The Statistics of the Second Order Response of an FPSO in Spreading Seas

2009 ◽  
Author(s):  
Yahui Zhang ◽  
Robin S. Langley
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Transfer Functions ◽  
Extreme Values ◽  
Second Order ◽  
Wave Direction ◽  
Hydrodynamic Approach ◽  
Force Transfer ◽  
Extreme Response

An expression for the probability density function of the second order response of a general FPSO in spreading seas is derived by using the Kac-Siegert approach. Various approximations of the second order force transfer functions are investigated for a ship-shaped FPSO. It is found that, when expressed in non-dimensional form, the probability density function of the response is not particularly sensitive to wave spreading, although the mean squared response and the resulting dimensional extreme values can be sensitive. The analysis is then applied to a Sevan FPSO, which is a large cylindrical buoy-like structure. The second order force transfer functions are derived by using an efficient semi-analytical hydrodynamic approach, and these are then employed to yield the extreme response. However, a significant effect of wave spreading on the statistics for a Sevan FPSO is found even in non-dimensional form. It implies that the exact statistics of a general ship-shaped FPSO may be sensitive to the wave direction, which needs to be verified in future work. It is also pointed out that the Newman’s approximation regarding the frequency dependency of force transfer function is acceptable even for the spreading seas. An improvement on the results may be attained when considering the angular dependency exactly.

Methods of Computing the Probability of Failure Under Extreme Values of Bending Moment

1972 ◽  
Vol 16 (02) ◽  
pp. 113-123
Author(s):  
Alaa Mansour
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Extreme Values ◽  
Bending Moment ◽  
Random Variable ◽  
Probability Of Failure ◽  
Short Term ◽  
Term Analysis

Methods for predicting the probability of failure under extreme values of bending moment (primary loading only) are developed. In order to obtain an accurate estimate of the extreme values of the bending moment, order statistics are used. The wave bending moment amplitude treated as a random variable is considered to follow, in general, Weibull distribution so that the results could be used for short-term as well as long-term analysis. The probability density function of the extreme values of the wave bending moment is obtained and an estimate is made of the most probable value (that is, the mode) and other relevant statistics. The probability of exceeding a given value of wave bending moment in "n" records and during the operational lifetime of the ship is derived. Using this information, the probability of failure is obtained on the basis of an assumed normal probability density function of the resistive strength and deterministic still-water bending moment. Charts showing the relation of the parameters in a nondimensional form are presented. Examples of the use of the charts for long-term and short-term analysis for predicting extreme values of wave bending moment and the corresponding probability of failure are given.

scholarly journals Estimacion de los valores de retorno de la altura de ola en la Provincia de Buenos Aires, Argentina

1997 ◽  
Vol 24 (1-2) ◽  
pp. 13
Author(s):  
FERNANDO CAVIGLIA ◽  
JORGE POUSA
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Wave Height ◽  
Standard Method ◽  
Buenos Aires ◽  
Extreme Values ◽  
Probability Distributions ◽  
Best Fit ◽  
Return Value

The wave height recorded at 8 stations along the oceanic coast of the Province of Buenos Aires, Argentina, was analysed to estimate the 50-year return value of wave height at each station. The probability distributions of wave height for the measurements made at Mar de Ajó (1976/85), punta Médanos (northern and southern waveriders, 1981/84), Pinamar (1976/91), Mar del Plata (1968/69), Puerto Quequén (1975/76), Pehuen-Có (1986/88) and El Cóndor (1988) summer resort were tested with the theoretical distributions of Rayleigh, Weibull and Fisher-Tippett I. Excluding Mar de Ajó and El Cóndor, the best fit was obtained with the Fisher-Tippett probability density function. The method of Battjes for estimating the return values of wave height was applied and the resulting 50-year return values were 2.80; 6.90; 7.90; 7.20; 7.21; 8.20; 4.30 and 2.84 m for Mar de Ajó, punta Médanos (northern waverider), punta Médanos (southern waverider), Pinamar, Mar del Plata, Puerto Quequén, Pehuen-Có and El Cóndor, respectively. Lastly, the standard method of extreme values was used to analyse 10 and 16 annual wave height maxima from Mar de Ajó and Pinamar, respectively. The 50-year return values were found to be 2.30 m for Mar de Ajó and 7.20 m for Piramar.

scholarly journals Inequalities Between First and Second Order Moments for Continuous Probability Distribution

2020 ◽  
Vol 9 (4) ◽  
pp. 744-747
Keyword(s):  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
Continuous Distribution ◽  
Random Variables ◽  
Second Order ◽  
Research Article ◽  
Probability Density Function Pdf ◽  
Better Than

In this research article we obtained some inequalities between moments of 1st and 2nd order for a continuous distribution over the interval [x, y], when infimum and supremum of the continuous probability distribution is taken into consideration. These inequalities have shown improvement and are better than those exist in literature. Inequalities also obtained for continuous random variables which vary in [x, y] interval, such that the probability density function (pdf) (t) become zero in [p, q]  [x, y].The improvement in inequalities have been shown graphically. Here in this paper we deduced some existing inequalities by using the inequalities obtained in Theorem 2.1 and Theorem 2.2.

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