Showing papers on "Stochastic simulation published in 1997"
TL;DR: In this paper, the authors propose an iterative technique that couples geostatistics and optimization to generate equally likely realizations of transmissivity fields conditional to both transmissivities and piezometric data.
347 citations
TL;DR: In this article, the authors show that the recently proposed concept of Brownian configuration fields in viscoelastic flow calculations can be regarded as an extremely powerful extension of variance reduction techniques based on parallel process simulation.
Abstract: Stochastic simulation techniques, such as Brownian dynamics, provide us an extremely powerful tool for solving the usually nonlinear equations describing polymer dynamics in solutions and melts [1]. However, the most challenging problems (e.g. the investigation of the universal behaviour of long polymer chains, or the flow calculation based on stochastic simulation techniques) involve a very large number of degrees of freedom and hence require an enomous amount of computer time. In order to solve such problems on currently available computers it is therefore necessary to develop strategies to drastically suppress the level of the fluctuations in the simulations. The purpose of this note is to show that the recently proposed concept of Brownian configuration fields [2] in viscoelastic flow calculations can be regarded as an extremely powerful extension of variance reduction techniques based on parallel process simulation.
123 citations
Book•
01 Nov 1997
TL;DR: The basic concepts the concept of a random variable a vector random variable introduction to estimation sequence of (IID) random variables random processes the Poisson and Gaussian random processes processing of random processes Markov chains case study - a bus-based switch architecture.
Abstract: The basic concepts the concept of a random variable a vector random variable introduction to estimation sequence of (IID) random variables random processes the Poisson and Gaussian random processes processing of random processes Markov chains case study - a bus-based switch architecture. Appendices: set theory primer counting methods the historical development of the theory modelling of randomness in engineering systems - a summary.
115 citations
TL;DR: This work demonstrates that the Gaussian linear random signals idea can be used to estimate the extreme response of a jack-up in a severe sea-state in a robust and efficient manner and in good agreement with those obtained from a full random time-domain simulation.
Abstract: Random simulations are often used to simulate the statistics of storm-driven waves. Work on Gaussian linear random signals has lead to a method for embedding a large wave into a random sequence in such a way that the composite signal is virtually indistinguishable (in a rigorous statistical limit) from a purely random occurrence of a large wave. We demonstrate that this idea can be used to estimate the extreme response of a jack-up in a severe sea-state in a robust and efficient manner. Results are in good agreement with those obtained from a full random time-domain simulation.
103 citations
01 Dec 1997
TL;DR: The paper summarizes some important results at the intersection of the elds of Bayesian statistics and stochastic simulation and presents a new Bayesian formulation for the problem of output analysis for a single system.
Abstract: The paper summarizes some important results at the intersection of the elds of Bayesian statistics and stochastic simulation. Two statistical analysis issues for stochastic simulation are discussed in further detail from a Bayesian perspective. First, a review of recent work in input distribution selection is presented. Then, a new Bayesian formulation for the problem of output analysis for a single system is presented. A key feature is analyzing simulation output as a random variable whose parameters are an unknown function of the simulation’s inputs. The distribution of those parameters is inferred from simulation output via Bayesian response-surface methods. A brief summary of Bayesian inference and decision making is included for reference.
82 citations
TL;DR: In this article, the kinetic master equation for the title processes can be formulated as a traditional deterministic set of coupled differential reaction-rate equations, or as a stochastic process in which each reaction is a random-walk transition in energy species space.
Abstract: The kinetic master equation for the title processes can be formulated as a traditional deterministic set of coupled differential reaction-rate equations, or, alternatively, as a stochastic process in which each reaction is a random–walk transition in energy–species space. This stochastic description is the basis for three methods we describe here to numerically solve the kinetic master equation for chemically activated unimolecular reactions. The first method allows the calculation of the complete time evolution within a given mechanism, and is based on Gillespie’s exact stochastic method (ESM). It is essentially a Monte Carlo simulation of the stochastic reaction processes. The second method allows for the direct calculation of the steady-state product distribution (DCPD). It describes the random walk within the framework of a discrete time Markov chain, and reduces the calculation of the steady-state product distribution to a fairly simple matrix algebra problem. The third method calculates the steady-s...
80 citations
TL;DR: In this paper, the influence of unmixedness on thermo-chemical properties of partially-stirred-reactors (PaSR) by stochastic simulation is investigated.
Abstract: Modeling of Partially-Stirred-Reactors (PaSR) by stochastic simulation is carried out for investigating the influence of unmixedness on thermo-chemical properties First, the joint scalar probability density function (pdf) of the PaSR is derived using a control volume analysis to provide theory for development of stochastic simulation procedures Second, through numerical exploration and analysis, an improved stochastic algorithm is developed to eliminate the dependence of solution on time step The limitations on age distribution from the stochastic simulation are identified For nonpremixed combustion with either the modified Curl's mixing model or the Linear-Mean-Square-Estimation (LMSE) mixing model, analytic expressions are derived for the unmixedness in terms of residence time and mixing frequency Numerical simulations have been performed revealing that the unmixed nature has profound influence on ignition delay and NO formation in PaSR with hydrogen combustion The performance of recently
73 citations
TL;DR: The stochastic finite element method relies on viewing the random aspect of the problem as an added dimension, and on treating random variables and processes as functions defined over that dimension.
Abstract: A formulation for the stochastic finite element method is presented which is a natural extension of the deterministic finite element method. Discretization of the random dimension is achieved via two spectral expansions. One of them is used to represent the coefficients of the differential, equation which model the random material properties, the other is used to represent the random solution process. The method relies on viewing the random aspect of the problem as an added dimension, and on treating random variables and processes as functions defined over that dimension. The versatility of the method is demonstrated by discussing, as well, some non-traditional problems of stochastic mechanics.
71 citations
Abstract: The study of the Burgers equation with a random force leads via a Hopf-Cole type transformation to a stochastic heat equation having a white noise with spatial parameters type potential The latter can be studied by means of a general model of directed polymers in random environments with two point random potentials These models exhibit a Gaussian behavior at large times and have certain stationary distributions which yield the corresponding results for the above stochastic heat and Burgers equations
49 citations
TL;DR: In this article, an efficient approach to the analysis of non-stationary random responses of structures subjected to evolutionary random excitation is proposed, which is first transformed into a pseudo excitation to generate deterministic equations of motion, which are then solved by means of a modified high precision direct integration method.
43 citations
Book•
05 Jun 1997
TL;DR: The basic theory of stochastic processes and their application in probability calculus with applications can be found in this article, with a focus on random excursions and failure probabilities of simple linear systems.
Abstract: Fundamentals of Probability Calculus with Applications. The Basic Theory of Stochastic Processes. Random Excitation and Response of Simple Linear Systems. Random Excursions and Failure Probabilities. Random Excitation and Response of Multiple and Continuous Systems. Some Fundamental Stochastic Processes. Fourier Analysis and Data Processing. Earthquake Hazard and Seismic Risk Analysis. References. Index.
01 Dec 1997
TL;DR: This paper summarizes the current state of the art on uniform random number generation for stochastic simulation, discusses some linear methods and their theoretical analysis, and provides pointers to further details and to recommended implementations.
Abstract: This paper summarizes the current state-of-the-art on uniform random number generation for stochastic simulation. It recalls the basic ideas, discusses some linear methods and their theoretical analysis, and provides pointers to further details and to recommended implementations.
TL;DR: In this article, a stochastic innovation diffusion model is proposed for electricity consumption in Greece, which is based on the Bass model and is solved analytically by using the theory of reducible Stochastic Di↵erential equations.
Abstract: SUMMARY In this paper a stochastic innovation di⁄usion model is proposed derived by introducing stochasticity into the well-known Bass model. The stochastic model is solved analytically by using the theory of reducible stochastic di⁄erential equations and the first moment of the resulting stochastic process is presented. The parameter estimators of the model are derived by using a procedure which provides the maximum likelihood estimators (MLE) using time series data. Finally, the model is applied to the data of electricity consumption in Greece. Using a simulation technique, it is possible to predict the performance of the consumption process by defining a subdomain to which all possible trajectories of the process should belong with a predefined probability. ( 1997 by John Wiley & Sons, Ltd.
TL;DR: In this article, an approach to the simulation of discretized, nonhomogeneous, spatial random fields is presented to solve the simulation problem, an effective version of the rejection method and conditional probability distributions is implemented.
21 Apr 1997
TL;DR: A stochastic simulation technique for subset selection in time series models, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework, which is applied to the selection of subset linear AR models.
Abstract: We present a stochastic simulation technique for subset selection in time series models, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework. As an example, the method is applied to the selection of subset linear AR models, in which only significant lags are included. Joint sampling of the indicators and parameters is found to speed convergence. We discuss the possibility of model mixing where the model is not well determined by the data, and the extension of the approach to include non-linear model terms.
TL;DR: In this paper, the authors consider discretized random perturbations of hyperbolic dynamical systems and prove that when perturbation tends to zero invariant measures, corresponding Markov chains converge to the Sinai-Bowen-Ruelle measure of the dynamical system.
Abstract: I consider discretized random perturbations
of hyperbolic dynamical systems
and prove that when perturbation
parameter tends to zero invariant measures
of corresponding Markov chains converge to
the Sinai-Bowen-Ruelle measure of the dynamical system. This
provides a robust method for computations of
such measures and for visualizations of some hyperbolic
attractors by modeling randomly perturbed
dynamical systems on a computer.
Similar results are true for
discretized random perturbations
of maps of the interval satisfying the Misiurewicz
condition considered in [KK].
01 Jan 1997
TL;DR: In this article, the distribution of the maximum score statistic for detecting a signal of known shape, but unknown amplitude, location, and scale is discussed when the underlying noise process is a homogeneous Poisson process.
Abstract: The distribution of the maximum score statistic for detecting a signal of known shape, but unknown amplitude, location, and scale is discussed when the underlying noise process is a homogeneous Poisson process. The approximation is based on an exponential change of measure to evaluate asymptotically the expected number of local maxima of a random field.
01 Dec 1997
TL;DR: This tutorial discusses some basic techniques for modeling dependence between the random variables that are inputs to a simulation model, with the main emphasis being continuous bivariate distributions that have flexible marginal distributions and that are readily extended to higher dimensions.
Abstract: We discuss some basic techniques for modeling dependence between the random variables that are inputs to a simulation model, with the main emphasis being continuous bivariate distributions that have flexible marginal distributions and that are readily extended to higher dimensions. First we examine the bivariate normal distribution and its advantages and drawbacks for use in simulation studies. To achieve a greater variety of distributional shapes while accurately reflecting a desired dependency structure, we discuss bivariate Johnson distributions. Although space limitations preclude inclusion in this article, the oral presentation of this tutorial will also include discussions of how to use (a) bivariate B ezier distributions as a means for achieving even greater flexibility in modeling the marginal distributions, and (b) ARTA (AutoRegressive To Anything) processes as a means for generating an entire stochastic process with specied marginals and a desired covariance structure.
TL;DR: In this paper, a necessary and sufficient condition is obtained for a Poisson binomial random variable to be stochastically larger (or smaller) than a binomial variable, which has obvious applications in the stochastic comparisons of lifetimes of k-out-of-n systems having independent components.
Abstract: A necessary and sufficient condition is obtained for a Poisson binomial random variable to be stochastically larger (or smaller) than a binomial random variable. It is then used to deal with the stochastic comparisons of order statistics from heterogeneous populations with those from a homogeneous population. The result has obvious applications in the stochastic comparisons of lifetimes of k-out-of-n systems having independent components.
01 Jan 1997
TL;DR: In this paper, the authors presented stochastic simulation methods for developing the distribution of fracture density in one of the highly fractured reservoirs in Saudi Arabia, and the resulting fracture density field was useful in generating a 3D fracture permeability field for reservoir simulation.
Abstract: One of the most difficult tasks in the characterization of reservoir heterogeneities is the representation of naturally fractured reservoirs. Geocellular models for reservoir simulation often require geological interpretation of the distribution of natural fractures both areally and vertically. The FMI data from horizontal wells provide valuable information about the distribution and orientation of natural fractures. Stochastic approaches can be useful in simulating fracture density derived from the FMI logs that would honor the known data. This paper presents stochastic simulation methods for developing the distribution of fracture density in one of the highly fractured reservoirs in Saudi Arabia. Sequential indicator simulation (SIS) method was used with two different variogram models, namely, the fractal and the spherical correlation models. The resulting fracture density field was useful in generating a 3D fracture permeability field for reservoir simulation by using it as a secondary data set in a permeability co-conditional simulation task reported elsewhere.
TL;DR: Three alternatives for combining a deterministic approximation with a stochastic simulation estimator are investigated: binary choice, linear combination, and Bayesian analysis.
TL;DR: In this article, a method of local multipliers is developed for treating the local stability of such dynamical processes corresponding to infinite-dimensional dynamical systems, in which the stochasticity is introduced through randomly fluctuating parameters.
Abstract: A particular type of random dynamical process is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical processes corresponding to infinite-dimensional dynamical systems. The method is illustrated by several examples, by the random diffusion equation, random wave equation, and random Schrodinger equation. The evolution equation for the density matrix of a quasiopen statistical system subject to the action of random surrounding is considered. The stationary solutions to this equation are found to be unstable against arbitrary small finite random perturbations. The notion of random structural stability is introduced.
01 Dec 1997
TL;DR: A trace collection technique capable of collecting accurate trace data from Novell Netware servers is described, which is used to construct accurate stochastic simulation models from acquired trace data.
Abstract: In this paper, we describe a technique to construct accurate stochastic simulation models from acquired trace data. The resulting simulation models accept input trace data and return estimates of disk request service times. In addition, we describe a trace collection technique capable of collecting accurate trace data from Novell Netware servers. These traces are used to construct a simulation model of a Novell Netware 1/0 subsystem that is used to study the impact of disk data reorganization on 1/0 performance.
TL;DR: In this article, stochastic simulation techniques were applied to GLEAMS, a deterministic vadose zone solute transport model, to simulate soil water changes and nitrate (NO 3 − ) concentrations at various depths in the top 1.2 m heterogeneous soil profiles of three research plots in southern Ohio.
TL;DR: In this article, the random finite element method is derived for structural response analysis under stochastic load actions, where the random processes of load actions are treated as random sequences and the random variables are expanded based on the second-order perturbation equations.
TL;DR: In this article, the acoustic impedance and porosity conditioned to seismic and well data are modeled using the linear relationship between reeection coeecients and seismic amplitude under a convolution model.
Abstract: Stochastic modeling of the acoustic impedance and poros-ity conditioned to seismic and well data can be done using the linear relationship between reeection coeecients and seismic amplitude under a convolution model.
TL;DR: In this paper, an efficient stochastic simulation method for generating sample time histories of multidimensional, spatially correlated, stationary Gaussian random fields is presented for generating seismic ground motion.
Abstract: An efficient stochastic simulation method is presented for generating sample time histories of multidimensional, spatially correlated, stationary Gaussian random fields. A key feature of the method is the use of filtering functions in directly expressing the conditional mean value of any component of the random field. The general formulation and an updating algorithm for determining the required filtering functions for simulation of any general multidimensional random field are established. Also, emphasis is placed on the efficiencies, which can be achieved when relatively simple restrictions are placed on the cross-spectral densities and the incoherence structure of the random field. These restrictions, which are commonly used in modeling seismic ground motion, are shown to allow the computational effort to be reduced by a factor of more than 100 for a three-dimensional random field. Numerical results are presented to illustrate the application of the direct simulation method to the generation of time histories of seismic ground motion. The method is shown to be both efficient and accurate.
TL;DR: An algorithm for the stochastic simulation of ligand-receptor interactions based on 10(4)-10(5) fictitious binding sites is developed, showing that the mathematical formalism of mass action kinetics is predicted on purely statistical grounds.
TL;DR: The aim of this paper is to reproduce the texture of rough surfaces by means of simulations of probabilistic random function models, and involves the use of a repulsion distance in the simulation, as could be expected from the variogram of the data.
Abstract: The aim of this paper is to reproduce the texture of rough surfaces by means of simulations of probabilistic random function models. The studied texture is obtained by a physical process, the electro-erosion discharge. After an introduction to this process and to the characterization of random functions, different morphological models are reviewed and tested: the Boolean random function, the dead leaves random function, the sequential alternate random function, and the dilution random function. They all involve a combination of a Poisson point process and of elementary patterns, the primary random function. For each model, the case of cylinder primary functions is first considered for illustration; then simulations with roughness craters are compared to rough surfaces. The final model involves the use of a repulsion distance in the simulation, as could be expected from the variogram of the data.