Structural instrumentation and monitoring of the Block Island Offshore Wind Farm

publishedVersio

Stochastic integral/calculus for non-Gaussian delta-correlated processes

In recent years there have been many publications studying dynamic systems subjected to non-Gaussian delta-correlated processes, but only a few address the fundamental stochastic integral and calculus associated with this kind of processes. Di Paola and Falson (1993) has attempted to derive the stochastic integral and calculus for non-Gaussian delta-correlated processes (called generalized Ito stochastic integral and calculus), but their derivations are not without controversy. This article, following an engineering-oriented proof approach, shows peculiar properties associated with generalized Ito stochastic integrals and calculus. Some results derived in this study are found in fundamental disagreement with those by Di Paola and Falson (1993)

Response cumulant equations for dynamic systems under delta-correlated processes

This paper develops response cumulant differential equations (CDEs) that can be used to calculate response cumulants for dynamic systems under non-Gaussian, delta-correlated excitations. The derived CDEs apply to both linear and nonlinear systems, an improvement over the previous CDEs that are only applicable to linear systems. The new CDEs also can be used much more efficiently than the previous version. The problem of a second-order, single-degree-of-freedom (SDOF) linear system subjected to non-Gaussian, delta-correlated excitations is given to illustrate how to use the new CDEs for calculating response cumulants. Closed-form solutions for the stationary response cumulants are presented

Cumulants of the nonlinear combination of independent random variables

A random variable of interest is often the sum of linear or nonlinear combinations of many independent random variables. In calculating the statistics of this random sum, advantages of simplicity and computational efficiency can be obtained by operating with cumulants

Response cumulant equations for dynamic systems under delta-correlated processes

Cumulant differential equations (CDEs) that can be employed to calculate response cumulants for linear/nonlinear dynamic systems under non-Gaussian, delta-correlated excitations are derived using a state-space method. General CDEs applicable to both linear and nonlinear systems are derived. The computational advantages of using CDEs over using moment differential equations (MDEs) in calculating response statistics when the systems are linear are illustrated

EFFECTS OF NONNORMALITY ON STOCHASTIC STRUCTURAL DYNAMICS AND FATIGUE

The use of stochastic process theory in a structural dynamic analysis is usually restricted to normal processes. Recent studies have shown that the influence of nonnormality on both fatigue failures and first-excursion failures cannot be neglected. Basically, the aim of this study is to understand the effects of nonnormality on structural dynamics and fatigue, particularly as related to offshore structures. Several related aspects of the problem are studied. The fourth order cumulant function is taken as a reasonable measure of the departure of a process from normality. However, in practice, it is not easy to see the degree of nonnormality of a process directly from the fourth order cumulant function, because of its multidimensional nature. Therefore, the kurtosis or the coefficient of excess is used as a simpler index to represent the degree of nonnormality. The study significantly extends the usual description of wave forces by deriving a description for the nonnormal part of the wave force. An approximation for the fourth cumulant function (and corresponding three-dimensional power spectral density) of a wave force is obtained. Because the degree of nonnormality of the response of a linear structure subjected to a wave force is not easily obtained, analytical studies are also made for a linear SDF structure subjected to somewhat simpler nonnormal forces. An efficient technique for calculating the response kurtosis is derived. Another aim of this study is to estimate the effect of nonnormality of fatigue damage. Both analytical and simulation results confirm that the effect of nonnormality should not be neglected. Simulation studies are also made for the dynamic response of an idealized structure subjected to a stochastic wave force. It is found the degree of nonnormality of the response is quite substantial, but never exceeds the degree of nonnormality of the excitation, at least for the situations considered

Responses of dynamic systems excited by non-gaussian pulse processes

This paper presents an efficient method for calculating the response statistics of dynamic systems subjected to Poisson-distributed (non-Gaussian) pulse processes. The procedure to be followed is based on an extension of the traditional method of the It6 stochastic differential equation, in which the increment of the Wiener process associated with the It0 stochastic differential equation has been substituted by the increment of a compound Poisson process. One major achievement here is the derivation of a general moment equation suitable to Poissondistributed pulse excitations. Two examples of application (for linear and nonlinear systems) are given to illustrate the use of the derived moment equation. Exact response moments for linear systems can be calculated efficiently. In studying a nonlinear oscillator with a use of fourth-order cumulant-neglect method, it is found that the calculation for response moments of second order is reasonably accurate, although this is not so for moments of fourth order. © ASCE

Refinement of reduced-models for dynamic systems

A refinement procedure for the reduced models of structural dynamic systems is presented in this article. The refinement procedure is to “tune” the parameters of a reduced model, which could be obtained from any traditional model reduction scheme, into an improved reduced model. Upon the completion of the refinement, the improved reduced model matches the dynamic characteristics – the chosen structural frequencies and their mode shapes – of the full order model. Mathematically, the procedure to implement the model refinement technique is an application of the recently developed cross-model cross-mode (CMCM) method for model updating. A numerical example of reducing a 5-DOF (degree-of-freedom) classical mass-spring (or shear-building) model into a 3-DOF generalized mass-spring model is demonstrated in this article

Simultaneous mass, damping, and stiffness updating for dynamic systems

This paper presents an efficient and systematic approach to simultaneously update the mass, damping, and stiffness matrices of linear dynamic systems, given few (say two) measured complex vibration modes (complex eigenvalues and eigenvectors). The method is termed the cross-model cross-mode method because it involves solving a set of linear simultaneous equations in which each equation is formulated based on the product terms from two same/different modes associated with the mathematical and experimental models, respectively. Two numerical examples are demonstrated: a 4-degree-of-freedom mass-spring-damper system and a 30-degree-of-freedom finite element model for a cantilever beam. The numerical updating by the cross-model cross-mode method is excellent for all system matrices when the measured modes are spatially complete and noise free. The cross-model cross-mode method, together with the Guyan reduction scheme, also performs reasonably well under a spatial incompleteness situation