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Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation.
We finish by presenting a strategy and pilot project which will develop an operational flood monitoring and forecasting system based in-situ data, earth observations, modelling, and extreme statistics.
A set of extreme statistics, commonly used in urban hydrology practice, have been extracted from simulated data and compared with the ones obtained after direct correction of a 12-year high resolution (1 min) RI series.
The narrow band feature of response is further considered in this study in the calculation of crossing rate using amplitude process, which leads to even better predictions of extreme statistics.
The approach presented is especially effective in practice, where the number of available response time histories is often very limited, and a direct use of extreme samples fails to provide accurate estimation of extreme statistics.
This mixture distribution method and the method based on curve-fitting of translation function derived from mapping of cumulative distribution functions are illustrated to be capable of capturing the upper tail of translation function, thus lead to satisfactory estimations of extreme statistics for a variety of non-Gaussian processes.
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Due to the close connection between extreme value statistics and first passage time statistics, a discussion of the impact of the results on the first passage time problem is also given.
Note that the analysis of large output data arrays needs the application of extreme value statistics for the assessment of their statistical significance.
In an attempt to link downscaling (i.e., relating large-scale atmosphere ocean circulation to smaller-scale hydrologic variables) with the statistics of extremes, statistical downscaling of hydrologic extremes is considered.
Hence, statistical significance of predicted targets is assessed with an extreme value statistics of length normalized minimum free energies and a Poisson approximation of multiple binding sites.
We find that using different detrending techniques biases the results from extreme value statistics.
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