Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems

Earthquake ground motion records are nonstationary in both amplitude and frequency content. However, the latter nonstationarity is typically neglected mainly for the sake of mathematical simplicity. To study the stochastic effects of the time‐varying frequency content of earthquake ground motions on the seismic response of structural systems, a pair of closely related stochastic ground motion models is adopted here. The first model (referred to as ground motion model I) corresponds to a fully nonstationary stochastic earthquake ground motion model previously developed by the authors. The second model (referred to as ground motion model II) is nonstationary in amplitude only and is derived from the first model. Ground motion models I and II have the same mean‐square function and global frequency content but different features of time variation in the frequency content, in that no time variation of the frequency content exists in ground motion model II. New explicit closed‐form solutions are derived for the response of linear elastic SDOF and MDOF systems subjected to stochastic ground motion model II. New analytical solutions for the evolutionary cross‐correlation and cross‐PSD functions between the ground motion input and the structural response are also derived for linear systems subjected to ground motion model I. Comparative analytical results are presented to quantify the effects of the time‐varying frequency content of earthquake ground motions on the structural response of linear elastic systems. It is found that the time‐varying frequency content in the seismic input can have significant effects on the stochastic properties of system response. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonstationarity-based evaluation of flood risk in the Pearl River basin: changing patterns,causes and implications

Nonstationary GEV-CDN models considering time as a covariate are built for evaluating the flood risk and failure risk of the major flood-control infrastructure in the Pearl River basin, China. The results indicate: (1) increasing peak flood flow is observed in the mainstream of the West River and North River basins and decreasing peak flood flow is observed in the East River basin; in particular, increasing peak flood flow is detected in the mainstream of the lower Pearl River basin and also in the Pearl River Delta region, the most densely populated region of the Pearl River basin; (2) differences in return periods analysed under stationarity and nonstationarity assumptions are found mainly for floods with return periods longer than 50 years; and (3) the failure risks of flood-control infrastructure based on failure risk analysis are higher under the nonstationarity assumption than under the stationarity assumption. The flood-control infrastructure is at higher risk of flood and failure under the influence of climate change and human activities in the middle and lower parts of Pearl River basin.

EDITOR D. Koutsoyiannis

ASSOCIATE EDITOR G. Thirel     

地理空间数据的空间性分析应用

“空间性”是地理空间数据有别于其他数据的显著特征,因此地理空间数据研究过程中必须反映和遵从其地理空间特性。本文将集中于两个领域,即统计分析和遥感图像分析领域,来论述地理空间数据分析中必须加强对空间异质性、空间结构和尺度的探讨。     

基于GAM和GWR模型分析环境因子对南极磷虾资源分布的非线性和非静态性影响

分析南极磷虾分布与环境因子的非线性和空间非静态性关系,对南极磷虾的高效捕捞和管理具有重要意义。本研究基于“龙腾”船2015、2016年在南设得兰群岛捕捞作业的渔捞日志数据,应用广义加模型(Generalized additive model,GAM)和地理权重回归模型(Geographical weighted regression,GWR)探究南极磷虾(Euphausia superba)渔场分布与环境因子的非线性和空间非静态性关系,并比较这2种模型的模拟性能,为南极磷虾的渔场渔情预报、资源评估和渔业管理提供基础数据。GAM模型结果显示,2015、2016年单位捕捞努力量渔获量(Catch per unit effort,CPUE)与作业水深均呈显著负相关关系(P<0.01),表明在作业水深范围内,南极磷虾在较浅水域集群密度较高;2015年CPUE与表层水温呈显著正相关关系(P<0.01),但在2016年呈显著负相关关系(P<0.01),推测是由于2年调查作业位置不同所致;CPUE与离岸距离关系不显著(P≥0.05)。GWR模型结果显示,作业水深对CPUE的影响无显著的空间变化(P>0.05);海水表温和离岸距离对CPUE的影响具显著的空间变化(P<0.01),表明这2个因子对南极磷虾渔场分布的影响在空间上不连续,存在显著空间非静态性。GAM模型可用于研究资源分布与驱动因子的一般规律;GWR模型作为全局回归模型的有效补充,可用于探究一般规律不适合的特殊区域,便于发现资源分布的“热点”区域,未来在海洋生物资源分布研究中将有广阔的应用前景。     

Geographically weighted principal components analysis

Principal components analysis (PCA) is a widely used technique in the social and physical sciences. However in spatial applications, standard PCA is frequently applied without any adaptation that accounts for important spatial effects. Such a naive application can be problematic as such effects often provide a more complete understanding of a given process. In this respect, standard PCA can be (a) replaced with a geographically weighted PCA (GWPCA), when we want to account for a certain spatial heterogeneity; (b) adapted to account for spatial autocorrelation in the spatial process; or (c) adapted with a specification that represents a mixture of both (a) and (b). In this article, we focus on implementation issues concerning the calibration, testing, interpretation and visualisation of the location-specific principal components from GWPCA. Here we initially consider the basics of (global) principal components, then consider the development of a locally weighted PCA (for the exploration of local subsets in attribute-space) and finally GWPCA. As an illustration of the use of GWPCA (with respect to the implementation issues we investigate), we apply this technique to a study of social structure in Greater Dublin, Ireland.     

中国年和季节极端降水时空特征 及极值分布函数上尾部性质

基于热带气旋时间、路径、强度数据和中国728个气象站点1951~2014年日降水数据,分析了年和季节极端降水广义极值（GEV）分布函数特征及受热带气旋的影响。通过检查年和各季节极端降水的非一致性,发现具有变异点或显著时间趋势的站点占总站点数的比例较低。仅考虑满足一致性的站点,年和各季节极端降水GEV分布上尾部在全国大部分区域表现出厚尾特征,且不具有上边界。总体来看北方厚尾特征重于南方,秋季和冬季明显高于年和夏季。年极端降水厚尾特征受到不同季节极端降水机制的混合影响。而且,热带气旋对中国沿海区域极端降水有重要影响,往往引发大量级极端降水。东南沿海地区最大10场极端降水由热带气旋引发的比例达到60%以上。因此热带气旋趋向于增加沿海区域年极端降水GEV分布形状参数的大小,并控制着曲线上尾部的形状。     

Analyzing the effect of moving resonance on seismic response of structures using wavelet transforms

There is a complex interaction between the seismic response (i.e., peak displacements) of a nonlinear structure and the characteristics of a ground motion. One ground motion characteristic that contributes to record‐to‐record variability is spectral nonstationarity, or the variation of signal's frequency content with time. When the predominant natural periods of a nonlinear structure elongate in such a way as to match with the predominant frequency content in the ground motion, a phenomenon called moving resonance occurs. The effect of moving resonance on the response of nonlinear structures is investigated. Continuous complex wavelet transforms are used to examine the spectral nonstationarity of ground motion acceleration histories and associated structural displacement histories to identify the occurrences of moving resonance. A three‐dimensional displacement response spectrum is used to determine which combinations of initial period and strength create the largest displacements and thus are candidate configurations for experiencing moving resonance. A method is then proposed for quantifying the effect of moving resonance on structural response. The method utilizes discrete wavelet transforms to decompose a ground motion into component signals with limited frequency band and examines the structural response due to each individual component. A discussion is provided as to how these tools can be used to identify ground motion characteristics that may be conducive to moving resonance. Copyright © 2013 John Wiley & Sons, Ltd.     

Use of a nonstationary copula to predict future bivariate low flow frequency in the Connecticut river basin

Frequency analysis of streamflow provides an essential ingredient in our understanding of hydrologic events and provides needed guidance in the design and management of water resources infrastructure. However, traditional hydrologic approaches often fail to include important external effects that can result in unpredictable or unforeseen changes in streamflow. Moreover, previous studies investigating multiple characteristics of streamflow do not address a nonstationary approach. This study explores nonstationary frequency analysis of bivariate characteristics, including occurrence and severity, of annual low flow in the Connecticut River Basin, United States. To investigate bivariate low flow frequency, copulas and their marginal distributions are constructed by using stationary and nonstationary approaches. Our study results indicate that streamflow used in this study demonstrate significant nonstationarity. Over time, the occurrence and severity of low flows are shown to be lower with the same probability based on the results of nonstationary copulas. Bivariate low flow frequencies in the years 1970, 2000, and 2030, and their joint return periods are estimated under the nonstationary copulas. Copyright © 2016 John Wiley & Sons, Ltd.     

A modification of minimum norm quadratic estimation of a generalized covariance function for use with large data sets

Marshall and Mardia (1985) and Kitanidis (1985) have suggested using minimum norm quadratic estimation as a method to estimate parameters of a generalized covariance function. Unfortunately, this method is difficult to use with large data sets as it requires inversion of an n × n matrix, where n is number of observations. These authors suggest replacing the matrix to be inverted by the identity matrix, which eliminates the computational burden, although with a considerable loss of efficiency. As an alternative, the data set can be broken into subsets, and minimum norm quadratic estimates of parameters of the generalized covariance function can be obtained within each subset. These local estimates can be averaged to obtain global estimates. This procedure also avoids large matrix inversions, but with less loss in efficiency.