Statistical Characterization of Viscoelastic Modulus using a Spectrum Function Approach

2015 ◽  
Author(s):  
Rani W. Sullivan ◽  
Jutima Simsiriwong
Keyword(s):  
Function Approach ◽  
Statistical Characterization ◽  
Spectrum Function ◽  
Viscoelastic Modulus

THE MULTIFRACTAL FORMALISM REVISITED WITH WAVELETS

1994 ◽  
Vol 04 (02) ◽  
pp. 245-302 ◽  
Author(s):  
J.F. MUZY ◽  
E. BACRY ◽  
A. ARNEODO
Keyword(s):  
Wavelet Transform ◽  
Structure Function ◽  
Discrete Dynamical System ◽  
Function Approach ◽  
Partition Functions ◽  
Statistical Characterization ◽  
Multifractal Formalism ◽  
Wavelet Transform Modulus Maxima ◽  
Modulus Maxima

The multifractal formalism originally introduced for singular measures is revisited using the wavelet transform. This new approach is based on the definition of partition functions from the wavelet transform modulus maxima. We demonstrate that the f(α) singularity spectrum can be readily determined from the scaling behavior of these partition functions. We show that this method provides a natural generalization of the classical box-counting techniques to fractal functions (the wavelets actually play the role of “generalized boxes”). We report on a systematic comparison between this alternative method and the structure function approach which is commonly used in the context of fully developed turbulence. We comment on the intrinsic limitations of the structure functions which possess fundamental drawbacks and do not provide a full characterization of the singularities of a signal in many cases. We show that our method based on the wavelet transform modulus maxima decomposition works in most situations and is likely to be the ground of a unified multifractal description of singular distributions. Our theoretical considerations are both illustrated on pedagogical examples, e.g., generalized devil staircases and fractional Brownian motions, and supported by numerical simulations. Recent applications of the wavelet transform modulus maxima method to experimental turbulent velocity signals at inertial range scales are compared to previous measurements based on the structure function approach. A similar analysis is carried out for the locally averaged dissipation and the validity of the Kolmogorov’s refined similarity hypothesis is discussed. To conclude, we elaborate on a wavelet based technique which goes further than a simple statistical characterization of the scaling properties of fractal objects and provides a very promising tool for solving the inverse fractal problem, i.e., for uncovering their construction rule in terms of a discrete dynamical system.

scholarly journals Critical Review of EMC Standards for the Measurement of Radiated Electromagnetic Emissions from Transit Line and Rolling Stock

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 759
Author(s):  
Andrea Mariscotti
Keyword(s):  
Time Distribution ◽  
Communication Systems ◽  
Electromagnetic Compatibility ◽  
Transportation Systems ◽  
Operating Conditions ◽  
Rolling Stock ◽  
Intrinsic Variability ◽  
Statistical Characterization ◽  
Electromagnetic Emissions

Accurate and comprehensive methods for the assessment of radiated electromagnetic emissions in modern electric transportation systems are a necessity. The characteristics and susceptibility of modern victim signaling and communication radio services, operating within and outside the right-of-way, require an update of the measurement methods integrating or replacing the swept frequency technique with time domain approaches. Applicable standards are the EN 50121 (equivalent to the IEC 62236) and Urban Mass Transport Association (UMTA) with additional specifications from project contracts. This work discusses the standardized methods and settings, and the representative operating conditions, highlighting areas where improvements are possible and opportune (statistical characterization of measurement results, identification and distinction of emissions and line resonances, and narrowband and broadband phenomena). In particular for the Electromagnetic Compatibility (EMC) assessment with new Digital Communication Systems, the characterization of time distribution of spectral properties is discussed, e.g., by means of Amplitude Probability Distribution and including time distribution information. The problem of determination of site and setup uncertainty and repeatability is also discussed, observing on one hand the lack of clear indications in standards and, on the other hand, the non-ideality and intrinsic variability of measurement conditions (e.g., rolling stock operating conditions, synchronization issues, and electric arc intermittence).

Statistical characterization of the signal-in-space errors of the BDS: a comparison between BDS-2 and BDS-3

GPS Solutions ◽  
2021 ◽  
Vol 25 (3) ◽  
Author(s):  
Guo Chen ◽  
Renyu Zhou ◽  
Zhigang Hu ◽  
Yifei Lv ◽  
Na Wei ◽  
...  
Keyword(s):  
Statistical Characterization

Statistical characterization of engineered tissues using confocal mosaic technology

2010 ◽  
Author(s):  
David Levitz ◽  
Ardalan Ardeshiri ◽  
Jabeer Ahmed ◽  
Daniel S. Gareau ◽  
Steven L. Jacques
Keyword(s):  
Statistical Characterization ◽  
Engineered Tissues
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