Stochastic Dynamic Analysis and Reliability of a Vessel Rolling in Random Beam Seas

2015 ◽  
Vol 59 (02) ◽  
pp. 113-131
Author(s):  
Wei Chai ◽  
Arvid Naess ◽  
Bernt J. Leira
Keyword(s):  
Dynamic System ◽  
Markov Property ◽  
Planck Equation ◽  
Linear Filter ◽  
Stochastic Dynamic ◽  
Theoretical Principle ◽  
Pi Method ◽  
Beam Seas ◽  
Stochastic Dynamic Analysis ◽  
High Level

This article presents a four-dimensional (4D) path integration (PI) approach to study the stochastic roll response and reliability of a vessel in random beam seas. Specifically, a 4D Markov dynamic system is established by combing the single-degree-of freedom model used to represent the ship rolling behavior in random beam seas with a second-order linear filter used to approximate the stationary roll excitation moment. On the basis of the Markov property of the coupled 4D dynamic system, the response statistics of roll motion can be obtained by solving the Fokker-Planck equation of the dynamic system via the 4D PI method. The theoretical principle and numerical implementation of the current state of the art 4D PI method are presented. Moreover, the numerical robustness and accuracy of the 4D PI method are evaluated by comparing with the results obtained by the application of Monte Carlo simulation (MCS). The influence of the restoring terms and the damping terms on the stochastic roll response are investigated. Furthermore, based on the well-known Poisson assumption and the response statistics yielded by the 4D PI technique, evaluation of the reliability associated with high-level response is performed. The performance of the Poisson estimate for different levels of external excitations is evaluated by the versatile MCS technique.

Long-Term Extreme Response of a Vessel Rolling in Random Seas

2016 ◽  
Author(s):  
Wei Chai ◽  
Arvid Naess ◽  
Bernt J. Leira
Keyword(s):  
Nonlinear Effects ◽  
Roll Motion ◽  
Response Analysis ◽  
Linear Filter ◽  
Beam Seas ◽  
Random Seas ◽  
Extreme Response ◽  
High Level ◽  
Nonlinear Roll Motion

In this paper, the long-term extreme response of a vessel rolling in random beam seas is addressed. The long-term response analysis is based on the upcrossing rates of the roll motion under different sea states. However, the nonlinear effects associated with the restoring and damping terms have a significant influence on the high-level response, assessing the corresponding statistics, such as the upcrossing rate, with low probability levels is difficult and time-consuming. In this work, the Markov theory is introduced in order to tackle this problem. Specifically, the random roll excitation moment is approximated as a filtered white noise process by applying a linear filter technique and an efficient four-dimensional (4D) path integration (PI) procedure is applied in order to calculate the response statistics. The long-term analysis of nonlinear roll motion in random seas that takes into considerations of the response statistics obtained by the 4D PI method as well as the variation of the sea states could be a valuable reference for ship stability research.

scholarly journals Stochastic Dynamic Analysis of an Offshore Wind Turbine Structure by the Path Integration Method

Energies ◽  
2019 ◽  
Vol 12 (16) ◽  
pp. 3051
Author(s):  
Yue Zhao ◽  
Jijian Lian ◽  
Chong Lian ◽  
Xiaofeng Dong ◽  
Haijun Wang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Wind Turbine ◽  
Path Integration ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Stochastic Dynamic ◽  
Pi Method ◽  
Sdof System ◽  
Stochastic Dynamic Analysis

Stochastic dynamic analysis of an offshore wind turbine (OWT) structure plays an important role in the structural safety evaluation and reliability assessment of the structure. In this paper, the OWT structure is simplified as a linear single-degree-of-freedom (SDOF) system and the corresponding joint probability density function (PDF) of the dynamic response is calculated by the implementation of the path integration (PI) method. Filtered Gaussian white noise, which is obtained from the utilization of a second-order filter, is considered as horizontal wind excitation and used to excite the SDOF system. Thus, the SDOF model and the second-order linear filter model constitute a four-dimensional dynamic system. Further, a detailed three-dimensional finite element model is applied to obtain the natural frequency of the OWT and the efficient PI method, which is modified based on the fast Fourier transform (FFT) convolution method, is also utilized to reduce the execution time to obtain the PDF of the response. Two important parameters of wind conditions, i.e., horizontal mean wind speed and turbulence standard deviation, are investigated to highlight the influences on the PDF of the dynamic response and the reliability of the OWT.

Stochastic Dynamic Analysis of Structures with Spatially Uncertain Material Parameters

2014 ◽  
Vol 14 (08) ◽  
pp. 1440029 ◽  
Author(s):  
Kheirollah Sepahvand ◽  
Steffen Marburg
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Polynomial Chaos ◽  
Element Model ◽  
Stochastic Dynamic ◽  
Stochastic Field ◽  
Structural Dynamic ◽  
Material Parameters ◽  
Material Uncertainties ◽  
Stochastic Dynamic Analysis

This paper investigates the uncertainty quantification in structural dynamic problems with spatially random variation in material and damping parameters. Uncertain and locally varying material parameters are represented as stochastic field by means of the Karhunen–Loève (KL) expansion. The stiffness and damping properties of the structure are considered uncertain. Stochastic finite element of structural modal analysis is performed in which modal responses are represented using the generalized polynomial chaos (gPC) expansion. Knowing the KL expansions of the random parameters, the nonintrusive technique is employed on a set of random collocation points where the structure deterministic finite element model is executed to estimate the unknown coefficients of the polynomial chaos expansions. A numerical case study is presented for a cantilever beam with random Young's modulus involving spatial variation. The proportional damping constants are estimated from the experimental modal analysis. The expected value, standard deviation, and probability distribution of the random eigenfrequencies and the damping ratios are evaluated. The results show high accuracy compared to the Monte-Carlo (MC) simulations with 3000 realizations. It is also demonstrated that the eigenfrequencies and the damping ratios are equally affected from material uncertainties.

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