Digital bispectral analysis applied to stationary response of flexible lines

In marine structures, the long‐term non‐stationary response of flexible lines, 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 characterized by its linear and non‐linear energy components: the linear energy defines a Gaussian process, and the additional nonlinear energy characterizes a non‐Gaussian process. Within this scope, digital bispectral analysis has enabled one to describe non‐linear stationary response of flexible lines in the frequency domain, so that the complex coefficients of a quadratic model, in the frequency domain, can be estimated. The real and symmetrical matrix constructed from these coefficients has eigenvalues and eigenvectors useful to describe the characteristic function of the response from where the probability density function can be obtained by using a fast Fourier transform algorithm. The bases of the method presented here have already been treated, in a similar but pure algebraic method, to obtain the asymptotic probability function applicable to the response of non‐linear systems in closed form.