Reduced order ARMA spectral estimation of ocean waves

Several system identification techniques are available for determining parametric models of dynamic systems based on the input and output of stochastic processes such as ocean waves. Here we establish a reduced order Autoregressive Moving Average (ARMA) algorithm which is based on the calculation of modal energies. We apply this system identification technique to reduce time series data or target spectra into a few parameters which are the coefficients of the ARMA model. After selecting the initial model order based on the Akaike Information Criterion method, a novel model order reduction technique is applied to obtain the final reduced order ARMA model. First estimates of the higher order autoregressive coefficients are determined using the modified Yule-Walker equations and then first and second order real modes are obtained from the autoregressive polynomial. The energy in each mode is then determined. Considering only the higher energy modes, the autoregressive part of the reduced order ARMA model is obtained. The moving average part is determined based on partial fraction and recursive methods. The above system identification models and model order reduction technique are shown here to be successfully applied to the estimation of ocean wave spectra.