Simulation of Stochastic Processes by Spectral Representation
01 Apr 1991-Applied Mechanics Reviews (American Society of Mechanical Engineers)-Vol. 44, Iss: 4, pp 191-204
About: This article is published in Applied Mechanics Reviews.The article was published on 1991-04-01. It has received 1069 citations till now. The article focuses on the topics: Random vibration & Applied mechanics.
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TL;DR: This paper proposes the use of outdoor millimeter wave communications for backhaul networking between cells and mobile access within a cell, and proposes an efficient beam alignment technique using adaptive subspace sampling and hierarchical beam codebooks.
Abstract: Recently, there has been considerable interest in new tiered network cellular architectures, which would likely use many more cell sites than found today. Two major challenges will be i) providing backhaul to all of these cells and ii) finding efficient techniques to leverage higher frequency bands for mobile access and backhaul. This paper proposes the use of outdoor millimeter wave communications for backhaul networking between cells and mobile access within a cell. To overcome the outdoor impairments found in millimeter wave propagation, this paper studies beamforming using large arrays. However, such systems will require narrow beams, increasing sensitivity to movement caused by pole sway and other environmental concerns. To overcome this, we propose an efficient beam alignment technique using adaptive subspace sampling and hierarchical beam codebooks. A wind sway analysis is presented to establish a notion of beam coherence time. This highlights a previously unexplored tradeoff between array size and wind-induced movement. Generally, it is not possible to use larger arrays without risking a corresponding performance loss from wind-induced beam misalignment. The performance of the proposed alignment technique is analyzed and compared with other search and alignment methods. The results show significant performance improvement with reduced search time.
975Â citations
Cites methods from "Simulation of Stochastic Processes ..."
..., SLd(f) = |Hm(t)|(2)SFd(f), SLc(f) = |Hm(t)|(2)SFc(f)), using the spectral representation method and the inverse FFT as in [34]....
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16 Jun 2003
TL;DR: In this article, the authors presented methods of bridge fragility curve development on the basis of statistical analysis, and applied these methods in the assessment of seismic performance of expressway network systems.
Abstract: This report presents methods of bridge fragility curve development on the basis of statistical analysis. Both empirical and analytical fragility curves are considered. The empirical fragility curves are developed utilizing bridge damage data obtained from past earthquakes, particularly the 1994 Northridge and 1995 Hyogo-ken Nanbu (Kobe) earthquakes. Analytical fragility curves are constructed for typical bridges in the Memphis, Tennessee area utilizing nonlinear dynamic analysis. Two-parameter lognormal distribution functions are used to represent the fragility curves. These two parameters (referred to as fragility parameters) are estimated by two distinct methods. The first method is more traditional and uses the maximum likelihood procedure treating each event of bridge damage as a realization from a Bernoulli experiment. The second method is unique in that it permits simultaneous estimation of the fragility parameters of the family of fragility curves, each representing a particular state of damage, associated with a population of bridges. The method still utilizes the maximum likelihood procedure, however, each event of bridge damage is treated as a realization from a multi-outcome Bernoulli type experiment. These two methods of parameter estimation are used for each of the populations of bridges inspected for damage after the Northridge and Kobe earthquakes and with numerically simulated damage for the population of typical Memphis area bridges. Corresponding to these two methods of estimation, this report introduces statistical procedures for testing goodness of fit of the fragility curves and of estimating the confidence intervals of the fragility parameters. Some preliminary evaluations are made on the significance of the fragility curves developed as a function of ground intensity measures other than PGA. Furthermore, applications of fragility curves in the seismic performance estimation of expressway network systems are demonstrated. Exploratory research was performed to compare the empirical and analytical fragility curves developed in the major part of this report with those constructed utilizing the nonlinear static method currently promoted by the profession in conjunction with performance-based structural design. The conceptual and theoretical treatment discussed herein is believed to provide a theoretical basis and practical analytical tools for the development of fragility curves, and their application in the assessment of seismic performance of expressway network systems.
894Â citations
TL;DR: In this article, a statistical analysis of structural fragility curves is presented for bridge damage data obtained from the 1995 Hyogo-ken Nanbu (Kobe) earthquake and two-parameter lognormal distribution functions are used to represent the fragility curve with the parameters estimated by the maximum likelihood method.
Abstract: This paper presents a statistical analysis of structural fragility curves. Both empirical and analytical fragility curves are considered. The empirical fragility curves are developed utilizing bridge damage data obtained from the 1995 Hyogo-ken Nanbu (Kobe) earthquake. The analytical fragility curves are constructed on the basis of the nonlinear dynamic analysis. Two-parameter lognormal distribution functions are used to represent the fragility curves with the parameters estimated by the maximum likelihood method. This paper also presents methods of testing the goodness of fit of the fragility curves and estimating the confidence intervals of the two parameters (median and log-standard deviation) of the distribution. An analytical interpretation of randomness and uncertainty associated with the median is provided.
867Â citations
Additional excerpts
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TL;DR: A state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future are provided.
851Â citations
Cites methods from "Simulation of Stochastic Processes ..."
...From the wide variety of methods developed for the simulation of Gaussian stochastic processes and fields, two are most often used in applications: the spectral representation method [167,168] and the...
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Journal Article•
TL;DR: This paper presents a review of the current state-of-the-art of numerical methods for stochastic computations, with a particular emphasis on those based on generalized polynomial chaos (gPC) methodology.
Abstract: This paper presents a review of the current state-of-the-art of numerical methods for stochastic computations. The focus is on efficient high-order methods suitable for practical applications, with a particular emphasis on those based on generalized polynomial chaos (gPC) methodology. The framework of gPC is reviewed, along with its Galerkin and collocation approaches for solving stochastic equations. Properties of these methods are summarized by using results from literature. This paper also attempts to present the gPC based methods in a unified framework based on an extension of the classical spectral methods into multi-dimensional random spaces. AMS subject classifications: 41A10, 60H35, 65C30, 65C50
665Â citations
Cites background from "Simulation of Stochastic Processes ..."
...This remains an active research, see, for example, [32, 60, 61, 63, 70, 102]....
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