175,973 research outputs found
A Method for the Combination of Stochastic Time Varying Load Effects
The problem of evaluating the probability that a structure becomes unsafe under a
combination of loads, over a given time period, is addressed. The loads and load effects
are modeled as either pulse (static problem) processes with random occurrence time, intensity and a specified shape or intermittent continuous (dynamic problem) processes which
are zero mean Gaussian processes superimposed 'on a pulse process. The load coincidence
method is extended to problems with both nonlinear limit states and dynamic responses,
including the case of correlated dynamic responses. The technique of linearization of a
nonlinear limit state commonly used in a time-invariant problem is investigated for timevarying
combination problems, with emphasis on selecting the linearization point. Results
are compared with other methods, namely the method based on upcrossing rate, simpler
combination rules such as Square Root of Sum of Squares and Turkstra's rule. Correlated
effects among dynamic loads are examined to see how results differ from correlated static
loads and to demonstrate which types of load dependencies are most important, i.e., affect'
the exceedance probabilities the most.
Application of the load coincidence method to code development is briefly discussed.National Science Foundation Grants CME 79-18053 and CEE 82-0759
Chord distribution functions of three-dimensional random media: Approximate first-passage times of Gaussian processes
The main result of this paper is a semi-analytic approximation for the chord
distribution functions of three-dimensional models of microstructure derived
from Gaussian random fields. In the simplest case the chord functions are
equivalent to a standard first-passage time problem, i.e., the probability
density governing the time taken by a Gaussian random process to first exceed a
threshold. We obtain an approximation based on the assumption that successive
chords are independent. The result is a generalization of the independent
interval approximation recently used to determine the exponent of persistence
time decay in coarsening. The approximation is easily extended to more general
models based on the intersection and union sets of models generated from the
iso-surfaces of random fields. The chord distribution functions play an
important role in the characterization of random composite and porous
materials. Our results are compared with experimental data obtained from a
three-dimensional image of a porous Fontainebleau sandstone and a
two-dimensional image of a tungsten-silver composite alloy.Comment: 12 pages, 11 figures. Submitted to Phys. Rev.
Large deviations for a damped telegraph process
In this paper we consider a slight generalization of the damped telegraph
process in Di Crescenzo and Martinucci (2010). We prove a large deviation
principle for this process and an asymptotic result for its level crossing
probabilities (as the level goes to infinity). Finally we compare our results
with the analogous well-known results for the standard telegraph process
Zero-Crossing Statistics for Non-Markovian Time Series
In applications spaning from image analysis and speech recognition, to energy
dissipation in turbulence and time-to failure of fatigued materials,
researchers and engineers want to calculate how often a stochastic observable
crosses a specific level, such as zero. At first glance this problem looks
simple, but it is in fact theoretically very challenging. And therefore, few
exact results exist. One exception is the celebrated Rice formula that gives
the mean number of zero-crossings in a fixed time interval of a zero-mean
Gaussian stationary processes. In this study we use the so-called Independent
Interval Approximation to go beyond Rice's result and derive analytic
expressions for all higher-order zero-crossing cumulants and moments. Our
results agrees well with simulations for the non-Markovian autoregressive
model
Level crossings and other level functionals of stationary Gaussian processes
This paper presents a synthesis on the mathematical work done on level
crossings of stationary Gaussian processes, with some extensions. The main
results [(factorial) moments, representation into the Wiener Chaos, asymptotic
results, rate of convergence, local time and number of crossings] are
described, as well as the different approaches [normal comparison method, Rice
method, Stein-Chen method, a general -dependent method] used to obtain them;
these methods are also very useful in the general context of Gaussian fields.
Finally some extensions [time occupation functionals, number of maxima in an
interval, process indexed by a bidimensional set] are proposed, illustrating
the generality of the methods. A large inventory of papers and books on the
subject ends the survey.Comment: Published at http://dx.doi.org/10.1214/154957806000000087 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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