Autoregressive spectral modeling: Difficulties and remedies

Many problems of non-linear mechanics can be treated only by the Monte Carlo method. An efficient approach for conducting Monte Carlo simulations relies on using digital filters. In this paper the difficulties associated with the computation of reliable digital autoregressive (AR) approximations of stochastic processes of engineering practice with troublesome spectra, such as the Pierson-Moskowitz sea waves spectrum and the Davenport wind spectrum, are investigated from a new perspective. It is known that the AR model whose coefficients are obtained as straightforward applications of the AR approximation technique can exhibit large spectral fluctuations. This symptom is explained by considering the mathematical peculiarities of the target spectra. Further, mitigation techniques that lead to reliable AR approximations are presented. Finally, a measure of the suitability of a given spectrum for AR modeling is presented. This measure can be used to predict the quality of a particular AR approximation or to select an appropriate AR system order.