Time-dependent Diffusion in Transient Splenial Lesion: Comparison between Oscillating-Gradient Spin-echo Measurements and Monte-Carlo Simulation

Time-dependent reliability analysis requires the use of the extreme value of a response. The extreme value function is usually highly nonlinear, and traditional reliability methods, such as the first order reliability method (FORM), may produce large errors. The solution to this problem is using a surrogate model of the extreme response. The objective of this work is to improve the efficiency of building such a surrogate model. A mixed efficient global optimization (m-EGO) method is proposed. Different from the current EGO method, which draws samples of random variables and time independently, the m-EGO method draws samples for the two types of samples simultaneously. The m-EGO method employs the adaptive Kriging–Monte Carlo simulation (AK–MCS) so that high accuracy is also achieved. Then, Monte Carlo simulation (MCS) is applied to calculate the time-dependent reliability based on the surrogate model. Good accuracy and efficiency of the m-EGO method are demonstrated by three examples.

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Monte Carlo simulation of time-dependent, transport-limited fluorescent boundary measurements in frequency domain

Medical Physics ◽

10.1118/1.2710549 ◽

2007 ◽

Vol 34 (4) ◽

pp. 1298-1311 ◽

Cited By ~ 7

Author(s):

Tianshu Pan ◽

John C. Rasmussen ◽

Jae Hoon Lee ◽

Eva M. Sevick-Muraca

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Frequency Domain ◽

Time Dependent ◽

Boundary Measurements ◽

Dependent Transport

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Probit-Based Time-Dependent Stochastic User Equilibrium Traffic Assignment Model

Transportation Research Record Journal of the Transportation Research Board ◽

10.3141/2085-10 ◽

2008 ◽

Vol 2085 (1) ◽

pp. 86-94 ◽

Cited By ~ 15

Author(s):

Kuilin Zhang ◽

Hani S. Mahmassani ◽

Chung-Cheng Lu

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Spatial Correlation ◽

Traffic Assignment ◽

User Equilibrium ◽

The Other ◽

Time Dependent ◽

Stochastic User Equilibrium ◽

Assignment Model ◽

Temporal And Spatial

This study presents a time-dependent stochastic user equilibrium (TDSUE) traffic assignment model within a probit-based path choice decision framework that explicitly takes into account temporal and spatial correlation (traveler interactions) in travel disutilities across a set of paths. The TDSUE problem, which aims to find time-dependent SUE path flows, is formulated as a fixed-point problem and solved by a simulation-based method of successive averages algorithm. A mesoscopic traffic simulator is employed to determine (experienced) time-dependent travel disutilities. A time-dependent shortest-path algorithm is applied to generate new paths and augment a grand path set. Two vehicle-based implementation techniques are proposed and compared in order to show their impact on solution quality and computational efficiency. One uses the classical Monte Carlo simulation approach to explicitly compute path choice probabilities, and the other determines probabilities by sampling vehicles’ path travel costs from an assumed perception error distribution (also using a Monte Carlo simulation process). Moreover, two types of variance-covariance error structures are discussed: one considers temporal and spatial path choice correlation (due to path overlapping) in terms of aggregated path travel times, and the other uses experienced (or empirical) path travel times from a sample of individual vehicle trajectories. A set of numerical experiments are conducted to investigate the convergence pattern of the solution algorithms and to examine the impact of temporal and spatial correlation on path choice behavior.

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