Statistical distributions of time series in the frequency domain and the patterns of violation of white noise conditions

2005 ◽  
Vol 74 (1) ◽  
pp. 103-108
Author(s):  
Peijie Wang
Keyword(s):  
Time Series ◽  
White Noise ◽  
Frequency Domain ◽  
Statistical Distributions

A Frequency-Domain Filtering Technique for Triple Decomposition of Unsteady Turbulent Flow

1992 ◽  
Vol 114 (1) ◽  
pp. 45-51 ◽  
Author(s):  
G. J. Brereton ◽  
A. Kodal
Keyword(s):  
Time Series ◽  
Turbulent Flow ◽  
Frequency Domain ◽  
Measurement Data ◽  
Averaging Technique ◽  
Phase Averaging ◽  
Spectral Estimates ◽  
Improved Performance ◽  
A New Technique ◽  
Flow Variables

A new technique is presented for decomposing unsteady turbulent flow variables into their organized unsteady and turbulent components, which appears to offer some significant advantages over existing ones. The technique uses power-spectral estimates of data to deduce the optimal frequency-domain filter for determining the organized and turbulent components of a time series of data. When contrasted with the phase-averaging technique, this method can be thought of as replacing the assumption that the organized motion is identically reproduced in successive cycles of known periodicity by a more general condition: the cross-correlation of the organized and turbulent components is minimized for a time series of measurement data, given the expected shape of the turbulence power spectrum. The method is significantly more general than the phase average in its applicability and makes more efficient use of available data. Performance evaluations for time series of unsteady turbulent velocity measurements attest to the accuracy of the technique and illustrate the improved performance of this method over the phase-averaging technique when cycle-to-cycle variations in organized motion are present.

scholarly journals Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use

1998 ◽  
Vol 28 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Terence Chan
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Investment Model ◽  
Stable Processes ◽  
Gamma Processes ◽  
Investment Models

AbstractThis paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained in the case where the SDEs are driven by Brownian motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving “noise” are stable processes and Gamma processes are considered.

A Novel Solution to Compute Stress Time Series in Nonlinear Hydro-Structure Simulations

2015 ◽  
Author(s):  
Fabien Bigot ◽  
François-Xavier Sireta ◽  
Eric Baudin ◽  
Quentin Derbanne ◽  
Etienne Tiphine ◽  
...  
Keyword(s):  
Time Series ◽  
Frequency Domain ◽  
Time Domain ◽  
Hot Spot ◽  
Structural Response ◽  
Container Ship ◽  
Time Step ◽  
Computation Cost ◽  
Hull Girder ◽  
Non Linear

Ship transport is growing up rapidly, leading to ships size increase, and particularly for container ships. The last generation of Container Ship is now called Ultra Large Container Ship (ULCS). Due to their increasing sizes they are more flexible and more prone to wave induced vibrations of their hull girder: springing and whipping. The subsequent increase of the structure fatigue damage needs to be evaluated at the design stage, thus pushing the development of hydro-elastic simulation models. Spectral fatigue analysis including the first order springing can be done at a reasonable computational cost since the coupling between the sea-keeping and the Finite Element Method (FEM) structural analysis is performed in frequency domain. On the opposite, the simulation of non-linear phenomena (Non linear springing, whipping) has to be done in time domain, which dramatically increases the computation cost. In the context of ULCS, because of hull girder torsion and structural discontinuities, the hot spot stress time series that are required for fatigue analysis cannot be simply obtained from the hull girder loads in way of the detail. On the other hand, the computation cost to perform a FEM analysis at each time step is too high, so alternative solutions are necessary. In this paper a new solution is proposed, that is derived from a method for the efficient conversion of full scale strain measurements into internal loads. In this context, the process is reversed so that the stresses in the structural details are derived from the internal loads computed by the sea-keeping program. First, a base of distortion modes is built using a structural model of the ship. An original method to build this base using the structural response to wave loading is proposed. Then a conversion matrix is used to project the computed internal loads values on the distortion modes base, and the hot spot stresses are obtained by recombination of their modal values. The Moore-Penrose pseudo-inverse is used to minimize the error. In a first step, the conversion procedure is established and validated using the frequency domain hydro-structure model of a ULCS. Then the method is applied to a non-linear time domain simulation for which the structural response has actually been computed at each time step in order to have a reference stress signal, in order to prove its efficiency.

CHARACTERIZATION OF NUCLEAR IMAGES BASED ON ANALYSIS OF FRACTIONAL SUMMATION SYSTEMS

Fractals ◽  
2004 ◽  
Vol 12 (02) ◽  
pp. 157-169 ◽  
Author(s):  
HAI-SHAN WU ◽  
ANDREW J. EINSTEIN ◽  
LIANE DELIGDISCH ◽  
TAMARA KALIR ◽  
JOAN GIL
Keyword(s):  
White Noise ◽  
Frequency Domain ◽  
Discrete System ◽  
Fractional Integral ◽  
Continuous System ◽  
Time Range ◽  
System Function ◽  
Autocovariance Function ◽  
Frequency Domain Methods

While frequency-based methods for the characterization of fractals are popular and effective in many applications, they have limitations when applied to irregularly shaped images, such as nuclear images. The irregularity renders texture characterization by frequency domain methods, based upon Fourier transform, problematic. To address this situation, this paper presents an algorithm based upon the signal analysis in the spatial domain. An autocovariance function can be estimated regardless of the shape and size of regions where the image is defined. As in the continuous fractional Brownian motion (FBM) that results from inputting white noise into a specific fractional integral system, a discrete FBM can be related to white noise by a specific fractional summation system (FSS) that is linear, causal and shift-invariant. Although the method of direct sampling is not valid for converting a continuous fractional integral to a discrete fractional summation, discrete fractional summations similar to the sampled system functions can be obtained through an iterative process. While the continuous system function of a fractional integral is linear in the frequency domain when plotted in log-log scales, unfortunately, it is not true for the comparable discrete system function. The discrete system function is actually approximately linear in the log-log scales over a very limited range. The slope of the straight line that approximates the function curve in the mean-square-error (MSE) sense in a specific time range provides a description of the autocovariance function that reveals the statistical relations among the local textures. Applications to characterization of ovary nuclear images in groups of normal, atypical and cancer cases are studied and presented.

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