scholarly journals THE ENERGY SPECTRA OF SURF WAVES ON A CORAL REEF

1978 ◽  
Vol 1 (16) ◽  
pp. 33 ◽  
Author(s):  
Theodore T. Lee ◽  
Kerry P. Black
Keyword(s):  
Time Series ◽  
Coral Reef ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Shallow Water ◽  
Probability Density ◽  
Density Function ◽  
Linear Wave ◽  
Gain Function ◽  
Fourier Spectra

The transformation of waves crossing a coral reef in Hawaii including the probability density function of the wave heights and periods and the shape of the spectrum is discussed. The energy attenuation and the change of height and period statistics is examined using spectral analysis and the zero up-crossing procedure. Measurements of waves at seven points along a 1650 ft transect in depths from 1 to 3.5 ft on the reef and 35 ft offshore were made. The heights were tested for Rayleigh, truncated Rayleigh and Wei bull distributions. A symmetrical distribution presented by Longuet-Higgins (1975) and the Weibull distribution were compared to the wave period density function. In both cases the Weibull probability density function fitted with a high degree of correlation. Simple procedures to obtain Weibull coefficients are given. Fourier spectra were generated and contours of cumulative energy against each position on the reef show the shifting of energy from the peak as the waves move into shallow water. A design spectrum, with the shape of the Weibull distribution, is presented with procedures given to obtain the coefficients which govern the distribution peakedness. Normalized non-dimensional frequency and period spectra were recommended for engineering applications for both reef and offshore locations. A zero up-crossing spectrum (ZUS) constructed from the zero upcrossing heights and periods is defined and compared with the Fourier spectrum. Also discussed are the benefits and disadvantages of the ZUS, particularly for non-linear wave environments in shallow water. Both the ZUS and Fourier spectra are used to test the adequacy of formulae which estimate individual wave parameters. Cross spectra analysis was made to obtain gain function and squared coherency for time series between two adjacent positions. It was found that the squared coherency is close to unity near the peak frequency. This means that the output time series can be predicted from the input by applying the gain function. However, the squared coherency was extremely small for other frequencies above 0.25 H2.

scholarly journals Finsler Geometry for Two-Parameter Weibull Distribution Function

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Emrah Dokur ◽  
Salim Ceyhan ◽  
Mehmet Kurban
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Cumulative Probability ◽  
Two Dimensional ◽  
Energy Potential ◽  
Two Parameter

To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape (k) and scale (c) parameters in two-dimensional Finsler space is realized using a different approach by Finsler geometry. In addition, new probability and cumulative probability density functions based on Finsler geometry are proposed which can be used in many real world applications. For future studies, it is aimed at proposing more accurate models by using this novel approach than the models which have two-parameter Weibull probability density function, especially used for determination of wind energy potential of a region.

scholarly journals Comparison Of Three Numerical Methods For Estimating Weibull Parameters Using Weibull Distribution Model In Nigeria

2020 ◽  
Vol 27 (2) ◽  
pp. 8-15
Author(s):  
J.A. Oyewole ◽  
F.O. Aweda ◽  
D. Oni
Keyword(s):  
Standard Deviation ◽  
Wind Speed ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Accurate Estimation ◽  
Weibull Parameters ◽  
Factor Method ◽  
Deviation Method

There is a crucial need in Nigeria to enhance the development of wind technology in order to boost our energy supply. Adequate knowledge about the wind speed distribution becomes very essential in the establishment of Wind Energy Conversion Systems (WECS). Weibull Probability Density Function (PDF) with two parameters is widely accepted and is commonly used for modelling, characterizing and predicting wind resource and wind power, as well as assessing optimum performance of WECS. Therefore, it is paramount to precisely estimate the scale and shape parameters for all regions or sites of interest. Here, wind data from year 2000 to 2010 for four different locations (Port Harcourt, Ikeja, Kano and Jos) were analysed and the Weibull parameters was determined. The three methods employed are Mean Standard Deviation Method (MSDM), Energy Pattern Factor Method (EPFM) and Method of Moments (MOM) for estimating Weibull parameters. The method that gave the most accurate estimation of the wind speed was MSDM method, while Energy Pattern Factor Method (EPFM) is the most reliable and consistent method for estimating probability density function of wind. Keywords: Weibull Distribution, Method of Moment, Mean Standard Deviation Method, Energy Pattern Method

Microstructural Constitutive Equation for Sprain Analysis

2008 ◽  
Author(s):  
Zheying Guo ◽  
Raffaella De Vita
Keyword(s):  
Experimental Data ◽  
Probability Density Function ◽  
Constitutive Equation ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Damage Evolution ◽  
Linear Elastic ◽  
Proposed Model ◽  
Collagenous Tissues

A new constitutive equation is presented to describe the damage evolution process in parallel fibered collagenous tissues such as ligaments and tendons. The model is formulated by accounting for the fibrous structure of the tissues. The tissue’s stress is defined as the average of the collagen fiber’s stresses. The fibers are assumed to be undulated and straighten out at different stretches that are defined by a Weibull probability density function. After becoming straight each fiber is assumed to be linear elastic. Its waviness is defined by a Weibull distribution. Tissue’s damage is assumed to occur at the fiber level and is defined as a reduction in the fiber’s stiffness. The proposed model is validated by using experimental data published in the biomechanics literature by Provenzano et al. [1].

On some distributional properties of a first-order nonnegative bilinear time series model

2001 ◽  
Vol 38 (3) ◽  
pp. 659-671 ◽  
Author(s):  
Zhiqiang Zhang ◽  
Howell Tong
Keyword(s):  
Time Series ◽  
Probability Density Function ◽  
Numerical Method ◽  
Probability Density ◽  
Density Function ◽  
Stationary Distribution ◽  
Time Series Model ◽  
First Order ◽  
Distributional Properties ◽  
Tail Behaviour

We study a simple first-order nonnegative bilinear time-series model and give conditions under which the model is stationary. The probability density function of the stationary distribution (when it exists) is found. We also discuss the tail behaviour of the stationary distribution and calculate the probability density function by a numerical method. Simulation is used to check the calculation.

A NEW IRREGULARITY CRITERION FOR DISCRIMINATION OF STOCHASTIC AND DETERMINISTIC TIME SERIES

Fractals ◽  
2008 ◽  
Vol 16 (02) ◽  
pp. 129-140 ◽  
Author(s):  
AMIR H. OMIDVARNIA ◽  
ALI M. NASRABADI
Keyword(s):  
Time Series ◽  
Fractal Dimension ◽  
Probability Density Function ◽  
State Space ◽  
Probability Density ◽  
Density Function ◽  
Confidence Level ◽  
Space Versus ◽  
Fractal Dimensions ◽  
Linear Region

In this paper, a new irregularity criterion based on fractal dimensions is introduced. In fact, this criterion (which is called ONH criterion) is the state space version of Higuchi fractal dimension, which can discriminate stochastic and deterministic time series from each other. To compute this criterion, we have exploited "the amount of state vectors fluctuations" in embedding space. By varying the reconstruction delay in embedding space, one can obtain a logarithmic diagram of overall changes corresponding to reconstructed state space versus delays. The slope of the linear region of this diagram could be considered as a new irregularity criterion. To discriminate random and deterministic time series, this criterion is adopted as a new statistic for hypothesis testing. Probability density function of this statistic under H0 hypothesis is constructed and regarding to a certain confidence level, one can determine whether randomness is accepted or rejected.

scholarly journals CLOSED-FORM SOLUTIONS FOR THE PROBABILITY DENSITY OF WAVE HEIGHT IN THE SURF ZONE

1988 ◽  
Vol 1 (21) ◽  
pp. 60 ◽  
Author(s):  
William R. Dally ◽  
Robert G. Dean
Keyword(s):  
Probability Density Function ◽  
Shallow Water ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Wave Height ◽  
Surf Zone ◽  
Wave Steepness ◽  
Bottom Slope ◽  
Closed Form Solutions

By invoking the assumption that in the surf zone, random waves behave as a collection of individual regular waves, two closed-form solutions for the probability density function of wave height on planar beaches are derived. The first uses shallow water linear theory for wave shoaling, assumes a uniform incipient condition, and prescribes breaking with a regular wave model that includes both bottom slope and wave steepness effects on the rate of decay. In the second model, the shallow water assumption is removed, and a distribution in wave period (incipient condition) is included. Preliminary results indicate that the models exhibit much of the behavior noted for random wave transformation reported in the literature, including bottom slope and wave steepness effects on the shape of the probability density function.

Concomitants of Order Statistics from Marshall and Olkin's Bivariate Weibull Distribution

2000 ◽  
Vol 50 (1-2) ◽  
pp. 65-70 ◽  
Author(s):  
Anjuman A. Begum ◽  
A. H. Khan
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Order Statistics ◽  
Density Function ◽  
Subject Classification ◽  
Concomitants Of Order Statistics ◽  
Ordered Statistics ◽  
Probability Density Function Pdf ◽  
Bivariate Weibull Distribution

The probability density function (pdf) of the rth, 1 ≤ r ≤ n, concomitants of ordered statistics are derived for Marshall and Olkin's bivariate Weibull distribution and their moments are obtained. Also their means and variances are tabulated. AMS (2000) Subject Classification: 62E15, 62G30.

Selective interaction of two independent recurrent processes

1965 ◽  
Vol 2 (02) ◽  
pp. 286-292 ◽  
Author(s):  
M. Ten Hoopen ◽  
H. A. Reuver
Keyword(s):  
Time Series ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Probability Density Functions ◽  
Density Functions ◽  
Selective Interaction ◽  
Mutually Independent

SummaryConsidered are two mutually independent recurrent processes each consisting of a time series of unitary stimuli. The durations of the intervals between the stimuli in each series are independent of each other and identically distributed with probability density functionsφ(t) andψ(t). Every stimulus of theψ(t) process annihilates the next stimulus of theφ(t) process. The probability density function of the intervals of the transformedφ(t) process is derived for the case where either theφ(t) or theψ(t) process is Poisson.

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