5,932 research outputs found
Practical implementation of nonlinear time series methods: The TISEAN package
Nonlinear time series analysis is becoming a more and more reliable tool for
the study of complicated dynamics from measurements. The concept of
low-dimensional chaos has proven to be fruitful in the understanding of many
complex phenomena despite the fact that very few natural systems have actually
been found to be low dimensional deterministic in the sense of the theory. In
order to evaluate the long term usefulness of the nonlinear time series
approach as inspired by chaos theory, it will be important that the
corresponding methods become more widely accessible. This paper, while not a
proper review on nonlinear time series analysis, tries to make a contribution
to this process by describing the actual implementation of the algorithms, and
their proper usage. Most of the methods require the choice of certain
parameters for each specific time series application. We will try to give
guidance in this respect. The scope and selection of topics in this article, as
well as the implementational choices that have been made, correspond to the
contents of the software package TISEAN which is publicly available from
http://www.mpipks-dresden.mpg.de/~tisean . In fact, this paper can be seen as
an extended manual for the TISEAN programs. It fills the gap between the
technical documentation and the existing literature, providing the necessary
entry points for a more thorough study of the theoretical background.Comment: 27 pages, 21 figures, downloadable software at
http://www.mpipks-dresden.mpg.de/~tisea
Detecting and quantifying stellar magnetic fields -- Sparse Stokes profile approximation using orthogonal matching pursuit
In the recent years, we have seen a rapidly growing number of stellar
magnetic field detections for various types of stars. Many of these magnetic
fields are estimated from spectropolarimetric observations (Stokes V) by using
the so-called center-of-gravity (COG) method. Unfortunately, the accuracy of
this method rapidly deteriorates with increasing noise and thus calls for a
more robust procedure that combines signal detection and field estimation. We
introduce an estimation method that provides not only the effective or mean
longitudinal magnetic field from an observed Stokes V profile but also uses the
net absolute polarization of the profile to obtain an estimate of the apparent
(i.e., velocity resolved) absolute longitudinal magnetic field. By combining
the COG method with an orthogonal-matching-pursuit (OMP) approach, we were able
to decompose observed Stokes profiles with an overcomplete dictionary of
wavelet-basis functions to reliably reconstruct the observed Stokes profiles in
the presence of noise. The elementary wave functions of the sparse
reconstruction process were utilized to estimate the effective longitudinal
magnetic field and the apparent absolute longitudinal magnetic field. A
multiresolution analysis complements the OMP algorithm to provide a robust
detection and estimation method. An extensive Monte-Carlo simulation confirms
the reliability and accuracy of the magnetic OMP approach.Comment: A&A, in press, 15 pages, 14 figure
Bayesian system identification for structures considering spatial and temporal correlation
The decreasing cost and improved sensor and monitoring system technology
(e.g. fiber optics and strain gauges) have led to more measurements in close
proximity to each other. When using such spatially dense measurement data in
Bayesian system identification strategies, the correlation in the model
prediction error can become significant. The widely adopted assumption of
uncorrelated Gaussian error may lead to inaccurate parameter estimation and
overconfident predictions, which may lead to sub-optimal decisions. This paper
addresses the challenges of performing Bayesian system identification for
structures when large datasets are used, considering both spatial and temporal
dependencies in the model uncertainty. We present an approach to efficiently
evaluate the log-likelihood function, and we utilize nested sampling to compute
the evidence for Bayesian model selection. The approach is first demonstrated
on a synthetic case and then applied to a (measured) real-world steel bridge.
The results show that the assumption of dependence in the model prediction
uncertainties is decisively supported by the data. The proposed developments
enable the use of large datasets and accounting for the dependency when
performing Bayesian system identification, even when a relatively large number
of uncertain parameters is inferred.Comment: 33 pages, 16 figures; Revised after reviewer comments, corrected
typos, recreated figure
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