3,159 research outputs found
Multiscale statistical process control with multiresolution data
An approach is presented for conducting multiscale statistical process control that adequately integrates data at different resolutions (multiresolution data), called MR-MSSPC. Its general structure is based on Bakshi's MSSPC framework designed to handle data at a single resolution. Significant modifications were introduced in order to process multiresolution information. The main MR-MSSPC features are presented and illustrated through three examples. Issues related to real world implementations and with the interpretation of the multiscale covariance structure are addressed in a fourth example, where a CSTR system under feedback control is simulated. Our approach proved to be able to provide a clearer definition of the regions where significant events occur and a more sensitive response when the process is brought back to normal operation, when it is compared with previous approaches based on single resolution data. © 2006 American Institute of Chemical Engineers AIChE J, 200
Time dependent intrinsic correlation analysis of temperature and dissolved oxygen time series using empirical mode decomposition
In the marine environment, many fields have fluctuations over a large range
of different spatial and temporal scales. These quantities can be nonlinear
\red{and} non-stationary, and often interact with each other. A good method to
study the multiple scale dynamics of such time series, and their correlations,
is needed. In this paper an application of an empirical mode decomposition
based time dependent intrinsic correlation, \red{of} two coastal oceanic time
series, temperature and dissolved oxygen (saturation percentage) is presented.
The two time series are recorded every 20 minutes \red{for} 7 years, from 2004
to 2011. The application of the Empirical Mode Decomposition on such time
series is illustrated, and the power spectra of the time series are estimated
using the Hilbert transform (Hilbert spectral analysis). Power-law regimes are
found with slopes of 1.33 for dissolved oxygen and 1.68 for temperature at high
frequencies (between 1.2 and 12 hours) \red{with} both close to 1.9 for lower
frequencies (time scales from 2 to 100 days). Moreover, the time evolution and
scale dependence of cross correlations between both series are considered. The
trends are perfectly anti-correlated. The modes of mean year 3 and 1 year have
also negative correlation, whereas higher frequency modes have a much smaller
correlation. The estimation of time-dependent intrinsic correlations helps to
show patterns of correlations at different scales, for different modes.Comment: 35 pages with 22 figure
Data-Adaptive Wavelets and Multi-Scale Singular Spectrum Analysis
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum
analysis (SSA) to the study of nonstationary time series of length whose
intermittency can give rise to the divergence of their variance. SSA relies on
the construction of the lag-covariance matrix C on M lagged copies of the time
series over a fixed window width W to detect the regular part of the
variability in that window in terms of the minimal number of oscillatory
components; here W = M Dt, with Dt the time step. The proposed multi-scale SSA
is a local SSA analysis within a moving window of width M <= W <= N.
Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the
eigenvectors of the corresponding lag-covariance matrix C_M as a data-adaptive
wavelets; successive eigenvectors of C_M correspond approximately to successive
derivatives of the first mother wavelet in standard wavelet analysis.
Multi-scale SSA thus solves objectively the delicate problem of optimizing the
analyzing wavelet in the time-frequency domain, by a suitable localization of
the signal's covariance matrix. We present several examples of application to
synthetic signals with fractal or power-law behavior which mimic selected
features of certain climatic and geophysical time series. A real application is
to the Southern Oscillation index (SOI) monthly values for 1933-1996. Our
methodology highlights an abrupt periodicity shift in the SOI near 1960. This
abrupt shift between 4 and 3 years supports the Devil's staircase scenario for
the El Nino/Southern Oscillation phenomenon.Comment: 24 pages, 19 figure
Beyond the noise : high fidelity MR signal processing
This thesis describes a variety of methods developed to increase the sensitivity and resolution of liquid state nuclear magnetic resonance (NMR) experiments. NMR is known as one of the most versatile non-invasive analytical techniques yet often suffers from low sensitivity. The main contribution to this low sensitivity issue is a presence of noise and level of noise in the spectrum is expressed numerically as “signal-to-noise ratio”. NMR signal processing involves sensitivity and resolution enhancement achieved by noise reduction using mathematical algorithms. A singular value decomposition based reduced rank matrix method, composite property mapping, in particular is studied extensively in this thesis to present its advantages, limitations, and applications. In theory, when the sum of k noiseless sinusoidal decays is formatted into a specific matrix form (i.e., Toeplitz), the matrix is known to possess k linearly independent columns. This information becomes apparent only after a singular value decomposition of the matrix. Singular value decomposition factorises the large matrix into three smaller submatrices: right and left singular vector matrices, and one diagonal matrix containing singular values. Were k noiseless sinusoidal decays involved, there would be only k nonzero singular values appearing in the diagonal matrix in descending order providing the information of the amplitude of each sinusoidal decay. The number of non-zero singular values or the number of linearly independent columns is known as the rank of the matrix. With real NMR data none of the singular values equals zero and the matrix has full rank. The reduction of the rank of the matrix and thus the noise in the reconstructed NMR data can be achieved by replacing all the singular values except the first k values with zeroes. This noise reduction process becomes difficult when biomolecular NMR data is to be processed due to the number of resonances being unknown and the presence of a large solvent peak
Underwater Acoustic Source Localization and Sounds Classification in Distributed Measurement Networks
info:eu-repo/semantics/publishedVersio
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