Journal Article•
Mathematical Analysis of Random Noise-Conclusion
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
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TL;DR: In this article, a new law called "M-Rice" is proposed for modeling wind speed frequency distributions, inspired by recent empirical findings that suggest the existence of some cascading process in the mesoscale range.
Abstract: Several known statistical distributions can describe wind speed data, the most commonly used being the Weibull family. In this paper, a new law, called "M-Rice", is proposed for modeling wind speed frequency distributions. Inspired by recent empirical findings that suggest the existence of some cascading process in the mesoscale range, we consider that wind speed can be described by a seasonal ARMA model where the noise term is "multifractal" i.e., associated with a random cascade. This leads to wind speeds distributed according to M-Rice pdf, i.e. a Rice distribution multiplicatively convolved with a normal law. Comparison based on the estimation of the mean wind speed and power density values as well as different goodness-of-fit tests (Kolmogorov-Smirnov, Kuiper test and the quantile-quantile plot) is made between this new distribution and the Weibull one, for 35 data sets of wind speed from Netherlands and Corsica (France) sites. Accordingly, the M-Rice and Weibull distributions provide comparable performances, while q-q plots suggest that M-rice distribution provides a better fit of extreme wind speed data. Beyond these good results, our approach allows one to interpret the observed values of Weibull parameters.
6 citations
TL;DR: A general regression model for non-central χ (NC-χ) distributed data is proposed, with the heteroscedastic Rician regression model as a prominent special case, and simulated regression data is used to demonstrate that the Rician model is able to detect the signal much more accurately than the traditionally used Gaussian model at low signal-to-noise ratios.
Abstract: It is well-known that data from diffusion weighted imaging (DWI) follow the Rician distribution. The Rician distribution is also relevant for functional magnetic resonance imaging (fMRI) data obtained at high temporal or spatial resolution. We propose a general regression model for non-central χ (NC-χ) distributed data, with the heteroscedastic Rician regression model as a prominent special case. The model allows both parameters in the Rician distribution to be linked to explanatory variables, with the relevant variables chosen by Bayesian variable selection. A highly efficient Markov chain Monte Carlo (MCMC) algorithm is proposed to capture full model uncertainty by simulating from the joint posterior distribution of all model parameters and the binary variable selection indicators. Simulated regression data is used to demonstrate that the Rician model is able to detect the signal much more accurately than the traditionally used Gaussian model at low signal-to-noise ratios. Using a diffusion dataset from the Human Connectome Project, it is also shown that the commonly used approximate Gaussian noise model underestimates the mean diffusivity (MD) and the fractional anisotropy (FA) in the single-diffusion tensor model compared to the Rician model.
6 citations
TL;DR: In this paper, the authors discuss the theories and designs for the structural reliability and durability of reinforced concrete structures over time and consider the benefits of assessing deterioration of structural performance over time in order to have a rational and cost-effective maintenance strategy.
Abstract: This paper discusses the theories and designs for the structural reliability and durability of reinforced concrete structures over time. The author considers the benefits of assessing deterioration of structural performance over time in order to have a rational and cost-effective maintenance strategy. The paper focuses on how to assess building structural performance and hence predict the appropriate maintenance intervals. Ongoing research activities in structural durability are discussed. More research is required to develop design tools to model expectations of required performance exists throughout the service life of structures. Cet expose examine les theories et conceptions concernant la fiabilite structurale et la durabilite des ossatures en beton arme au cours du temps. L'auteur considere les avantages d'une estimation de la tenue structurale au cours du temps, en vue d'elaborer une strategie d'entretien rationuelle et economique. L'expose est centre sur la facon d'evaluer la tenue structurale des ...
6 citations
TL;DR: In this paper, the authors investigated the accuracy of the magnetic field gradient waveform monitor (MFGM) technique through a treatment of the noise present in a magnetic resonance (MR) signal and examined the overall impact of noise on the phase accumulated in a pure phase encoded MR signal.
Abstract: The magnetic field gradient waveform monitor (MFGM) technique permits characterization of the temporal evolution of magnetic field gradients in magnetic resonance (MR) instruments (MRIs). Knowledge of the gradient waveform performance permits the development of further techniques, such as gradient waveform pre-equalization, that correct and optimize gradient waveform distortions due to eddy currents induced during the application of switched magnetic fields and other system limitations. The accuracy of the MFGM technique is important since the overall uncertainty of the gradient waveform measurement will propagate into an uncertainty in corrected gradient waveforms impacting the precision of the resulting MR/MRI measurements. The accuracy of MFGM is investigated through a treatment of the noise present in a MRI. A noisy receiver model provides the basis for characterization of the noise and permits examination of the overall impact of noise on the phase accumulated in a pure-phase encoded MR signal. Ultimately, a relationship between the signal-to-noise ratio of a measurement and the corresponding MFGM uncertainty is developed. The theoretical development is supported through simulation in conjunction with experimental results. The propagation of uncertainties to gradient waveform pre-equalization is also discussed.
6 citations
TL;DR: An intuitive argument is given for the measurement of the fraction of information that is lost, if any, when Gaussian noise is ‘clipped.’
Abstract: An intuitive argument is given for the measurement of the fraction of information that is lost, if any, when Gaussian noise is ‘clipped.’ For white noise band-limited to the range ( W 1 , W 2 ), it is suggested that the entire waveform is overdetermined by its zeros when W 2 /W 1 is less than (7 + √33)/4 = 3.186.
6 citations