57,490 research outputs found
Detecting structural breaks in seasonal time series by regularized optimization
Real-world systems are often complex, dynamic, and nonlinear. Understanding
the dynamics of a system from its observed time series is key to the prediction
and control of the system's behavior. While most existing techniques tacitly
assume some form of stationarity or continuity, abrupt changes, which are often
due to external disturbances or sudden changes in the intrinsic dynamics, are
common in time series. Structural breaks, which are time points at which the
statistical patterns of a time series change, pose considerable challenges to
data analysis. Without identification of such break points, the same dynamic
rule would be applied to the whole period of observation, whereas false
identification of structural breaks may lead to overfitting. In this paper, we
cast the problem of decomposing a time series into its trend and seasonal
components as an optimization problem. This problem is ill-posed due to the
arbitrariness in the number of parameters. To overcome this difficulty, we
propose the addition of a penalty function (i.e., a regularization term) that
accounts for the number of parameters. Our approach simultaneously identifies
seasonality and trend without the need of iterations, and allows the reliable
detection of structural breaks. The method is applied to recorded data on fish
populations and sea surface temperature, where it detects structural breaks
that would have been neglected otherwise. This suggests that our method can
lead to a general approach for the monitoring, prediction, and prevention of
structural changes in real systems.Comment: Safety, Reliability, Risk and Life-Cycle Performance of Structures
and Infrastructures (Edited by George Deodatis, Bruce R. Ellingwood and Dan
M. Frangopol), CRC Press 2014, Pages 3621-362
Modelling and identification of a six axes industrial robot
This paper deals with the modelling and identification of a six axes industrial St ĀØaubli RX90 robot. A non-linear finite element method is used to generate the dynamic equations of motion in a form suitable for both simulation and identification. The latter requires that the equations of motion are linear in the inertia parameters. Joint friction is described by a friction model that describes the friction behaviour in the full velocity range necessary for identification. Experimental parameter identification by means of linear least squares techniques showed to be very suited for identification of the unknown parameters, provided that the problem is properly scaled and that the influence of disturbances is sufficiently analysed and managed. An analysis of the least squares problem by means of a singular value decomposition is preferred as it not only solves the problem of rank deficiency, but it also can correctly deal with measurement noise and unmodelled dynamics
Robust regularized singular value decomposition with application to mortality data
We develop a robust regularized singular value decomposition (RobRSVD) method
for analyzing two-way functional data. The research is motivated by the
application of modeling human mortality as a smooth two-way function of age
group and year. The RobRSVD is formulated as a penalized loss minimization
problem where a robust loss function is used to measure the reconstruction
error of a low-rank matrix approximation of the data, and an appropriately
defined two-way roughness penalty function is used to ensure smoothness along
each of the two functional domains. By viewing the minimization problem as two
conditional regularized robust regressions, we develop a fast iterative
reweighted least squares algorithm to implement the method. Our implementation
naturally incorporates missing values. Furthermore, our formulation allows
rigorous derivation of leave-one-row/column-out cross-validation and
generalized cross-validation criteria, which enable computationally efficient
data-driven penalty parameter selection. The advantages of the new robust
method over nonrobust ones are shown via extensive simulation studies and the
mortality rate application.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS649 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Multisource Self-calibration for Sensor Arrays
Calibration of a sensor array is more involved if the antennas have direction
dependent gains and multiple calibrator sources are simultaneously present. We
study this case for a sensor array with arbitrary geometry but identical
elements, i.e. elements with the same direction dependent gain pattern. A
weighted alternating least squares (WALS) algorithm is derived that iteratively
solves for the direction independent complex gains of the array elements, their
noise powers and their gains in the direction of the calibrator sources. An
extension of the problem is the case where the apparent calibrator source
locations are unknown, e.g., due to refractive propagation paths. For this
case, the WALS method is supplemented with weighted subspace fitting (WSF)
direction finding techniques. Using Monte Carlo simulations we demonstrate that
both methods are asymptotically statistically efficient and converge within two
iterations even in cases of low SNR.Comment: 11 pages, 8 figure
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