# Time Domain Motion Analysis Results

Discussion in 'Hydrodynamics and Aerodynamics' started by OhMyBrain, Nov 21, 2023.

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1. Joined: Oct 2023
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### OhMyBrainNew Member

Hello everyone,

I am new to this forum and have already learned so much by reading many threads. I have few doubts about motion results obtained from a time domain analysis using irregular waves. I have performed frequency domain analyses for 99% of the cases in the past. So my understanding about the time domain results is not very concrete. I am required to do some time domain simulations as part of my work. In frequency domain, the maximum response was calculated from the response spectrum by multiplying a factor (~1.87) to the significant response. I want to know the relation between frequency domain and time domain results assuming all other inputs are the same.

I am using Ansys Aqwa. I tried fitting a Weibull distribution to a roll response time series data selecting only the peaks, both +ve and negative. Going by the definition of significant response, I calculated the average of highest 1/3rd peaks. This value was comparable to the significant response obtained from frequency domain. Now, what is the maximum response from time domain? I assume it is not the MPM of the Weibull distribution as it is coming out to be much lower. How are these values correlated? I hope some experts can help me understand.

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### jehardimanSenior Member

Welcome to the forums.

As you know, frequency domain response analysis is the preferred arena for maximum motion analysis. A Weibull distribution is probably not what you want unless you are required to fit some specific kappa and lambda. However, a Weibull distribution of kappa = 2 and lambda = SQRT(2) sigma approximates the Rayleigh distribution which is used for the random seaway motion analysis, where sigma is determined from the data.

The real problem with "solvers" in the time domain like AQWA is the "causality loop" problem; i.e. you determined the solution by what you defined at the start of the problem. In this way you get a specific solution for that one case; not a general one. This is similar to having a single pixel and trying to say it is representative of the whole picture. If you really wanted a general solution you would need to run thousands of AQWA analysis, each subtly different in how you define the "randomness".

If you have time stamped data (real or generated) with a periodicity of 0.5 second or less; it is possible to convert it over to the frequency domain with reasonable results. You will need about 20+ minutes of "clean" data (i.e. most transients are gone). You can then move the response over to the frequency domain using a FFT of 2048 ~0.5 second data points. By stepping through the data you can generate many response spectra then used to generate a "representative" response spectra which can then be analyzed in the normal methods. See Chapter 5 and 6 of Dynamics of Marine Vehicles by Bhattacharyya.

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### OhMyBrainNew Member

Thank you for the explanation. I will definitely refer Bhattacharya. To give more details about the analysis I am trying to perform, it's actually a seakeeping analysis for a fishing vessel with forward speed. We are thinking of time domain because we want to simulate a more realistic condition taking into consideration the non-linear nature of motions and possibility of adding passive stabilizer fins later.

I found a method recommended in DNV for calculating the maximum mooring line tension from time domain simulation. It recommends running around 20 simulations. Then take the absolute maximum from each simulation and consider them as a sample of extreme values that follow a Gumbel distribution. The required maximum is the MPM of Gumbel Distribution. I was wondering whether this can be applied for motions as well. Obviously in case of mooring lines only the positive peaks are considered whereas for motions like roll we need to consider both +ve and -ve peaks.

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For seakeeping analysis, frequency domain is better, as this directly relates to the vessel's natural period of motions and the encounter periods in said sea state under investigation.

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### jehardimanSenior Member

If that is your given requirement, so be it. But all in all I would never use a MPM value for "must work, can't fail, lives depend on it" design. The most probable maximum (MPM) is the value for which the probability density function of the maxima of the variable has its peak. This means that for most
distributions there is a 50% probability (or more) of the actual experienced maxima being greater. Rather, I typically worked with a non-exceedance probability (p) based on exposure. For an exposure of 'n' peaks, the MPM is m0*sqrt(2*ln(n)) where m0 is the area under the response spectra and 'n' is assumed large. However, as stated, this is only the median of the probable values; i.e. for 2 peaks MPM = 1.17*m0 which is obviously too small to be realistic for a design value. When using a non-exceedance value of p=0.001 (i.e. 99..9% probability of non-exceedance) the formula becomes m0*sqrt(2*ln(n/p)) and the not to exceed maxima then becomes 3.89*m0, which is a far more realistic value for a not to exceed single event. This method works especially well when there is enough data to conduct the FFT to transfer the response to the frequency domain, as m0 and 'n' are easily calculable.

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