The crossing rates, exceedance probabilities, and maximum values of a random frequency response function

This work is concerned with the statistical properties of the frequency response function (FRF) of the energy of a random system. Earlier studies have considered the statistical distribution of the function at a single frequency, or alternatively the statistics of a bandaverage of the function. In contrast the present analysis considers the statistical fluctuations over a frequency band, and results are reported for the mean rate at which the function crosses a specified level (or equivalently, the average number of times the level is crossed within the band). Results are also reported for the probability of crossing a specified level at least once. The results presented here for a single component comprise a summary of a recent publication by the author; this previous work is extended in the present paper to the case of multiple coupled components.