scholarly journals Commercial wind turbines modeling using single and composite cumulative probability density functions

2021 ◽  
Vol 11 (1) ◽  
pp. 47
Author(s):  
Othman A. M. Omar ◽  
Hamdy M. Ahmed ◽  
Reda A. Elbarkouky
Keyword(s):  
Probability Density ◽  
Density Function ◽  
Wind Turbines ◽  
Electrical Power ◽  
Probability Density Functions ◽  
Cumulative Probability ◽  
Density Functions ◽  
Invasive Weed ◽  
Power Curves ◽  
Optimal Site

As wind turbines more widely used with newer manufactured types and larger electrical power scales, a brief mathematical modelling for these wind turbines operating power curves is needed for optimal site matching selections. In this paper, 24 commercial wind turbines with different ratings and different manufactures are modelled using single cumulative probability density functions modelling equations. A new mean of a composite cumulative probability density function is used for better modelling accuracy. Invasive weed optimization algorithm is used to estimate different models designing parameters. The best cumulative density function model for each wind turbine is reached through comparing the RMSE of each model. Results showed that Weibull-Gamma composite is the best modelling technique for 37.5% of the reached results.

A Comparison of Some Multivariate Weibull Distributions

2010 ◽  
Author(s):  
Bernt J. Leira
Keyword(s):  
Probability Density ◽  
Density Function ◽  
Statistical Models ◽  
Mechanical Design ◽  
Bending Moment ◽  
Probability Density Functions ◽  
Density Functions ◽  
Weibull Distributions ◽  
Linear Combinations ◽  
Simplified Procedure

Three different possible choices of statistical models for multivariate Weibull distributions are considered and compared. The concept of “a correlation field” is introduced and is subsequently applied for the purpose of comparing the different models. Linear combinations of Weibull distributed random variables are considered, and expressions for the corresponding probability density functions are established. Furthermore, a simplified procedure for approximating the resulting density function is described. Comparison is made between the statistical moments of increasing order for the specific case of two Weibull components. This example of application arises e.g. in connection with mechanical design of a column which is subjected to a bi-axial bending moment.

scholarly journals An inequality for probability density functions arising from a distinguishability problem

1998 ◽  
Vol 39 (3) ◽  
pp. 350-354
Author(s):  
Boris Guljaš ◽  
C. E. M. Pearce ◽  
Josip Pečarić
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Real Line ◽  
Integral Inequality ◽  
Probability Density Functions ◽  
Density Functions ◽  
The Real ◽  
Image Position

AbstractAn integral inequality is established involving a probability density function on the real line and its first two derivatives. This generalizes an earlier result of Sato and Watari. If f denotes the probability density function concerned, the inequality we prove is thatunder the conditions β > α 1 and 1/(β+1) < γ ≤ 1.

scholarly journals A Characterization Related to the Equilibrium Distribution Associated with a Polynomial Structure

2010 ◽  
Vol 47 (01) ◽  
pp. 293-299 ◽  
Author(s):  
Shaul K. Bar-Lev ◽  
Onno Boxma ◽  
Gérard Letac
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Equilibrium Distribution ◽  
Renewal Theory ◽  
Probability Density Functions ◽  
Density Functions ◽  
Surprising Result ◽  
Polynomial Structure ◽  
Equilibrium Probability

Let f be a probability density function on (a, b) ⊂ (0, ∞), and consider the class C f of all probability density functions of the form Pf, where P is a polynomial. Assume that if X has its density in C f then the equilibrium probability density x ↦ P(X &gt; x) / E(X) also belongs to C f : this happens, for instance, when f(x) = Ce−λx or f(x) = C(b − x)λ−1. We show in the present paper that these two cases are the only possibilities. This surprising result is achieved with an unusual tool in renewal theory, by using ideals of polynomials.

scholarly journals Probability Density Functions for Prediction Using Normal and Exponential Distribution

2021 ◽  
pp. 40-52
Author(s):  
Kunio Takezawa
Keyword(s):  
Probability Density Function ◽  
Normal Distribution ◽  
Probability Density ◽  
Density Function ◽  
Exponential Distribution ◽  
Predictive Ability ◽  
Probability Density Functions ◽  
Density Functions ◽  
Specific Distribution ◽  
Using Data

When data are found to be realizations of a specific distribution, constructing the probability density function based on this distribution may not lead to the best prediction result. In this study, numerical simulations are conducted using data that follow a normal distribution, and we examine whether probability density functions that have shapes different from that of the normal distribution can yield larger log-likelihoods than the normal distribution in the light of future data. The results indicate that fitting realizations of the normal distribution to a different probability density function produces better results from the perspective of predictive ability. Similarly, a set of simulations using the exponential distribution shows that better predictions are obtained when the corresponding realizations are fitted to a probability density function that is slightly different from the exponential distribution. These observations demonstrate that when the form of the probability density function that generates the data is known, the use of another form of the probability density function may achieve more desirable results from the standpoint of prediction.

Study on Nonlinear Vibration Characteristic Evaluation of Nonlinear Vibration System With Gaps by Transition Probability Density Function

2004 ◽  
Author(s):  
Masanori Shintani ◽  
Hiroyuki Ikuta ◽  
Hajime Takada
Keyword(s):  
Probability Density Function ◽  
Nonlinear Vibration ◽  
Probability Density ◽  
Density Function ◽  
Transition Probability ◽  
Probability Density Functions ◽  
Force Characteristic ◽  
Density Functions ◽  
Restoring Force ◽  
Transition Probability Density

In this paper, the transition probability density functions between response velocity and response displacement in nonlinear vibration systems which have the restoring force characteristic of a cubic equation are governed by the Fokker-Planck Equation. The experimental probability density functions are compared with analytical results. The analytical model of the cubic equation as Duffing Equation is proposed by the restoring force characteristic of the nonlinear vibration system with gaps in the experiments. However, a slight difference for the frequency range of the transfer function was shown by simulation results. Then, it is considered using transition probability density functions in the response characteristic. For stationary random input waves, the probability density function between the response displacement and the response velocity are easily estimated by the Fokker-Planck Equation and the Duffing Equation. The slight difference of the transfer function of the response acceleration is evaluated by the scattering of the restoring force characteristic estimated by the probability density function and self-natural frequency curve. The R.M.S. value and the transfer function of the experimental results are compared with the analytical results. It is thought that the estimation of the probability density function of the response has validity. It is thought that the evaluation of the nonlinear vibration characteristics by the probability density function is valid.

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.

Normalized structure factor analysis with theCentroMKprogram

2013 ◽  
Vol 46 (1) ◽  
pp. 88-92 ◽  
Author(s):  
Marcin Kowiel
Keyword(s):  
Factor Analysis ◽  
Probability Density Function ◽  
Probability Density ◽  
Crystal Structures ◽  
Density Function ◽  
Structure Factor ◽  
Probability Density Functions ◽  
Density Functions ◽  
Exact Probability ◽  
Space Group

Statistical analysis of the normalized structure factorEis important during space-group determination. Several approaches to solve this problem have been described in the literature. In this paper, the most popular approach, the ideal asymptotic probability density function developed by Wilson, is compared with the more accurate exact probability density functions described by Shmueli and co-workers. Furthermore, a new computer program,CentroMK, for normalized structure factor analysis, is presented. The program is capable of plotting histograms of the normalized structure factors and exact probability density functions. Moreover, the program calculates five estimators helpful during the space-group determination: 〈|E|〉, 〈|E2 − 1|〉, %E> 2, %E< 0.25 and the discrepancyRfunction. The two approaches and the error rates of the five listed estimators are compared for nearly 30 600 crystal structures obtained fromActa Crystallographica Section E.It is shown that within a space group the means 〈|E|〉 and 〈|E2 − 1|〉 of real crystal structures show high variability. The comparison shows that decisions based on the exact probability density function are more accurate, the computing time is reasonable, and estimators 〈|E|〉, %E< 0.25 andRare the most accurate and should be preferred during space-group determination.

Selective interaction of two independent recurrent processes

1965 ◽  
Vol 2 (2) ◽  
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 functions φ (t) and ψ (t). Every stimulus of the ψ (t) process annihilates the next stimulus of the φ (t) process. The probability density function of the intervals of the transformed φ (t) process is derived for the case where either the φ (t) or the ψ (t) process is Poisson.

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