Digital bispectral analysis applied to stationary response of flexible lines

In marine structures, the long-term non-stationary response of flexible lin es, due to random environmental loads, may be regarded as successive short- term stationary processes in which current, wind and ocean wave conditions remain constant The power spectrum of each stationary process can be charac terized by its linear and non-linear energy components: the linear energy d efines a Gaussian process, and the additional nonlinear energy characterize s a non-Gaussian Process. Within this scope, digital bispectral analysis ha s enabled one to describe nonlinear stationary response of flexible lines i n the frequency domain, so that the complex coefficients of a quadratic mod el, in the frequency domain, can be estimated The real and symmetrical matr ix constructed from these coefficients has eigenvalues and eigenvectors use ful to describe the characteristic function of the response from where the Probability density function can be obtained by using a fast Fourier transf orm algorithm. The bases of the method presented here have already been tre ated in a similar but pure algebraic method, to obtain the asymptotic Proba bility function applicable to the response of non-linear systems in closed form.