Extreme Response Predictions for Jack-Up Units in Second Order Stochastic Waves by FORM

2007 ◽  
Author(s):  
Jo̸rgen Juncher Jensen
Keyword(s):  
Second Order ◽  
Sea State ◽  
First Order ◽  
Reliability Method ◽  
Extreme Response ◽  
Stochastic Waves ◽  
Short Time ◽  
Wave Induced ◽  
Jack Up ◽  
Operational Time

The aim of the present paper is to advocate for a very effective stochastic procedure, based on the First Order Reliability Method (FORM), for extreme value predictions related to wave induced loads. All kinds of non-linearities can be included, as the procedure makes use of short time-domain simulations of the response in question. The procedure will be illustrated with a jack-up rig where second order stochastic waves are included in the analysis. The result is the probability of overturning as function of sea state and operational time.

Long Term Failure Probability Calculation Method Applied to Riser Design

2008 ◽  
Author(s):  
Timothe´e Perdrizet ◽  
Daniel Averbuch
Keyword(s):  
Failure Probability ◽  
Sea State ◽  
Reliability Method ◽  
Extreme Response ◽  
Probability Calculation ◽  
Riser Design ◽  
The Mean ◽  
Time Invariant ◽  
Wave Induced

A time efficient methodology is described to evaluate the non linear extreme response of a riser connected to a FPSO subjected to wave induced loads in a stationary sea state. It is extended to cover all sea states and thus to assess the long term failure probability of the riser. The short term procedure is based on a classic time variant reliability method. It uses an approximation of the mean outcrossing rate, which is computed with the time invariant reliability method FORM (First Order Reliability Method).

Extreme Load Predictions for Floating Offshore Wind Turbines

2009 ◽  
Author(s):  
Jo̸rgen Juncher Jensen
Keyword(s):  
Wind Turbines ◽  
Offshore Wind ◽  
Offshore Wind Turbines ◽  
First Order ◽  
Floating Offshore Wind Turbines ◽  
Extreme Load ◽  
Reliability Method ◽  
Short Time ◽  
Wave Induced ◽  
Stochastic Loads

An effective stochastic procedure for extreme value predictions related to wave and wind induced stochastic loads is applied to a tension-leg concept for floating offshore wind turbines. The method is based on the First Order Reliability Method (FORM) and as the procedure makes use of only short time-domain simulations all kinds of non-linearities can be included. The procedure has been used previously for wave induced loads and is in this note extended to combined wave and wind loads.

Second-Order Reliability Method With First-Order Efficiency

2010 ◽  
Author(s):  
Xiaoping Du ◽  
Junfu Zhang
Keyword(s):  
Limit State ◽  
Saddlepoint Approximation ◽  
Quadratic Function ◽  
Second Order ◽  
State Function ◽  
Limit State Function ◽  
First Order ◽  
Reliability Method ◽  
Order Of Magnitude ◽  
Univariate Function

The widely used First Order Reliability Method (FORM) is efficient, but may not be accurate for nonlinear limit-state functions. The Second Order Reliability Method (SORM) is more accurate but less efficient. To maintain both high accuracy and efficiency, we propose a new second order reliability analysis method with first order efficiency. The method first performs the FORM and identifies the Most Probable Point (MPP). Then the associated limit-state function is decomposed into additive univariate functions at the MPP. Each univariate function is further approximated as a quadratic function, which is created with the gradient information at the MPP and one more point near the MPP. The cumulant generating function of the approximated limit-state function is then available so that saddlepoint approximation can be easily applied for computing the probability of failure. The accuracy of the new method is comparable to that of the SORM, and its efficiency is in the same order of magnitude as the FORM.

Metocean Design Criteria for Pipeline On-Bottom Stability

2011 ◽  
Author(s):  
Richard Gibson
Keyword(s):  
Parametric Representation ◽  
Extreme Value Analysis ◽  
Design Criteria ◽  
Value Analysis ◽  
Reliability Method ◽  
Extreme Response ◽  
Wave Cycle ◽  
Induced Velocity ◽  
Pipeline Design ◽  
Wave Induced

This paper is concerned with a response based method for determining metocean design criteria for offshore pipelines. The method determines a set of metocean parameters that are consistent with the extreme response of the pipeline, and hence, incorporates the dependence between them implicitly. However, there are a number of challenges in its application. Firstly, the loading on a pipeline is dependent on the previous wave cycle, and hence, the drag and inertia coefficients vary within a sea-state. Secondly, along many pipeline routes the waves are depth limited and the short-term distribution of wave induced velocity and pipeline response can be difficult to define. These challenges are overcome through a number of approaches that include a parametric representation of the distribution of the response and the application of multivariate extreme value analysis. Furthermore, the sensitivity of the method to assumptions about the pipeline design is examined, and the problems with using the combined wave and current induced velocity as a proxy for the response are discussed. The method is applied to a site in the Mediterranean Sea and the results are compared to those from the application of the first order reliability method.

A Second-Order Reliability Method With First-Order Efficiency

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Junfu Zhang ◽  
Xiaoping Du
Keyword(s):  
Limit State ◽  
Saddlepoint Approximation ◽  
Quadratic Function ◽  
Second Order ◽  
State Function ◽  
Limit State Function ◽  
First Order ◽  
Reliability Method ◽  
Order Of Magnitude ◽  
Univariate Function

The first-order reliability method (FORM) is efficient but may not be accurate for nonlinear limit-state functions. The second-order reliability method (SORM) is more accurate but less efficient. To maintain both high accuracy and efficiency, we propose a new second-order reliability analysis method with first-order efficiency. The method first performs the FORM to identify the most probable point (MPP). Then, the associated limit-state function is decomposed into additive univariate functions at the MPP. Each univariate function is further approximated by a quadratic function. The cumulant generating function of the approximated limit-state function is then available so that saddlepoint approximation can be easily applied in computing the probability of failure. The accuracy of the new method is comparable to that of the SORM, and its efficiency is in the same order of magnitude as the FORM.

Deficits and Recovery of First-Order and Second-Order Motion Perception in Patients with Unilateral Posterior Parietal Lesions

Perception ◽  
1996 ◽  
Vol 25 (1_suppl) ◽  
pp. 22-22 ◽  
Author(s):  
D Braun ◽  
M Fahle ◽  
P Schönle ◽  
J Zanker
Keyword(s):  
Motion Perception ◽  
Time Course ◽  
Random Noise ◽  
Second Order ◽  
The Other ◽  
Rectangular Region ◽  
First Order ◽  
Posterior Parietal ◽  
Short Time ◽  
Visual Hemifields

Our aim was to test whether unilateral posterior parietal lesions degrade first-order and second-order motion differentially, and to investigate the time course of any potential recovery. We tested ten patients with circumscribed parietal lesions. Thresholds were measured for the discrimination of the direction of motion of stimuli presented 5.5° peripherally in the ipsilesional and contralesional visual hemifields. Subjects had to indicate whether a rectangular region (1.6 deg × 3 deg) embedded in dynamic random noise background moved up or down. The region contained moving (signal) and flickering (background) dots and moved for 1 s at 2.36 deg s−1. Signal dots were either (a) coherently moving in the same direction as the region (first-order), (b) stationary (second-order), or (c) coherently moving in the opposite direction (theta). Thresholds were defined as percentage of signal dots within the region yielding 75% correct responses. All patients had higher thresholds for second-order than for first-order motion. When contralesional and ipsilesional thresholds were compared, three patients showed proportional threshold elevations for all three types of motion stimuli in the contralesional hemifield. Two of these three patients were tested again five months later. Both showed considerable recovery: in one patient, the contralesional deficit was no longer present; in the other, it was reduced by about half. None of our patients had lesions affecting first-order or second-order motion differentially; lesions always affected first-order and second-order motion similarly. Owing to recovery, these deficits might be detectable only for a short time.

Long-Term Extreme Response of a Straight Floating Bridge Across the Bjørnafjord

2019 ◽  
Author(s):  
Finn-Idar Grøtta Giske ◽  
Arnt Fredriksen
Keyword(s):  
Computational Effort ◽  
Response Analysis ◽  
Peak Period ◽  
First Order ◽  
Environmental Models ◽  
Reliability Method ◽  
Extreme Response ◽  
Floating Bridge ◽  
The Given

Abstract In this paper, long-term extreme response analysis is performed for a straight floating bridge across the Bjørnafjord, using a recently developed inverse first-order reliability method (IFORM) approach. Full integration of the long-term extreme response formulation is also performed for comparison. Two different environmental models are estimated based on a scatter diagram of significant wave height and peak period for the given location. The IFORM method is seen to provide reasonable estimates of the long-term extreme response, at a significantly reduced computational effort.

Time Domain Simulation of Jack-up Dynamics With the Extremes of a Gaussian Process

1997 ◽  
Vol 119 (4) ◽  
pp. 624-628 ◽  
Author(s):  
P. H. Taylor ◽  
P. Jonathan ◽  
L. A. Harland
Keyword(s):  
Time Domain ◽  
Random Sequence ◽  
Time Domain Simulation ◽  
Sea State ◽  
Efficient Manner ◽  
Large Wave ◽  
Random Occurrence ◽  
Statistical Limit ◽  
Extreme Response ◽  
Jack Up

Random simulations are often used to simulate the statistics of storm-driven waves. Work on Gaussian linear random signals has lead to a method for embedding a large wave into a random sequence in such a way that the composite signal is virtually indistinguishable (in a rigorous statistical limit) from a purely random occurrence of a large wave. We demonstrate that this idea can be used to estimate the extreme response of a jack-up in a severe sea-state in a robust and efficient manner. Results are in good agreement with those obtained from a full random time-domain simulation.

Second-Order Reliability Method Based on Edgeworth Expansion With Application to Reliability-Based Design Optimization

2019 ◽  
Author(s):  
Rami Mansour ◽  
Mårten Olsson
Keyword(s):  
Design Optimization ◽  
Limit State ◽  
Probability Of Failure ◽  
Second Order ◽  
State Function ◽  
Reliability Based Design Optimization ◽  
First Order ◽  
Reliability Based Design ◽  
Statistical Measures ◽  
Reliability Method

Abstract In the Second-Order Reliability Method, the limit-state function is approximated by a hyper-parabola in standard normal and uncorrelated space. However, there is no exact closed form expression for the probability of failure based on a hyper-parabolic limit-state function and the existing approximate formulas in the literature have been shown to have major drawbacks. Furthermore, in applications such as Reliability-based Design Optimization, analytical expressions, not only for the probability of failure but also for probabilistic sensitivities, are highly desirable for efficiency reasons. In this paper, a novel Second-Order Reliability Method is presented. The proposed expression is a function of three statistical measures: the Cornell Reliability Index, the skewness and the Kurtosis of the hyper-parabola. These statistical measures are functions of the First-Order Reliability Index and the curvatures at the Most Probable Point. Furthermore, analytical sensitivities with respect to mean values of random variables and deterministic variables are presented. The sensitivities can be seen as the product of the sensitivities computed using the First-Order Reliability Method and a correction factor. The proposed expressions are studied and their applicability to Reliability-based Design Optimization is demonstrated.

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