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Dynamic network models
Published in Harry Crane, Probabilistic Foundations of Statistical Network Analysis, 2018
For n ≥ 1, let Wn be the space of rewiring maps acting on {0,1}n×n $ \{ 0, 1\}^{n \times n} $ . To construct a continuous time rewiring process Y = (Y(t))t≥0 on {0,1}n×n $ \{ 0, 1\}^{n \times n} $ , we let ω be a finite measure on Wn and write dt to denote Lebesgue measure on [0,∞) $ [0, \infty ) $ 4 Let W = {(t, Wt)} ⊆ [0, ∞) × ω be a Poisson point process with intensity measure dt ⊗ ω, where dt denotes Lebesgue measure on [0, ∞) and dt ⊗ ω denotes the product measure of dt and ω. Given W, construct Y $ {\text{Y}} $ by fixing any initial state Y(0) and defining Y(t) for each t > 0 byΨ(τ)=Ωτ(Ψ(τ−))Ζ ift is an atom time ofW $ of\,\,W $ , i.e., if (t, Wt) ∊ W for some Wt ∊ Wn, where Y(t-)=lims↑tY(s) $ Y(t - ) = \mathop {\lim }\limits_{s \uparrow t} Y(s) $ is the state of the process in the instant immediately preceding time t, andΨ(τ)=Ψ(τ−)Ζ otherwise.
Simulation of Cumulative Absolute Velocity Consistent Endurance Time Excitations
Published in Journal of Earthquake Engineering, 2021
Mohammadreza Mashayekhi, Homayoon E. Estekanchi, Abolhassan Vafai, Seyyed Ali Mirfarhadi
Several attempts were made by a number of researchers in the field to address the aforementioned difficulties. In this context, endurance time (ET) analysis had been developed to function as a simple yet efficient tool for time history dynamic analyses. Inspired by an exercise test in medicine [Riahi et al., 2009], the concept of the ET method was established by Estekanchi et al. [2004]. In the ET method, structures are subjected to a set of intensifying acceleration functions (endurance time excitation functions, ETEFs) and response of structures are monitored versus the analysis time passed. Furthermore, the time is an indication of seismic-intensity level in this method. The intensification of ETEFs lead to create a wide range of intensity levels in a single time history analysis. By correlating time and intensity measure, maximum seismic demand of structures for various intensity levels are determined as a function of intensity measure. Therefore, in the ET method, structural responses at different intensity levels are obtained in a single time history analysis, thereby reducing the computational demand. This is the main difference between the ET method and conventional time history analyses which require separate analyses for each intensity level.
Modelling and Seismic Response Analysis of Italian Code-Conforming Base-Isolated Buildings
Published in Journal of Earthquake Engineering, 2018
L. Ragni, D. Cardone, N. Conte, A. Dall’Asta, A. Di Cesare, A. Flora, G. Leccese, F. Micozzi, C. Ponzo
The seismic vulnerability of the selected case study buildings has been assessed by means of multi-stripe non-linear dynamic analyses carried out by considering 10 intensity levels with 20 ground motions per stripe. In particular, the Intensity Measure (IM) selected to represent the earthquake intensity levels is the spectral acceleration (5%-damped) corresponding to a reference period (conditioning period) chosen as close as possible to the design value of the fundamental period of vibration of the base-isolated building. The compatibility with a Conditional Mean Spectrum (CSM) assures that all the selected records are scaled so that they have the same spectral ordinate at the conditioning period for each intensity levels. Reference to [Iervolino et al., 2017, 2018] can be made for details about records selection procedure. The seismic response of isolated buildings has been evaluated at two Limit States: Global Collapse (GC_LS) and Usability-Preventing Damage (UPD_LS) according to criteria illustrated in the following sections.
Appropriate ground motion intensity measures for estimating the earthquake demand of floor acceleration-sensitive elements in super high-rise buildings
Published in Structure and Infrastructure Engineering, 2018
As a quantitative factor in describing uncertainties in ground motions, intensity measure (IM) plays a key role in the framework of performance-based earthquake engineering (Moehle & Deierlein, 2004; Stewart et al., 2002). Selection of IM depends not only on the structural system under consideration but also on the engineering performance demand measure (DM) of concern (Riddell 2007). Several studies (Guan, Du, Cui, Zeng, & Jiang, 2015; Lu, Ye, Lu, Li, & Ma, 2013b; Zhang, He, & Yang, 2018) have focussed on the selection and development of IMs for super high-rise buildings to account for the effects of long vibration period and higher vibration modes, where the inter-story drift ratio is used as a DM. For drift-sensitive non-structural elements, e.g. infill walls, curtain walls and glasses, the output from those studies can also be applied. However, for floor acceleration-sensitive non-structural elements, e.g. building contents and equipment, the observations from those studies are not applicable. It is necessary to choose or develop an appropriate IM regarding this DM concern.