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Wavelet Transformation (wavelet + transformation)
Selected AbstractsIterative solution of large linear systems with non-smooth submatrices using partial wavelet transforms and split-matrix matrix,vector multiplicationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004Patricia González Abstract The iterative solution of large linear systems with highly irregular matrices cannot be accelerated by wavelet transformation and subsequent sparsification if the transformed matrix is still highly irregular. In this paper we show that if the irregularity of the original matrix is limited to a relatively small known set of rows or columns (as is the case in significant applications), then acceleration can be achieved by a mixed approach in which only the ,smooth' submatrix is transformed and iterative solution is implemented using a novel ,split-matrix' form of matrix,vector multiplication. Copyright © 2003 John Wiley & Sons, Ltd. [source] Fast principal component analysis of large data sets based on information extractionJOURNAL OF CHEMOMETRICS, Issue 11 2002F. Vogt Abstract Principal component analysis (PCA) and principal component regression (PCR) are routinely used for calibration of measurement devices and for data evaluation. However, their use is hindered in some applications, e.g. hyperspectral imaging, by excessive data sets that imply unacceptable calculation time. This paper discusses a fast PCA achieved by a combination of data compression based on a wavelet transformation and a spectrum selection method prior to the PCA itself. The spectrum selection step can also be applied without previous data compression. The calculation speed increase is investigated based on original and compressed data sets, both simulated and measured. Two different data sets are used for assessment of the new approach. One set contains 65,536 synthetically generated spectra at four different noise levels with 256 measurement points each. Compared with the conventional PCA approach, these examples can be accelerated 20 times. Evaluation errors of the fast method were calculated and found to be comparable with those of the conventional approach. Four experimental spectra sets of similar size are also investigated. The novel method outperforms PCA in speed by factors of up to 12, depending on the data set. The principal components obtained by the novel algorithm show the same ability to model the measured spectra as the conventional time-consuming method. The acceleration factors also depend on the possible compression; in particular, if only a small compression is feasible, the acceleration lies purely with the novel spectrum selection step proposed in this paper. Copyright © 2002 John Wiley & Sons, Ltd. [source] Multiresolution analysis on identification and dynamics of clusters in a circulating fluidized bedAICHE JOURNAL, Issue 3 2009Tung-Yu Yang Abstract A new wavelet-threshold criterion was developed to distinguish the cluster and the void phases from the transient solids holdup/concentration fluctuation signals when measured in a 108 mm-i.d. × 5.75 m-high circulating fluidized bed with FCC particles (dp = 78 ,m, ,p = 1,880 kg/m3). An appropriate level of approximation subsignal was systematically specified as a threshold for cluster identification, based on multiresolution analysis (MRA) of wavelet transformation. By the established threshold, the dynamic properties of clusters including the appearance time fraction of clusters Fcl, average cluster duration time ,cl, cluster frequency fcl, and local average solids holdup in clusters ,sc, at different radial and axial positions were determined under the turbulent, transition and fast fluidization flow regimes. The results also describe the dynamic properties of clusters and flow patterns in the splash zone along with the dense bottom region of the circulating fluidized beds. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source] The redshift distribution of absorption-line systems in QSO spectraMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2007A. I. Ryabinkov ABSTRACT A statistical analysis of the space,time distribution of absorption-line systems (ALSs) observed in QSO spectra within the cosmological redshift interval z= 0.0,3.7 is carried out on the base of our catalogue of absorption systems (Ryabinkov et al. 2003). We confirm our previous conclusion that the z -distribution of absorbing matter contains non-uniform component displaying a pattern of statistically significant alternating maxima (peaks) and minima (dips). Using the wavelet transformation, we determine the positions of the maxima and minima and estimate their statistical significance. The positions of the maxima and minima of the z -distributions obtained for different celestial hemispheres turn out to be weakly sensitive to orientations of the hemispheres. The data reveal a regularity (quasi-periodicity) of the sequence of the peaks and dips with respect to some rescaling functions of z. The same periodicity was found for the one-dimensional correlation function calculated for the sample of the ALSs under investigation. We assume the existence of a regular structure in the distribution of absorption matter, which is not only spatial but also temporal in nature with characteristic time varying within the interval 150,650 Myr for the cosmological model applied. [source] Principal-component analysis of multiscale data for process monitoring and fault diagnosisAICHE JOURNAL, Issue 11 2004Seongkyu Yoon Abstract An approach is presented to multivariate statistical process control (MSPC) for process monitoring and fault diagnosis based on principal-component analysis (PCA) models of multiscale data. Process measurements, representing the cumulative effects of many underlying process phenomena, are decomposed by applying multiresolution analysis (MRA) by wavelet transformations. The decomposed process measurements are rearranged according to their scales, and PCA is applied to these multiscale data to capture process variable correlations occurring at different scales. Choosing an orthonormal mother wavelet allows each principal component to be a function of the process variables at only one scale level. The proposed method is discussed in the context of other multiscale approaches, and illustrated in detail using simulated data from a continuous stirred tank reactor (CSTR) system. A major contribution of the paper is to extend fault isolation methods based on contribution plots to multiscale approaches. In particular, once a fault is detected, the contributions of the variations at each scale to the fault are computed. These scale contributions can be very helpful in isolating faults that occur mainly at a single scale. For those scales having large contributions to the fault, one can further compute the variable contributions to those scales, thereby making fault diagnosis much easier. A comparison study is done through Monte Carlo simulation. The proposed method can enhance fault detection and isolation (FDI) performance when the frequency content of a fault effect is confined to a narrow-frequency band. However, when the fault frequency content is not localized, the multiscale approaches perform very comparably to the standard single-scale approaches, and offer no real advantage. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2891,2903, 2004 [source] Error-correction methods and evaluation of an ensemble based hydrological forecasting system for the Upper Danube catchmentATMOSPHERIC SCIENCE LETTERS, Issue 2 2008K. Bogner Abstract Within the EU Project PREVention, Information and Early Warning (PREVIEW), ensembles of discharge series have been generated for the Danube catchment by the use of various weather forecast products. Hydrological models applied for streamflow prediction often have simulation errors that degrade forecast quality and limit the operational usefulness of the forecasts. Therefore, error-correction methods have been tested for adjusting the ensemble traces using a transformation derived with simulated and observed flows. This article presents first results of the combination of state-space models and wavelet transformations in order to update errors between the simulated (forecasted) and the observed discharge. Copyright © 2008 Royal Meteorological Society [source] | ||||||||||