How Spectral moments are correlated to RMS value while using multipliers to find maximum values when computing connector force statistics.

In Moses, I performed a mooring analysis and computed connector force statistics. I noticed that the maximum values reported are multiplied by 3.72 to the RMS values. I looked on the forum for an explanation and found the responses presented below.

A: There are several way of estimating the maximum. Normally, one does this statistically by assuming that the peaks are Raleigh distributed. If one makes this assumption, then he only needs to define what he means by maximum. In MOSES, you define what you mean. This is done by giving a duration to the seastate, or defining a multiplier. If you give a duration, MOSES will use the moments of the response spectrum and the duration to produce the probable maximum value. Alternatively, you can define a multiplier for the RMS of the spectrum. The default is to use a multiple of 3.72 which defines the maximum to be the average of the 1/1000th highest values. Other values for this multiplier are:

        2.00 - Significant value

        2.54 - average of 1/10th highest values

        3.03 - average of 1/100th highest values

A: As stated in the MOSES Reference Manual, &DEFAULT -PROBABILITY STAT PDATA controls the statistics which will be defined when computing the statistics of quantities in an irregular sea. The default is for STAT to refer to the MAXIMUM, and PDATA is 3.72 which provides the 1/1000 highest response, based on a Rayleigh distribution. This is the statistical multiplier the root mean square will be multiplied by to obtain a maximum. When DURATION is used for STAT, the time specified is used to determine the statistical multiplier. See equation 11.22 of the Time Series, Spectra and Extreme section in How MOSES Deals With: (PDF).

According to the above responses, a multiplier of 3.72 to the RMS value is used to obtain a maximum of 1/1000th response. However, in the deals document equation 11.22, the multiplier of the square root of the 0th spectral moment is shown as 3.72.

 

My questions are

  • How spectral moments are correlated to RMS value when using a 3.72 multiplier?
  • Can anyone explain why Moses refers to spectral moments in the deals document, but when calculating they actually multiply RMS value with the multiplier?