102,929 research outputs found
A comparative analysis of fault detection schemes for stochastic continuous-time dynamical systems
This paper addresses a comparative analysis of the existing schemes for fault detection in continuous-time stochastic dynamical systems. Such schemes prove to be efficient when dealing with specific types of fault functions; on the other hand, they show very different performance sensitivity when dealing with new fault profiles and system noise. The study suggests the use of a combined scheme, supervised by a high level decision rule set
A New Approach To Estimate The Collision Probability For Automotive Applications
We revisit the computation of probability of collision in the context of
automotive collision avoidance (the estimation of a potential collision is also
referred to as conflict detection in other contexts). After reviewing existing
approaches to the definition and computation of a collision probability we
argue that the question "What is the probability of collision within the next
three seconds?" can be answered on the basis of a collision probability rate.
Using results on level crossings for vector stochastic processes we derive a
general expression for the upper bound of the distribution of the collision
probability rate. This expression is valid for arbitrary prediction models
including process noise. We demonstrate in several examples that distributions
obtained by large-scale Monte-Carlo simulations obey this bound and in many
cases approximately saturate the bound. We derive an approximation for the
distribution of the collision probability rate that can be computed on an
embedded platform. In order to efficiently sample this probability rate
distribution for determination of its characteristic shape an adaptive method
to obtain the sampling points is proposed. An upper bound of the probability of
collision is then obtained by one-dimensional numerical integration over the
time period of interest. A straightforward application of this method applies
to the collision of an extended object with a second point-like object. Using
an abstraction of the second object by salient points of its boundary we
propose an application of this method to two extended objects with arbitrary
orientation. Finally, the distribution of the collision probability rate is
identified as the distribution of the time-to-collision.Comment: Revised and restructured version, discussion of extended vehicles
expanded, section on TTC expanded, references added, other minor changes, 17
pages, 18 figure
Levy stable noise induced transitions: stochastic resonance, resonant activation and dynamic hysteresis
A standard approach to analysis of noise-induced effects in stochastic
dynamics assumes a Gaussian character of the noise term describing interaction
of the analyzed system with its complex surroundings. An additional assumption
about the existence of timescale separation between the dynamics of the
measured observable and the typical timescale of the noise allows external
fluctuations to be modeled as temporally uncorrelated and therefore white.
However, in many natural phenomena the assumptions concerning the
abovementioned properties of "Gaussianity" and "whiteness" of the noise can be
violated. In this context, in contrast to the spatiotemporal coupling
characterizing general forms of non-Markovian or semi-Markovian L\'evy walks,
so called L\'evy flights correspond to the class of Markov processes which
still can be interpreted as white, but distributed according to a more general,
infinitely divisible, stable and non-Gaussian law. L\'evy noise-driven
non-equilibrium systems are known to manifest interesting physical properties
and have been addressed in various scenarios of physical transport exhibiting a
superdiffusive behavior. Here we present a brief overview of our recent
investigations aimed to understand features of stochastic dynamics under the
influence of L\'evy white noise perturbations. We find that the archetypal
phenomena of noise-induced ordering are robust and can be detected also in
systems driven by non-Gaussian, heavy-tailed fluctuations with infinite
variance.Comment: 7 pages, 8 figure
- …