Probability of Capsizing in Beam Seas with Piecewise Linear Stochastic GZ Curve

Belenky, Vadim; Reed, Annette Yoshiko; Weems, Kenneth

doi:10.1007/978-94-007-1482-3_30

Cited by 3 publications

(4 citation statements)

References 6 publications

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“…Both phenomena have certain inertia, so the parameters of time-varying stability are described by stochastic processes rather than random variables. Belenky et al (2011) describes a simple mathematical model where the intercept in Range 1 is a linear function of heave:…”

Section: Piecewise Linear Systemmentioning

confidence: 99%

“…As the intercept is a linear function of heave, the time-dependent boundary  m (t) is also a linear function of the heave displacement, which is also linear. A Fourier series presentation for x(t) is available from Belenky et al (2011), which allows the upcrossing rate to be expressed using formula (11):…”

Section: Non-rare Problemmentioning

confidence: 99%

“…The process y(t) is a linear combination of normal processes and can be presented with a Fourier series (Belenky et al, 2011). The capsizing event is associated with a negative value of y at the instant of upcrossing.…”

Section: Rare Problemmentioning

confidence: 99%

“…are the conditional mean and the conditional standard deviation of the derivative of the process x(t) if the processes x(t) and y(t) took particular values (see formulations in Belenky et al, 2011). Note that the conditional mean is a function of the value of the process y at upcrossing, while the standard deviation is a constant; erf() is the standard error function (see Belenky et al (2013) for details).…”

Section: Rare Problemmentioning

confidence: 99%

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Split-time method for estimation of probability of capsizing caused by pure loss of stability

Belenky¹,

Weems²,

Lin

2016

Ocean Engineering

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The paper reviews a multi-year research effort for using the split-time method to calculate the probability of ship capsizing due to pure loss of stability in irregular waves. The idea of the splittime method is to separate the complex problem into two less complex problems: a non-rare problem that involves the upcrossing of an intermediate level of roll and a rare problem that focuses on capsizing after an upcrossing. An initial implementation using a dynamic model with piecewise linear stiffness, which can be considered to be the simplest model of capsizing in beam seas, led to the concept of critical roll rate as the smallest roll rate at the instant of upcrossing that inevitably leads to capsizing. The extension of the split-time method to pure loss of stability required the consideration of the change of roll stiffness in waves and led to calculating the critical roll rate at each upcrossing. A metric of the likelihood of capsizing has been defined as the difference between the observed and critical roll rate at the instances of upcrossing. The probability of capsizing after upcrossing is found by approximating the tail with the Generalized Pareto Distribution.

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Section: Piecewise Linear Systemmentioning

confidence: 99%

Section: Non-rare Problemmentioning

confidence: 99%

Section: Rare Problemmentioning

confidence: 99%

Section: Rare Problemmentioning

confidence: 99%

See 2 more Smart Citations