Topic
Stochastic process
About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.
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01 Jan 2003TL;DR: In this paper, a method of RBD with the mixture of random variables with distributions and uncertain variables with intervals is proposed, where the reliability is considered under the condition of the worst combination of interval variables.
Abstract: In Reliability-Based Design (RBD), uncertainties usually imply for randomness. Nondeterministic variables are assumed to follow certain probability distributions. However, in real engineering applications, some of distributions may not be precisely known or uncertainties associated with some uncertain variables are not from randomness. These nondeterministic variables are only known within intervals. In this paper, a method of RBD with the mixture of random variables with distributions and uncertain variables with intervals is proposed. The reliability is considered under the condition of the worst combination of interval variables. In comparison with traditional RBD, the computational demand of RBD with the mixture of random and interval variables increases dramatically. To alleviate the computational burden, a sequential single-loop procedure is developed to replace the computationally expensive double-loop procedure when the worst case scenario is applied directly. With the proposed method, the RBD is conducted within a series of cycles of deterministic optimization and reliability analysis. The optimization model in each cycle is built based on the Most Probable Point (MPP) and the worst case combination obtained in the reliability analysis in previous cycle. Since the optimization is decoupled from the reliability analysis, the computational amount for MPP search is decreased to the minimum extent. The proposed method is demonstrated with a structural design example.Copyright © 2003 by ASME
245 citations
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TL;DR: This work considers a distributed team decision problem in which different agents obtain from the environment different stochastic measurements related to the same uncertain random vector, and assumes that each agent can compute an optimal tentative decision based upon his own observation.
Abstract: We consider a distributed team decision problem in which different agents obtain from the environment different stochastic measurements, possibly at different random times, related to the same uncertain random vector. Each agent has the same objective function and prior probability distribution. We assume that each agent can compute an optimal tentative decision based upon his own observation and that these tentative decisions are communicated and received, possibly at random times, by a subset of other agents. Conditions for asymptotic convergence of each agent's decison sequence and asymptotic agreement of all agents' decisions are derived.
245 citations
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TL;DR: In this article, a detailed examination of the relationship between stochastic Lagrangian models and second-moment closures is performed, in terms of the second-order tensor that defines a stochastically Lagrangians model.
Abstract: A detailed examination is performed of the relationship between stochastic Lagrangian models—used in PDF methods—and second‐moment closures. To every stochastic Lagrangian model there is a unique corresponding second‐moment closure. In terms of the second‐order tensor that defines a stochastic Lagrangian model, corresponding models are obtained for the pressure‐rate‐of‐strain and the triple‐velocity correlations (that appear in the Reynolds‐stress equation), and for the pressure‐scrambling term in the scalar flux equation. There is an advantage in obtaining second‐moment closures via this route, because the resulting models automatically guarantee realizability. Some new stochastic Lagrangian models are presented that correspond (either exactly or approximately) to popular Reynolds‐stress models.
245 citations
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TL;DR: A probabilistic model of the time spent in a state (referred to as duration) is developed, and the approach used for estimating its parameters is described and the method for determining the corresponding state transition probabilities from the estimated duration models is derived.
Abstract: Sound infrastructure deterioration models are essential for accurately predicting future conditions that, in turn, are key inputs to effective maintenance and rehabilitation decision making. The challenge central to developing accurate deterioration models is that condition is often measured on a discrete scale, such as inspectors’ ratings. Furthermore, deterioration is a stochastic process that varies widely with several factors, many of which are generally not captured by available data. Consequently, probabilistic discrete-state models are often used to characterize deterioration. Such models are based on transition probabilities that capture the nature of the evolution of condition states from one discrete time point to the next. However, current methods for determining such probabilities suffer from several serious limitations. An alternative approach addressing these limitations is presented. A probabilistic model of the time spent in a state (referred to as duration) is developed, and the approach used for estimating its parameters is described. Furthermore, the method for determining the corresponding state transition probabilities from the estimated duration models is derived. The testing for the Markovian property is also discussed, and incorporating the effects of history dependence, if found present, directly in the developed duration model is described. Finally, the overall methodology is demonstrated using a data set of reinforced concrete bridge deck observations.
245 citations