithm incorporating algorithmic damping. The displacement for a Single-Degree-of-Freedom system is approximated within a time step by a function which is cubic in time. The four coefficients of the cubic are chosen to satisfy the two initial conditions and two weighted integral equations. By considering general weight functions, eight additional coefficients arise. These coefficients are selected to (i) minimize the difference between exact and approximate solutions for small time steps, (ii) incorporate specified algorithmic damping for large time steps, (iii) ensure unconditional stability and (iv) minimize numerical operations in forming the amplification matrix. The accuracy of the procedure is discussed, and the solution time is compared with a widely used algorithm. Copyright © 1999 John Wiley & Sons, Ltd.     

Forced vibration testing of buildings using the linear shaker seismic simulation (LSSS) testing method

This paper describes the development and numerical verification of a test method to realistically simulate the seismic structural response of full‐scale buildings. The result is a new field testing procedure referred to as the linear shaker seismic simulation (LSSS) testing method. This test method uses a linear shaker system in which a mass mounted on the structure is commanded a specified acceleration time history, which in turn induces inertial forces in the structure. The inertia force of the moving mass is transferred as dynamic force excitation to the structure. The key issues associated with the LSSS method are (1) determining for a given ground motion displacement, x_g, a linear shaker motion which induces a structural response that matches as closely as possible the response of the building if it had been excited at its base by x_g (i.e. the motion transformation problem) and (2) correcting the linear shaker motion from Step (1) to compensate for control–structure interaction effects associated with the fact that linear shaker systems cannot impart perfectly to the structure the specified forcing functions (i.e. the CSI problem). The motion transformation problem is solved using filters that modify x_g both in the frequency domain using building transfer functions and in the time domain using a least squares approximation. The CSI problem, which is most important near the modal frequencies of the structural system, is solved for the example of a linear shaker system that is part of the NEES@UCLA equipment site. Copyright © 2005 John Wiley & Sons, Ltd.     

非平稳地震激励下隔震曲线梁桥振动控制研究

曲线梁桥由于其平面不规则性导致结构在地震激励下产生弯扭耦合效应,使得隔震曲线梁桥的地震响应更加复杂。目前常用的控制方法是将隔震技术与附加减震装置相结合对曲线梁桥进行控制。本文将地震动考虑为一均匀调制非平稳随机过程,针对隔震曲线梁桥长周期、低频率的特点,选取Clough-Pension平稳地震动功率谱模型作为随机地震动输入模型,对无控(NON-C)、经典线性最优控制(COC)以及序列最优控制算法(SOC)三种状态下的曲线桥梁进行随机响应分析。通过建立曲线梁桥在随机地震动作用下的运动方程,求出减震控制结构的位移谱密度、加速度谱密度响应及时变方差。分析结果表明:序列最优控制算法(SOC)在使隔震层位移得到减小的同时,可以更有效地控制上部结构的地震响应,具有更好的控制效果。     

弹性波的三维有限元模拟

本文讨论了弹性波瞬态传播问题的三维有限元计算方法及当前存在的实际困难.针对要求计算机内存大和计算时间长的问题,采取了改进措施.由于采用了集中质量矩阵和修正的中心差分时间积分显格式相结合的方法,可以使计算机内存和计算时间大为减少;由于采用结点定位法,最适合用于目前发展的并行计算机系统,可使计算速度大大增快;还采用了有效激发震源法,有效激发区是随时间步进的增加而逐步增大,这不仅能节省计算时间,而且使波场的传播过程一目了然,本文计算了由两种介质组成的三维楔形问题,得到若干典型剖面的瞬时波场图及随时间变化的合成地震图.     

Enrichment of seismic ground motion databases using Karhunen–Loève expansion

Best estimate seismic analysis are generally based on time‐domain simulations of structural responses. The seismic load is then modeled by a stochastic process representing ground motion. For this purpose, the analyst can use recorded accelerograms or work with synthetically generated ones. The number of ground motion time‐histories available for a given scenario and site condition is limited and generally not sufficient for carrying out more advanced probabilistic structural response analysis. It is then necessary to have at our disposal methods that allow for generating synthetic accelerograms that realistically characterize earthquake ground motions. However, most of the methods proposed in literature for generating synthetic accelerograms do not accurately reproduce the natural variability of ground motion parameters (such as PGA, cumulative absolute velocity, and Arias intensity) observed for recorded time histories. In this paper, we introduce a new method for generating synthetic ground motion, based on Karhunen‐Loève decomposition and a non‐Gaussian stochastic model. The proposed method enables the structural analyst to simulate ground motion time histories featuring the properties mentioned above. To demonstrate its capability, we study the influence of the simulation method on different ground motion parameters and on soil response spectra. We finally compute fragility curves to illustrate the practical application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Constant‐ductility response spectra for sequential earthquake and tsunami loading

Simplified approaches for examining structural system response under sequential earthquake and tsunami loading are helpful for understanding response trends. To aid understanding, nonlinear (constant‐ductility) response spectra are developed for elastoplastic single degree of freedom systems subjected to seismic loads followed by hydrodynamic tsunami loads. The forcing function is composed of long‐duration earthquake motion concatenated with a range of tsunami hydrodynamic forces that are proportional to the pseudo‐spectral acceleration produced by the earthquake motion. The constant‐ductility spectra are thus constructed for scenarios where the loading imposed by one hazard is not dominant over the other. The spectra and basic intensity measures indicate that the amplification of response for sequential earthquake and tsunami loading over the earthquake only case is most significant for systems with long natural periods and high‐ductility capacity under seismic loading. Copyright © 2017 John Wiley & Sons, Ltd.     

Developing efficient scalar and vector intensity measures for IDA capacity estimation by incorporating elastic spectral shape information

Scalar and vector intensity measures are developed for the efficient estimation of limit‐state capacities through incremental dynamic analysis (IDA) by exploiting the elastic spectral shape of individual records. IDA is a powerful analysis method that involves subjecting a structural model to several ground motion records, each scaled to multiple levels of intensity (measured by the intensity measure or IM), thus producing curves of structural response parameterized by the IM on top of which limit‐states can be defined and corresponding capacities can be calculated. When traditional IMs are used, such as the peak ground acceleration or the first‐mode spectral acceleration, the IM‐values of the capacities can display large record‐to‐record variability, forcing the use of many records to achieve reliable results. By using single optimal spectral values as well as vectors and scalar combinations of them on three multistorey buildings significant dispersion reductions are realized. Furthermore, IDA is extended to vector IMs, resulting in intricate fractile IDA surfaces. The results reveal the most influential spectral regions/periods for each limit‐state and building, illustrating the evolution of such periods as the seismic intensity and the structural response increase towards global collapse. The ordinates of the elastic spectrum and the spectral shape of each individual record are found to significantly influence the seismic performance and they are shown to provide promising candidates for highly efficient IMs. Copyright © 2005 John Wiley & Sons, Ltd.     

基于矩阵预处理和BPT-SIRT非线性加权反演成像法

为提高弹性波CT层析成像中反演成像的质量,同时考虑到CT走时方程中系数矩阵的病态性和BPT-SIRT算法重建图像质量较低的问题,提出基于主元加权预处理和对BPT-SIRT算法加权的方法。该方法对BPT得到的初始迭代值进行加权预处理,在CT走时方程中的系数矩阵主元上叠加一个权值,再通过非线性的指数加权函数对射线路径矩阵中的元素进行加权。通过数值模拟和预制含缺陷的钢管混凝土试件对该方法进行验证,结果表明本文的方法具有更好的收敛速度和精度,对缺陷的识别效果更好。      

高频GPS双差残差模型监测强震地表运动

根据震时地表震动持续时间短的特点,以及双差残差的相关性,提出了基于双差残差建模的高频GPS强震位移监测方法.首先对震前若干历元各双差残差进行建模,地震发生后,利用模型对各双差残差进行预报,最后利用预报残差实现短时间尺度内的位移解算.利用一条长约1100 km基线的静态数据和El Mayor-Cucapah 7.2级地震的94个测站数据进行试验分析,结果表明,5 min预测时间内,静态数据的动态位移在N、E、U三个方向的定位中误差分别为6 mm、6 mm和13 mm,地震数据的解算结果与实际情况有较好的一致性.     

Intelligent fuzzy weighted input estimation method for the multi-story buildings with unknown ground motion acceleration

This paper presents a novel intelligent fuzzy weighted input estimation method which effiviently and robustly estimates the unknown ground motion accelerations. The new input estimation method includes the Kalman Filter (KF) and the recursive least square estimator (RLSE), which is weighted by the fuzzy weighting factor proposed based on the fuzzy logic inference system. By directly synthesizing the Kalman filter with the estimator, this work presents an efficient robust forgetting zone, which is capable of providing a reasonable compromise between the tracking capability and the flexibility against noises. The excellent performace of this inverse method is demonstrated by solving the earthquake-excitation estimation problem, and the proposed algorithm is compared by alternating between the constant and adaptive weighting factors. The results reveal that this method has the properties of better target tracking capability and more effective noise reduction.     

Assessment of terrestrial water contributions to polar motion from GRACE and hydrological models

The hydrological contribution to polar motion is a major challenge in explaining the observed geodetic residual of non-atmospheric and non-oceanic excitations since hydrological models have limited input of comprehensive global direct observations. Although global terrestrial water storage (TWS) estimated from the Gravity Recovery and Climate Experiment (GRACE) provides a new opportunity to study the hydrological excitation of polar motion, the GRACE gridded data are subject to the post-processing de-striping algorithm, spatial gridded mapping and filter smoothing effects as well as aliasing errors. In this paper, the hydrological contributions to polar motion are investigated and evaluated at seasonal and intra-seasonal time scales using the recovered degree-2 harmonic coefficients from all GRACE spherical harmonic coefficients and hydrological models data with the same filter smoothing and recovering methods, including the Global Land Data Assimilation Systems (GLDAS) model, Climate Prediction Center (CPC) model, the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis products and European Center for Medium-Range Weather Forecasts (ECMWF) operational model (opECMWF). It is shown that GRACE is better in explaining the geodetic residual of non-atmospheric and non-oceanic polar motion excitations at the annual period, while the models give worse estimates with a larger phase shift or amplitude bias. At the semi-annual period, the GRACE estimates are also generally closer to the geodetic residual, but with some biases in phase or amplitude due mainly to some aliasing errors at near semi-annual period from geophysical models. For periods less than 1-year, the hydrological models and GRACE are generally worse in explaining the intraseasonal polar motion excitations.     

基于加权K均值聚类的多属性初至拾取方法

为提高初至拾取方法的准确性和自适应能力,将变异系数加权K均值聚类算法引入初至拾取中。首先提取均方根振幅、相邻道相关性、线积分、振幅谱主频等多种地震属性;然后针对地震属性进行加权K均值聚类,自动识别初至所在时窗;最后结合相位校正法,实现时窗内初至波起跳时间的拾取。在此基础上通过实际数据测试,并与长短时窗能量比法、反向传播神经网络方法对比,验证了本文方法的有效性与可行性。结果表明,基于加权K均值聚类的多属性初至拾取方法能较快速、准确地拾取低信噪比数据的初至,并且无需人为判断时窗,从而提高了拾取的自适应能力。      

微地震资料贝叶斯理论差分进化反演方法

微地震监测难以拾取准确初至,为了提高反演定位精度和减小多解性,研究了微地震贝叶斯差分进化反演方法.从分析讨论理论模型反演残差及其协方差分布特征出发,结合对比不加噪音和加入不同程度的噪音后残差协方差极小点位置移动、分布梯度变化特征,提出了先验信息解估计方法.针对后验估计中,由于难以获得先验信息解的方差估计致使无法计算加权系数问题,通过分析残差变化特征和解的变化关系,研究了利用残差求取加权系数的方法.为了加快寻优速度,讨论了差分进化反演方法,在变异操作方面使用差分策略,即利用种群中个体间的差分向量对个体进行扰动,实现个体变异,充分有效利用群体分布特性,提高算法的搜索能力,避免遗传算法中变异方式的不足.通过理论模型测试本方法的反演效果,并且和搜索方法反结果进行比较.测试结果证明本反演方法,对于不同程度初至干扰,反演结果向准确解逼近程度比搜索方法要好得多,实际资料的反演结果也好于搜索方法.     

Response variability in structural dynamics

This paper presents a technique for treating uncertainties in the dynamic models of a structural system. The formulation of the method is presented for a simple case of a single-degree-of-freedom linear oscillator. The uncertainties are modelled as random variables and are assumed to be time-independent. The solution is expanded as a series involving the random terms, and a system of linear ordinary differential equations for the unknowns of the problem is derived using the weighted residual method. The system of equations is then integrated in time and the response variability is computed. Validation calculations show that the results from the method agree well with those obtained by other solution techniques. Finally, some possible applications and extensions of the present work are discussed.