Digital bispectral analysis applied to stationary response of flexible lines

Abstract

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.

3D tolerance modeling and geometric precision analysis of plane features for flexible parts

“…In this paper, the least square method is used to fit the deformation surface point cloud data of the joint surface under load based on the N-GPS so as to complete the conversion from the non-ideal element to the ideal element. The fitting diagram is shown in Figure 8, and its mathematical model is (Dias and Petreche, 2000): where, i is the spatial discrete points; p is the function series; n is the number of non-ideal element point; r i is the distances margin between the spatial discrete points and the ideal fitting elements.…”