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, three different methods for statistical load extrapolation of wind-turbine response are studied using a stationary Gaussian process model, which has approximately the same spectral properties as the response for the out-of-plane bending moment of a wind turbine blade.
Abstract: In the present paper, methods for statistical load extrapolation of wind-turbine response are studied using a stationary Gaussian process model, which has approximately the same spectral properties as the response for the out-of plane bending moment of a wind-turbine blade. For a Gaussian process, an approximate analytical solution for the distribution of the peaks is given by Rice. In the present paper, three different methods for statistical load extrapolation are compared with the analytical solution for one mean wind speed. The methods considered are global maxima, block maxima, and the peak over threshold method with two different threshold values. The comparisons show that the goodness of fit for the local distribution has a significant influence on the results, but the peak over threshold method with a threshold value on the mean plus 1.4 standard deviations generally gives the best results. By considering Gaussian processes for 12 mean wind speeds, the "fitting before aggregation" and "aggregation before fatting" approaches are studied. The results show that the fitting before aggregation approach gives the best results.
25 citations
TL;DR: In this paper, the authors revisit recent work on the generation of extreme optical events via nonlinear dynamics in silicon waveguides, where the underlying processes, modulation instability and stimulated Raman scattering, are able to reshape normally distributed initial conditions into skewed output statistics whose properties can be tailored by controlling experimental variables.
Abstract: We revisit recent work on the generation of extreme optical events via nonlinear dynamics in silicon waveguides. The underlying processes, modulation instability and stimulated Raman scattering, are able to reshape normally distributed initial conditions into skewed output statistics whose properties can be tailored by controlling experimental variables. While these are both gain processes, they bear fundamental differences: modulation instability is a broadband parametric process, whereas stimulated Raman scattering is a narrowband inelastic process. As a result, they respond to different forms of input noise. Specifically, the extreme events generated spontaneously by modulation instability evidence a strong sensitivity to a particular input noise component. This sensitivity can be controllably seeded to generate coherent supercontinuum radiation, which also offers a means to alleviate conventional free-carrier limitations to chip-scale spectral broadening.
25 citations
TL;DR: In this paper, a one-step Markov matrix is developed for fast direct simulation of the extremes of a normal process with unimodal power spectral density, which is determined from the joint probability density of a maximum and a minimum of given magnitudes occurring with a certain time separation.
25 citations
TL;DR: Rice's theory of shot noise random processes is used to provide a statistical analysis of the evolution of the amplitude and phase of the chaotic optical field from a high-gain, self-amplified, spontaneous-emission SASE free-electron laser.
Abstract: We use Rice's theory of shot noise random processes to provide a statistical analysis of the evolution of the amplitude and phase of the chaotic optical field from a high-gain, self-amplified, spontaneous-emission (SASE) free-electron laser. The theoretical framework developed is compared with recent frequency-resolved optical-gating measurements of the SASE output at the LEUTL facility at Argonne National Laboratory.
25 citations
TL;DR: The application of conditional sampling to turbulent combustion has been reviewed in this article, where more detailed, more informative data from experiments involving turbulent reacting flows available from the permanent recording of the output from various sensors.
25 citations