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Infection Risk Mitigation Using Pedestrian Dynamics
Published in AnnaMarie Bliss, Dak Kopec, Architectural Factors for Infection and Disease Control, 2023
Ashok Srinivasan, Sirish Namilae
Low-Discrepancy Sequence. A low-discrepancy sequence (LDS) can cover the space more efficiently theoretically, with star discrepancy asymptotically proportional to logdN/N (Chunduri et al., 2018). It also permits a check for convergence, enabling us to stop quickly once convergence is reached. However, when d is large, one is often not in the asymptotic region. Recent work has indicated that a pseudorandom sweep is computationally more efficient when moderate accuracy is adequate and that an LDS sweep is preferable when high accuracy is required.
Uncertainty quantification of offshore wind farms using Monte Carlo and sparse grid
Published in Energy Sources, Part B: Economics, Planning, and Policy, 2022
Pascal Richter, Jannick Wolters, Martin Frank
An improvement to the classical Monte Carlo method is the quasi-Monte Carlo method (QMC). It relies on the sample principle like the classical Monte Carlo method with the difference being that it makes use of a low-discrepancy sequence in order to generate its quasi-random numbers. Morokoff and Caflisch (1995) examined three different low discrepancy sequences: the Halton, Sobol, and Faure sequence. The result indicated that Halton sequences are best for up to six dimensions and the Sobol sequence is best for all higher dimensions. As we are interested in these high-dimensional cases, the Sobol sequence is used in this paper. The Sobol sequence can be briefly explained as a sequential instruction set that fills a multi-dimensional hypercube, while trying to avoid the creation of void regions. These created values are deterministic and thus are called pseudo-random, but they evenly fill the hypercube and therefore potentially lead to a faster convergence compared to the pure Monte–Carlo method. The more equally spaced sample points can be seen in Figure 9b. For a detailed explanation regarding the generation of the sequence, see Bratley and Fox (1988). By using the Sobol sequence to generate pseudo-random numbers, the convergence of the quasi-Monte Carlo is of the order , see Caflisch (1998). This means that for small dimensions, the quasi-Monte Carlo simulation only needs to compute roughly five to ten times fewer samples in order to achieve one additional digit of accuracy compared to the classical Monte Carlo method.
Seismic reliability evaluation of spatially correlated pipeline networks by
Published in Structure and Infrastructure Engineering, 2022
Benwei Hou, Qianyi Xu, Zilan Zhong, Junyan Han, Huiquan Miao, Xiuli Du
As shown in Eq. (17), the standard MC converges with the sample numbers N as O(N−1/2). One can reduce the variance σg or increase the sample numbers N to improve the computational convergence. Thus, to improve the performance of standard MC by random samples, many variance reduction methods namely, Latin hypercube sampling, stratified sampling and importance sampling have been implemented in the previous studies (Eskandari et al., 2020; Jayaram & Baker, 2010). In addition, QMC simulation is another approach to speed up the convergence of standard MC, which generates sample by low-discrepancy sequence (LDS). By using this method, more evenly distributed sample points can be obtained, resulting in better computational convergence.
Effect of Damping Modeling and Characteristics on Seismic Vulnerability Assessment of Multi-Frame Bridges
Published in Journal of Earthquake Engineering, 2021
Mohammad Abbasi, Mohamed A. Moustafa
When a proper suite of ground motions is chosen, a bridge model must be sampled. The probabilistic sampling of the bridge models allows for incorporating uncertainties such as those associated with material and geometric properties. In case of geometry, each bridge sub-class was produced by Latin-hypercube sampling. Other modeling parameters uncertainties included material strength, deck gap, mass, damping, and load direction, and were taken into account using Quasi-Monte Carlo sampling [Morokoff and Caflisch, 1995]. Quasi-Monte Carlo sampling is a technique used to sample random variables governed by probability density functions. It uses quasi-random (also known as low-discrepancy) sequences instead of random or pseudorandom sequences and, in turn, is more accurate than other sampling techniques. Table 3 summarizes some of the uncertainties modeling parameters and their relevant probability distributions. Note that λ, μ are mean and ζ, σ are dispersion values in lognormal and normal distributions, respectively, while l and u are the lower and upper limits in uniform distribution, respectively.