Semi-Empirical Single Realization and Ensemble Crest Distributions of Long-Crest Nonlinear Waves

2018 ◽  
Author(s):  
Zhenjia (Jerry) Huang ◽  
Yu Zhang
Keyword(s):  
Probability Distribution ◽  
Model Test ◽  
Nonlinear Waves ◽  
Probability Distributions ◽  
Wave Crest ◽  
Empirical Formulas ◽  
Peak Period ◽  
Single Realization ◽  
Empirical Probability ◽  
Semi Empirical

In wave basin model test of an offshore structure, waves that represent the given sea states have to be generated, qualified and accepted for the model test. We normally accept waves in wave calibration tests if the significant wave height, spectral peak period and spectrum match the specified target values. However, for model tests where the responses depend highly on the local wave motions (wave elevation and kinematics) such as wave impact on hull, green water impact on deck and air gap tests, additional qualification checks may be required. For instance, we may need to check wave crest probability distributions to avoid unrealistic wave crest in the test. To date, acceptance criteria of wave crest distribution calibration tests of large and steep waves of three-hour duration (full scale) have not been established. Two purposes of the work presented in the paper are: 1. to define and clarify the wave crest probability distribution of single realization (PDSR) and the probability distribution of wave crest for an ensemble of realizations (PDER) of a given sea state in order to use them appropriately; and 2. to develop semi-empirical probability distributions of nonlinear waves for both PDSR and PDER for easy, practical use. We found that in current practice ensemble and single realization distributions have the potential to be misinterpreted and misused. Clear understanding of the two kinds of distributions will help appropriate offshore design and production unit performance assessments. The semi-empirical formulas proposed in this paper were developed through regression analysis of crest distributions from a large number of sea states and realizations. Wave time series from potential flow simulations, computational fluid dynamics (CFD) simulations and model test results were used to establish the probability distributions. The nonlinear wave simulations were performed for three-hour duration assuming that they were long-crested. The sea states are assumed to be represented by JONSWAP spectrum, where a wide range of significant wave height, peak period, spectral peak parameter, and water depth were considered. Coefficients of the proposed semi-empirical probability distribution formulas, comparisons among crest distributions from numerical simulations and the semi-empirical formulas are presented in this paper.

Semi-Empirical Crest Distributions of Long-Crest Nonlinear Waves of Three-Hour Duration

2017 ◽  
Author(s):  
Zhenjia (Jerry) Huang ◽  
Qiuchen Guo
Keyword(s):  
Nonlinear Wave ◽  
Wave Height ◽  
Model Test ◽  
Significant Wave Height ◽  
Spectral Peak ◽  
Wave Crest ◽  
Empirical Formulas ◽  
Peak Period ◽  
Significant Wave ◽  
Semi Empirical

In wave basin model test of an offshore structure, waves that represent the given sea states have to be generated, qualified and accepted for the model test. For seakeeping and stationkeeping model tests, we normally accept waves in wave calibration tests if the significant wave height, spectral peak period and spectrum match the specified target values. However, for model tests where the responses depend highly on the local wave motions (wave elevation and kinematics) such as wave impact, green water impact on deck and air gap tests, additional qualification checks may be required. For instance, we may need to check wave crest probability distributions to avoid unrealistic wave crest in the test. To date, acceptance criteria of wave crest distribution calibration tests of large and steep waves of three-hour duration (full scale) have not been established. The purpose of the work presented in the paper is to provide a semi-empirical nonlinear wave crest distribution of three-hour duration for practical use, i.e. as an acceptance criterion for wave calibration tests. The semi-empirical formulas proposed in this paper were developed through regression analysis of a large number of fully nonlinear wave crest distributions. Wave time series from potential flow simulations, computational fluid dynamics (CFD) simulations and model test results were used to establish the probability distribution. The wave simulations were performed for three-hour duration assuming that they were long-crested. The sea states are assumed to be represented by JONSWAP spectrum, where a wide range of significant wave height, peak period, spectral peak parameter, and water depth were considered. Coefficients of the proposed semi-empirical formulas, comparisons among crest distributions from wave calibration tests, numerical simulations and the semi-empirical formulas are presented in this paper.

Prediction of Green Water Events on FPSO Vessels

2003 ◽  
Author(s):  
Alexander Fyfe ◽  
Edward Ballard
Keyword(s):  
Probability Distributions ◽  
Green Water ◽  
Design Stage ◽  
Wave Crest ◽  
Peak Period ◽  
Wave Conditions ◽  
Motion Characteristics ◽  
Central North Sea

Most floating vessels experience some sea states, not necessarily extreme storms, which cause large volumes of green water to flow across the deck. Due to the location of safety critical equipment on the deck of FPSOs, the determination of the likely occurrences and the magnitudes of such events are critical to safe design and operation. A method for the determination of green water heights on the deck of an FPSO has been presented in references 1–5. This paper examines the long-term distributions of heights implied by these references and the identification of sea states in which extreme events are likely to occur. The method is based upon the long term distribution of sea states at the intended location, combined with the motion characteristics of the vessel. Freeboard exceedance at the bow and at a point along the side is considered for two typical FPSO configurations. The methodology presented is widely applicable to many locations but wave conditions typical of the Central North Sea are used by way of illustration. The results presented include long term probability distributions of green water height on deck at locations of interest. Relative contributions of each combination of significant wave height and peak period to the probability of the largest single event in a defined return period are determined and discussed. It is shown that the wave conditions most likely to give rise to the most severe green water events are seldom those characterized by the largest wave crest heights. Instead, there exists a complex dependence on characteristic periods associated with vessel motions and on the long-term occurrences of particular sea states. The ability to predict conditions in which the largest green water events are most likely to occur offers the possibility of providing improved operational guidelines for FPSOs, allowing action to be taken to avoid unfavourable loading conditions and/or vessel headings in certain sea conditions. However, it is also shown that it may be difficult to identify some severe green water sea states from normally available forecast data and hence it is important that appropriate provision is made at the design stage.

scholarly journals Empirical probability distribution validity based on accumulating statistics of observations by controlling the moving average and root-mean-square deviation

2020 ◽  
Keyword(s):  
Probability Distribution ◽  
Root Mean Square ◽  
Empirical Distribution ◽  
Probability Distributions ◽  
Expected Value ◽  
Engineering Practice ◽  
Mean Square ◽  
Real Distribution ◽  
Empirical Probability ◽  
Empirical Probability Distribution

Knowing probability distributions for calculating expected values is always required in the engineering practice and other fields. Commonly, probability distributions are not always available. Moreover, the distribution type may not be reliably determined. In this case, an empirical distribution should be built directly from the observations. Therefore, the goal is to develop a methodology of accumulating and processing observation data so that the respective empirical distribution would be close enough to the unknown real distribution. For this, criteria regarding sufficiency of observations and the distribution validity are to be substantiated. As a result, a methodology is presente О.М. Мелкозьорова1, С.Г. Рассомахінd that considers the empirical probability distribution validity with respect to the parameter’s expected value. Values of the parameter are registered during a period of observations or measurements of the parameter. On this basis, empirical probabilities are calculated, where every next period the previous registration data are used as well. Every period gives an approximation to the parameter’s expected value using those empirical probabilities. The methodology using the moving averages and root-mean-square deviations asserts that the respective empirical distribution is valid (i.e., it is sufficiently close to the unknown real distribution) if the parameter’s expected value approximations become scattered very little for at least the three window multiple-of-2 widths by three successive windows. This criterion also implies the sufficiency of observation periods, although the sufficiency of observations per period is not claimed. The validity strongly depends on the volume of observations per period.

Application of Semi-Empirical Probability Distributions in Wave-Structure Interaction Problems

2012 ◽  
Author(s):  
Amir H. Izadparast ◽  
John M. Niedzwecki
Keyword(s):  
Probability Distribution ◽  
Wave Structure ◽  
Random Variable ◽  
Ocean Wave ◽  
Ocean Engineering ◽  
Structure Interaction ◽  
Wide Range ◽  
Empirical Probability ◽  
Semi Empirical ◽  
Wave Structure Interaction

Ocean engineers are routinely faced with design problems for coastal and deepwater structures that must survive a wide range of environmental conditions. One of the most challenging problems in the field of ocean engineering is the accurate characterization and modeling of the interaction of ocean waves with these offshore structures. The random characteristic of ocean environment requires engineers to consider the effects of random variability of the pertinent variables in their predictive models and design processes. Thus, for ocean engineering purposes, one needs to have accurate estimates of the probability distribution of the key random variables that will be used in sensitivity studies, reliability analysis, and risk assessment in the design process. In this study, a family of semi-empirical probability distribution is developed based on the quadratic transformation of linear random variable assuming that the linear random variable follows a Rayleigh distribution law. The estimates of model parameters are obtained from two moment based parameter estimation methods, i.e. method of moments and method of linear moments. The studied semi-empirical distribution can be applied to estimate the probability distribution of a wide range of non-linear random variables in the fields of ocean wave mechanics and wave-structure interaction. As examples, the application of the semi-empirical model in estimation of probability distribution of: a) ocean wave power, b) ocean wave crests interacting with an offshore structure is illustrated. For this purpose, numerically generated timeseries and experimentally measured data sets are utilized.

Joint Distributions of Successive Wave Crest Heights and Successive Wave Trough Depths for Second-Order Nonlinear Waves

2002 ◽  
Vol 46 (03) ◽  
pp. 175-185
Author(s):  
Hanne T. Wist ◽  
Dag Myrhaug ◽  
Håvard Rue
Keyword(s):  
Nonlinear Waves ◽  
Probability Distributions ◽  
Field Measurements ◽  
Second Order ◽  
Wave Crest ◽  
Wave Statistics ◽  
Joint Distributions ◽  
Wave Trough ◽  
Successive Wave ◽  
Central North Sea

Joint distributions of successive wave crest heights and successive wave trough depths for nonlinear waves are presented. Two different approaches are used in order to derive the probability distributions. The first method includes the effect of second-order Stokes-type nonlinearity on successive wave statistics in finite water depth, and the second method is a parametric model only for crest heights based on second-order simulations. The theoretical distributions are compared with observed wave data obtained from field measurements in the central North Sea.

WIGNER FUNCTION OF PULSED FIELDS RECONSTRUCTED BY DIRECT DETECTION

2011 ◽  
Vol 09 (supp01) ◽  
pp. 39-47
Author(s):  
ALESSIA ALLEVI ◽  
MARIA BONDANI ◽  
ALESSANDRA ANDREONI
Keyword(s):  
Probability Distribution ◽  
Wigner Function ◽  
Beam Splitter ◽  
Direct Detection ◽  
Probability Distributions ◽  
Linear Regime ◽  
Wigner Functions ◽  
Intensity Measurements ◽  
Pulsed Fields

We present the experimental reconstruction of the Wigner function of some optical states. The method is based on direct intensity measurements by non-ideal photodetectors operated in the linear regime. The signal state is mixed at a beam-splitter with a set of coherent probes of known complex amplitudes and the probability distribution of the detected photons is measured. The Wigner function is given by a suitable sum of these probability distributions measured for different values of the probe. For comparison, the same data are analyzed to obtain the number distributions and the Wigner functions for photons.

Analysis of Magnitude and Frequency of Floods in the Damanganga Basin: Western India

2021 ◽  
Vol 5 (1) ◽  
pp. 1-11
Author(s):  
Vitthal Anwat ◽  
Pramodkumar Hire ◽  
Uttam Pawar ◽  
Rajendra Gunjal
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Western India ◽  
Type I ◽  
Return Periods ◽  
Pearson Type ◽  
Kolmogorov Smirnov ◽  
Anderson Darling

Flood Frequency Analysis (FFA) method was introduced by Fuller in 1914 to understand the magnitude and frequency of floods. The present study is carried out using the two most widely accepted probability distributions for FFA in the world namely, Gumbel Extreme Value type I (GEVI) and Log Pearson type III (LP-III). The Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) methods were used to select the most suitable probability distribution at sites in the Damanganga Basin. Moreover, discharges were estimated for various return periods using GEVI and LP-III. The recurrence interval of the largest peak flood on record (Qmax) is 107 years (at Nanipalsan) and 146 years (at Ozarkhed) as per LP-III. Flood Frequency Curves (FFC) specifies that LP-III is the best-fitted probability distribution for FFA of the Damanganga Basin. Therefore, estimated discharges and return periods by LP-III probability distribution are more reliable and can be used for designing hydraulic structures.

Analysis and Synthesis of Mechanical Error in Universal Joints

1990 ◽  
Author(s):  
J. L. Cagney ◽  
S. S. Rao
Keyword(s):  
Probability Distribution ◽  
Real World ◽  
Probability Distributions ◽  
Manufacturing Cost ◽  
Universal Joint ◽  
Accuracy Requirement ◽  
Output Error ◽  
Manufacturing Errors ◽  
Analysis And Synthesis ◽  
Limiting Value

Abstract The modeling of manufacturing errors in mechanisms is a significant task to validate practical designs. The use of probability distributions for errors can simulate manufacturing variations and real world operations. This paper presents the mechanical error analysis of universal joint drivelines. Each error is simulated using a probability distribution, i.e., a design of the mechanism is created by assigning random values to the errors. Each design is then evaluated by comparing the output error with a limiting value and the reliability of the universal joint is estimated. For this, the design is considered a failure whenever the output error exceeds the specified limit. In addition, the problem of synthesis, which involves the allocation of tolerances (errors) for minimum manufacturing cost without violating a specified accuracy requirement of the output, is also considered. Three probability distributions — normal, Weibull and beta distributions — were used to simulate the random values of the errors. The similarity of the results given by the three distributions suggests that the use of normal distribution would be acceptable for modeling the tolerances in most cases.

Field-theoretic density estimation for biological sequence space with applications to 5′ splice site diversity and aneuploidy in cancer

2021 ◽  
Vol 118 (40) ◽  
pp. e2025782118
Author(s):  
Wei-Chia Chen ◽  
Juannan Zhou ◽  
Jason M. Sheltzer ◽  
Justin B. Kinney ◽  
David M. McCandlish
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Density Estimation ◽  
Sequence Space ◽  
Chromosomal Abnormalities ◽  
Fundamental Problem ◽  
Probability Distributions ◽  
Biological Sequence ◽  
Point Estimates ◽  
Site Diversity

Density estimation in sequence space is a fundamental problem in machine learning that is also of great importance in computational biology. Due to the discrete nature and large dimensionality of sequence space, how best to estimate such probability distributions from a sample of observed sequences remains unclear. One common strategy for addressing this problem is to estimate the probability distribution using maximum entropy (i.e., calculating point estimates for some set of correlations based on the observed sequences and predicting the probability distribution that is as uniform as possible while still matching these point estimates). Building on recent advances in Bayesian field-theoretic density estimation, we present a generalization of this maximum entropy approach that provides greater expressivity in regions of sequence space where data are plentiful while still maintaining a conservative maximum entropy character in regions of sequence space where data are sparse or absent. In particular, we define a family of priors for probability distributions over sequence space with a single hyperparameter that controls the expected magnitude of higher-order correlations. This family of priors then results in a corresponding one-dimensional family of maximum a posteriori estimates that interpolate smoothly between the maximum entropy estimate and the observed sample frequencies. To demonstrate the power of this method, we use it to explore the high-dimensional geometry of the distribution of 5′ splice sites found in the human genome and to understand patterns of chromosomal abnormalities across human cancers.

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