16,477 research outputs found
Stochastic Stability Analysis of Discrete Time System Using Lyapunov Measure
In this paper, we study the stability problem of a stochastic, nonlinear,
discrete-time system. We introduce a linear transfer operator-based Lyapunov
measure as a new tool for stability verification of stochastic systems. Weaker
set-theoretic notion of almost everywhere stochastic stability is introduced
and verified, using Lyapunov measure-based stochastic stability theorems.
Furthermore, connection between Lyapunov functions, a popular tool for
stochastic stability verification, and Lyapunov measures is established. Using
the duality property between the linear transfer Perron-Frobenius and Koopman
operators, we show the Lyapunov measure and Lyapunov function used for the
verification of stochastic stability are dual to each other. Set-oriented
numerical methods are proposed for the finite dimensional approximation of the
Perron-Frobenius operator; hence, Lyapunov measure is proposed. Stability
results in finite dimensional approximation space are also presented. Finite
dimensional approximation is shown to introduce further weaker notion of
stability referred to as coarse stochastic stability. The results in this paper
extend our earlier work on the use of Lyapunov measures for almost everywhere
stability verification of deterministic dynamical systems ("Lyapunov Measure
for Almost Everywhere Stability", {\it IEEE Trans. on Automatic Control}, Vol.
53, No. 1, Feb. 2008).Comment: Proceedings of American Control Conference, Chicago IL, 201
Data-driven and Model-based Verification: a Bayesian Identification Approach
This work develops a measurement-driven and model-based formal verification
approach, applicable to systems with partly unknown dynamics. We provide a
principled method, grounded on reachability analysis and on Bayesian inference,
to compute the confidence that a physical system driven by external inputs and
accessed under noisy measurements, verifies a temporal logic property. A case
study is discussed, where we investigate the bounded- and unbounded-time safety
of a partly unknown linear time invariant system
A Bayesian framework for verification and recalibration of ensemble forecasts: How uncertain is NAO predictability?
Predictability estimates of ensemble prediction systems are uncertain due to
limited numbers of past forecasts and observations. To account for such
uncertainty, this paper proposes a Bayesian inferential framework that provides
a simple 6-parameter representation of ensemble forecasting systems and the
corresponding observations. The framework is probabilistic, and thus allows for
quantifying uncertainty in predictability measures such as correlation skill
and signal-to-noise ratios. It also provides a natural way to produce
recalibrated probabilistic predictions from uncalibrated ensembles forecasts.
The framework is used to address important questions concerning the skill of
winter hindcasts of the North Atlantic Oscillation for 1992-2011 issued by the
Met Office GloSea5 climate prediction system. Although there is much
uncertainty in the correlation between ensemble mean and observations, there is
strong evidence of skill: the 95% credible interval of the correlation
coefficient of [0.19,0.68] does not overlap zero. There is also strong evidence
that the forecasts are not exchangeable with the observations: With over 99%
certainty, the signal-to-noise ratio of the forecasts is smaller than the
signal-to-noise ratio of the observations, which suggests that raw forecasts
should not be taken as representative scenarios of the observations. Forecast
recalibration is thus required, which can be coherently addressed within the
proposed framework.Comment: 36 pages, 10 figure
Simulator Semantics for System Level Formal Verification
Many simulation based Bounded Model Checking approaches to System Level
Formal Verification (SLFV) have been devised. Typically such approaches exploit
the capability of simulators to save computation time by saving and restoring
the state of the system under simulation. However, even though such approaches
aim to (bounded) formal verification, as a matter of fact, the simulator
behaviour is not formally modelled and the proof of correctness of the proposed
approaches basically relies on the intuitive notion of simulator behaviour.
This gap makes it hard to check if the optimisations introduced to speed up the
simulation do not actually omit checking relevant behaviours of the system
under verification.
The aim of this paper is to fill the above gap by presenting a formal
semantics for simulators.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Log-normal distribution based EMOS models for probabilistic wind speed forecasting
Ensembles of forecasts are obtained from multiple runs of numerical weather
forecasting models with different initial conditions and typically employed to
account for forecast uncertainties. However, biases and dispersion errors often
occur in forecast ensembles, they are usually under-dispersive and uncalibrated
and require statistical post-processing. We present an Ensemble Model Output
Statistics (EMOS) method for calibration of wind speed forecasts based on the
log-normal (LN) distribution, and we also show a regime-switching extension of
the model which combines the previously studied truncated normal (TN)
distribution with the LN.
Both presented models are applied to wind speed forecasts of the eight-member
University of Washington mesoscale ensemble, of the fifty-member ECMWF ensemble
and of the eleven-member ALADIN-HUNEPS ensemble of the Hungarian Meteorological
Service, and their predictive performances are compared to those of the TN and
general extreme value (GEV) distribution based EMOS methods and to the TN-GEV
mixture model. The results indicate improved calibration of probabilistic and
accuracy of point forecasts in comparison to the raw ensemble and to
climatological forecasts. Further, the TN-LN mixture model outperforms the
traditional TN method and its predictive performance is able to keep up with
the models utilizing the GEV distribution without assigning mass to negative
values.Comment: 24 pages, 10 figure
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