A formulation for the estimation of the low frequency damping and the quadratic wave drift force transfer function will be presented in this paper.

Synthesized time series of the waves and low frequency motions are analyzed. Parameters influencing the stochastical nature of the estimation of the quadratic transfer functions, such as length of time series, number of time segments and frequency resolution, will be discussed.

From the simulated low frequency damping and the quadratic transfer function the input signals for the analysis will be reconstructed as a means for a quality check.

In this paper two estimation methods will be discussed. One method based on cross-bi-spectral analysis and a method which is based on a minimization scheme involving the quadratic transfer coefficients and the reconstruction of the second order time series.


In the day to day practice of performing model tests on moored floating structures in waves one is often faced with the question of the validation of computed motion or force RAO's against the measured ones.

Especially for floating structures where non-linear effects can play a significant role, such as semi-submersibles in survival wave conditions. Since the beginning of the 60's analysis procedures for non-linear identification techniques have been developed (see Tick (1961)). These techniques were based on a volterra series expansion of the kernels.

The analysis of non-linear processes has been put in a more rigorous mathematical frame work by Brillinger (1972), where he introduces the description of poly spectra and higher order transfer functions. A deconvolution technique making it possible to separate linear and higher order responses has been demonstrated by Bendat (1990).

Later Dalzell (1972,1975) used cross-bi(tri)-spectral techniques, based on cross-bi-covariance estimators to determine the mean added resistance transfer function and the cubic transfer function for roll of vessels sailing in waves.

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