Stochastic nonlinear ship rolling in random beam seas by the path integration method

Chai, Wei; Næss, Arvid; Leira, Bernt J.

doi:10.1016/j.probengmech.2015.10.002

Cited by 35 publications

(25 citation statements)

References 21 publications

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“…While establishing the mathematical model, the couplings between the roll motion and other modes of ship motion are ignored to make the equation of roll motion simpler [5][6][7][8][9]. This assumption is based on the idea that roll motion has a greater influence on the ship stability in beam seas rather than the other modes of ship motion.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The single degree of freedom (SDOF) roll motion equation in random beam seas can be represented by the equation (1) [5][6][7][8].…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The stochastic roll response and reliability of a ship in random beam seas is studied by using a four-dimensional (4D) path integration (PI) approach in the studies of Chai et al [5][6][7][8] where a 4D Markov dynamic system is established by combining the single-degree-of freedom model used to represent the ship rolling behaviour in random beam seas with a second-order linear filter used to approximate the stationary roll excitation moment.…”

Section: Introductionmentioning

confidence: 99%

“…In this study, firstly the roll motion in beam seas is represented by the mathematical model derived by Chai et al [5][6][7][8]. Secondly, the methodology of constructing a Lyapunov function of randomly exerted system is outlined.…”

Section: Introductionmentioning

confidence: 99%

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Lyapunov Function based Criteria for Ship Rolling in Random Beam Seas

Üçer

2019

Polish Maritime Research

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The aim of this study is to present a Lyapunov function which can be used to derive an intact stability criterion for a ship in random beam seas. First, the mathematical model of the rolling motion of ships in random beam seas is introduced. The random wave excitation is described by a spectrum which is depended on the wave energy spectrum and the amplitude of the moment of roll. This spectrum is generated by a second order linear filter. Second, the methodology of creating a Lyapunov function is explained briefly. Then, there is outlined the way by which Lyapunov function can be used as the intact stability criterion for a ship. The proposed criterion is derived by considering the weather criteria for German naval vessels. Finally, the coherence of the boundary of safe basin obtained by Lyapunov function with the numerical results obtained by Euler-Maruyama Method is presented. From the results it can be deduced that the Lyapunov function can be used to define an intact stability criterion.

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Section: Mathematical Modelmentioning

confidence: 99%

“…The single degree of freedom (SDOF) roll motion equation in random beam seas can be represented by the equation (1) [5][6][7][8].…”

Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lyapunov Function based Criteria for Ship Rolling in Random Beam Seas

Üçer

2019

Polish Maritime Research

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“…Dimentberg et al applied the path integration method of Naess et al [25,26] to obtain the response PDF of vibro-impact nonlinear systems [28]. Chai et al applied a path integration method to study nonlinear ship rolling in random beam seas [29]. Di Paola and Bucher adopted a path integration method to solve the PDF of nonlinear system with ideal or physical barriers [30].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Analysis of a Nonlinear Business Cycle Model with Correlated Random Income Disturbance

Zhao

2018

Mathematical Problems in Engineering

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The economic cycle has always been an important feature of the evolution of an economic system. In the presence of many uncertain factors, it appears in the manner of very complex nonlinearity and randomness. Based on the theory of stochastic nonlinear dynamics, a nonlinear economic cycle model with correlated random income disturbance is established. The probability density evolution of the nonlinear economic cycle model under random disturbance is numerically analyzed by using a path integration method. The analysis shows the high saving rate reduces the investment and improves the probabilities of low income and low income change rate. In order to achieve a higher income, the saving rate should be controlled to some reasonable small value. The nonlinearity of the economic cycle model increases the probabilities of high income and high income change rate, which can lead to the increase of income in a probabilistic sense. The increase of random income interference enhances the uncertainty of income. Meanwhile, the increase of correlated random income disturbance can lead to a nonsymmetric distribution of the probability distributions of income and income change rate. In such cases, the income is more difficult to forecast and control.

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A comparative study of the stochastic averaging method and the path integration method for nonlinear ship roll motion in random beam seas

et al. 2017

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In this paper, the energy-based stochastic averaging method and the path integration (PI) method are applied to study the stochastic response of the nonlinear roll motion in random beam seas. Specifically, the Markov diffusion theory is applied to describe the random roll motion such that the probabilistic properties of the ship roll motion are governed by the Fokker-Planck (FP) equation. The stochastic averaging method focuses on the roll energy envelope process and reduces the difficulty in calculating the stochastic response via a dimensional reduction of the original system. In contrast, the path integration method is based on the Markov property of the original dynamical system and provides approximate solutions to the FP equation by linking the explicitly known local solutions. Although the stochastic averaging technique is well established in the study of the stochastic responses of various dynamical systems, its accuracy for determining the high-level roll response has not yet been a focus of study. This paper aims to provide a comparative study for the performance of the two abovementioned methods, additionally, the advantages and shortcomings of using each method for studying the nonlinear roll motion in beam seas are demonstrated by practical calculations.

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Stochastic nonlinear ship rolling in random beam seas by the path integration method

Cited by 35 publications

References 21 publications

Lyapunov Function based Criteria for Ship Rolling in Random Beam Seas

Lyapunov Function based Criteria for Ship Rolling in Random Beam Seas

Stochastic Analysis of a Nonlinear Business Cycle Model with Correlated Random Income Disturbance

A comparative study of the stochastic averaging method and the path integration method for nonlinear ship roll motion in random beam seas

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