Dynamic analysis: Time history synthesis

The results of a frequency domain analysis are necessarily statistical in nature: the statistics are those of the result over all possible realisations, and any quantitative judgements of the model should be based on these statistics. An understanding of the underlying system, and the ability to make qualitative judgements, is, however, often more naturally gained by viewing the results in the time domain; time history synthesis is a way of doing so.

Time history synthesis is the process of generating a single, deterministic time domain realisation from the stochastic processes arising from the frequency domain solution. OrcaFlex does this internally, enabling you to see time domain replays, time histories and envelope range graphs from frequency domain results.

Replays and time history reporting of frequency domain results are much the same as for time domain results. In the absence of a time step and simulation start and finish times, however, the period over which they are defined needs to be specified. For a replay, the start time, finish time, and the sample interval are all defined by the replay parameters. For time histories and envelope range graphs, the start time and finish time are given on the results form and the sample interval is given on the results page of the general data form.

When synthesising a replay, contact drawing is intentionally based on the static state model. Contact is drawn in this way because this is the model state in which the system is linearised for frequency domain solution.

Synthesis method

Broadly speaking, to synthesise a time history of a particular result, the harmonic components of the result process (which define the dynamic part of the result) are each assigned a random phase and superimposed on the static part.

For a process associated with first order wave loading, i.e. following a solve at wave frequency, the user-defined wave seed is used to assign random phases consistently with time domain analysis. This means that for a system which is well approximated as linear, undergoing only wave frequency loading, a realisation synthesised from the frequency domain solution will show strong correlation with the corresponding time domain simulation. Similarly, realisations synthesised from processes associated with wind velocity, i.e. following a low frequency solve with only wind loading present, will also show strong correlation – in this case, the user-defined wind seed is used to assign random phases in a manner consistent with time domain analysis.

The wave drift load process is not, however, correlated with the wave elevation process in the frequency domain treatment. To synthesise a realisation from processes mapped from the wave drift load process, i.e. following a low frequency solve with a vessel that includes wave drift load, the user-defined wave drift load component seed is used to assign random phase. In time domain analysis there is no requirement for such a seed because the wave drift load is entirely deterministic and can be calculated directly at each time step, from the wave components, through a nonlinear relationship. This means that realisations synthesised from such processes will not be correlated with time domain simulation: it is not possible to tie them to a common time origin.