Simulation Of Random Processes Research Articles

Stability of elastic and viscoelastic systems under action of random stationary narrow-band loads

The stability is considered of the equilibrium state of elastic and viscoelastic systems, subjected to random parametric loads, with respect to perturbations of initial conditions. The stability is explored in the sense of Liapunov. The loads are assumed in the form of random narrow-band stationary processes. A numerical method for the analysis of the stability of such systems is offered, which is based on a method of statistical simulation of random processes, and on the determination of maximum Liapunov exponents. With the help of the method proposed the influence of the form of probability distributions, and of characteristics of the material, on the asymptotic stability of elastic and viscoelastic rods is investigated.

Simulation of random processes and rate-distortion theory

We study the randomness necessary for the simulation of a random process with given distributions, on terms of the finite-precision resolvability of the process. Finite-precision resolvability is defined as the minimal random-bit rate required by the simulator as a function of the accuracy with which the distributions are replicated. The accuracy is quantified by means of various measures: variational distance, divergence, Orstein (1973), Prohorov (1956) and related measures of distance between the distributions of random process. In the case of Ornstein, Prohorov and other distances of the Kantorovich-Vasershtein type, we show that the finite-precision resolvability is equal to the rate-distortion function with a fidelity criterion derived from the accuracy measure. This connection leads to new results on nonstationary rate-distortion theory. In the case of variational distance, the resolvability of stationary ergodic processes is shown to equal entropy rate regardless of the allowed accuracy. In the case of normalized divergence, explicit expressions for finite-precision resolvability are obtained in many cases of interest; and connections with data compression with minimum probability of block error are shown.

Numerical Methods for Stochastic Processes

Preliminaries. Computation of Expectations in Finite Dimension. Simulation of Random Processes. Deterministic Resolution of Some Markovian Problems. Stochastic Differential Equations and Brownian Functionals. Notes. References. Index.

Random process simulation of strong ground motion

The state-of-art of random process simulation model research of strong ground motion are analysed and the shortcomings of previous models is pointed out in this paper. Based on these, a random process model of ground motion with color spectrum on bedrock is presented which can give expression to the recent results in engineering seismology and near-field seismology and simulate the practioal spectrum function of strong ground motion as well. Moreover, the presented model can solve the incompatible problem between the horizontal model and the rotational model, and it is easy to determine the model parameters and to set up a practical design criterion of random seismic motion by use of the basic parameters used in the present aseismic design.

Seismic ground motion simulations from a class of spatial variability models

AbstractAn improved version of the spectral representation method (References 12–14) for the generation of simulations of random processes and random fields by means of the Fast Fourier Transform algorithm is developed. The new formulation produces simulations that are ergodic in the mean without any restricting assumptions at the origin of the spectra and leads to a faster convergence rate of the stochastic characteristics of the simulations to those of the random field. As an example of the methodology, simulations in space and time based on a spatial variability model for the seismic ground motions are generated.

Methods for correlation analysis of toxins and species present in random samples of phytoplankton

We developed and tested two new procedures to find which species present in samples of phytoplankton is responsible for the production of a toxin. The procedures represent a different form of correlation analysis that uses information on the presence or absence of the toxin, and on the relative abundance of each species of plankton in the samples. The efficiency of the algorithms is tested by random process simulation. The algorithms were clearly superior to known techniques dealing with correlations between binary variables to show the toxin producing microorganism. We used experimental toxin isolation from phytoplankton as an example of practical success using the most efficient of the algorithms tested.

Errors in Simulation of Random Processes

Simulation of random processes is frequently based on discrete approximations of the power spectral density of these processes. This study evaluates effects of these approximations on simulation-based estimates of the mean rate at which a Gaussian process crosses a level. The mean upcrossing rate is a useful probabilistic descriptor for the analysis of fatigue and first-excursion failures.

Random process simulation using a continuous system simulation language

Computer simulations of physical systems often include effects of random disturbances. A method is derived for including those disturbances in continuous system simulation language (CSSL) computations. This note shows that the effects of white (or colored) noise are easily implemented by using a random number generator of proper variance. The numerical example of an exponentially correlated random variable illustrates the simulation technique.

The simulation of random processes on digital computers: Unavoidable order

Nonrandom features of pseudorandom number generators are usually regarded as defects which may be minimized by improving the algorithms or resorting to larger computers. There are, however, certain elements of order which cannot be avoided even on digital devices of arbitrarily large capacity. For instance, on an N-state machine, pseudorandom number generators will terminate on fixed points or fall into loops after approximately √ N steps. Combinatorial arguments then can be used to show that for any given algorithm and any finite device it is highly improbable that there are more than three or four distinct terminal loops. All pseudorandom sequences merging into these loops can be traced backwards to their initial numbers; and the resulting pattern of ”ancestor numbers“ can be charted in detail for any computer, even for noninvertible algorithms. The conflicting requirements of randomness and finite numerical precision lead to an ordered distribution of the set of initial numbers. In this sense neither the initial nor the final states of a simulation of chaotic behavior can ever be random. The ”few loop“ constraint could generate patterns of self-organization in nonequilibrium systems. Experimental evidence from the hysteresis of Ewing arrays supports this conjecture.

Simulation of random processes with various probability density functions

Various relationships are derived for simulation of random processes with simple or composite probability density functions. Depending on the properties of the corresponding parameters the resulting process is either stationary or non-stationary. Practical digital simulation with the formulas derived is fast enough to be used in real time with computer controlled simulators.

A unified model for non-stationary and/or non-Gaussian random processes

An analytical model for non-stationary and/or non-Gaussian random processes described in the paper is based on a normal stationary random process. The non-stationarity is introduced as a deterministic dependence of the parameters of the marginal distribution function or those of the correlation function upon the argument t. Consideration that the mentioned parameters are random variables or stationary random processes results in generating non-Gaussian distributions of the unconditioned process. By combining deterministic and random components of the parameters' dependencies, non-stationary and simultaneously non-Gaussian random processes may be easily specified. The model described may be useful for analytical treatment, for identification of experimentally obtained realizations of random processes and for simulation of random processes on computers as well as in the laboratory.

The simulation of random processes on digital computers with Čebyšev mixing transformations

The iteration of the Čebyšev polynomial x 2 − 2 generates a mixing transformation on the interval x ε [−2, 2]. Extensive computer experiments have demonstrated that this is a convenient method for generating sequences of pseudo-random numbers. Despite the eventual domination of cumulative roundoff errors the asymptotic statistical features of the mixing are preserved. Multiple sequences of stochastically independent variables may be generated by these techniques. In practical computations the Čebyšev mixing eventually terminates in long pseudo-ergodic cycles. These results are linked with the general problem of simulating the stochastic behavior of physical systems by means of functional iteration. Contents. 1. Introduction. 2. Randomness Criteria. 3. Computer Simulation of Čebyšev Mixing—3.1. Single Sequences of Pseudo-random Numbers; 3.2. Computer Simulations: Growth of Round-off Errors; 3.3. Computer Simulations: Free Running and Terminal Cycles; 3.4. Multiple Sequences of Pseudo-random Numbers; 4. Čebyšev Mixing Theorems; Product Transformations; Probabilistic Metrics—Asymptotic Dispersion; Kolmogorov Entropy. 5. Variable Precision Simulations. 6. Terminal Cycles; Simulation of Pre-image Chains; Memory-Dependent Feedback. 7. Other Simulations of Random Processes; Probabilistic Metric for Baker's Transformation; Brolin's Theorem; Šarkovskii's Theorem; Hamiltonian Mechanics; Flow Equation; Non-embeddable Functions.

Digital simulation of environmental processes with respect to fatigue

To estimate the service fatigue life of dynamically loaded components and structures, fatigue tests with simulated loads must be carried out. This paper presents various methods of on-line digital simulation of real environmental processes, representing inputs of fatigue machines. According to the method of analysis adopted, this simulation can be based either on sinusoidal amplitudes in the form of blocks or individual cycles, or on random processes. The random process simulation can reproduce the probability density of amplitudes, the power spectral density, or both of them, depending on the fatigue damage hypothesis and philosophy of testing accepted.

The simulation of random processes in monte-carlo problems

The simulation of random processes in monte-carlo problems

Digital simulation of random processes and its applications

Efficient methods are presented for digital simulation of a general homogeneous process (multidimensional or multivariate or multivariate-multidimensional) as a series of cosine functions with weighted amplitudes, almost evenly spaced frequencies, and random phase angles. The approach is also extended to the simulation of a general non-homogeneous oscillatory process characterized by an evolutionary power spectrum. Generalized forces involved in the modal analysis of linear or non-linear structures can be efficiently simulated as a multivariate process using the cross-spectral density matrix computed from the spectral density function of the multidimensional excitation process. Possible applications include simulation of (i) wind-induced ocean wave elevation, (ii) spatial random variation of material properties, (iii) the fluctuating part of atmospheric wind velocities and (iv) random surface roughness of highways and airport runways.

Numerical Simulation of Stationary and Non-Stationary Gaussian Random Processes

The purpose of this paper is to present numerical methods for the computation of samples of a Gaussian random process x(t) with prescribed autocorrelation or power spectral density.

Deterministic simulation of random processes

and the sciences we are required to simulate random processes. The simulation is usually effected by a computer program which generates a non-random, deterministic sequence of numbers xl, x2, I * which is supposed to resemble a sequence of independent, random samples from the uniform probability distribution on the interval 0 ? < 1. The purpose of this paper is to define some general properties of random sequences and to investigate certain deterministic sequences which have some or all of these properties. We shall ignore the limitation that a digital computer with a finite word-length and a finite memory, operating under a single stored program, can produce only sequences of limited precision which are ultimately periodic. This limitation is a kind of round-off error. We shall take as a model of a deterministic mechanism any of the stored-program digital computers now commonly used for scientific computation modified in a single respect: let the wordlength be infinite; let rational and irrational numbers be recorded and computed with perfect precision. The fundamental problem approached in this paper is to construct an infinite, deterministic sequence xi which has every property shared by all infinite, random sequences of independent samples from the uniform distribution. Equidistribution is a first requirement of randomness. The sequence x is equidistributed in 0 < < 1 if, for 0 < a < b < 1,

Deterministic Simulation of Random Processes

Deterministic Simulation of Random Processes