scholarly journals A New Modeling Approach for the Probability Density Distribution Function of Wind power Fluctuation

2019 ◽  
Vol 11 (19) ◽  
pp. 5512 ◽  
Author(s):  
Lingzhi Wang ◽  
Jun Liu ◽  
Fucai Qian
Keyword(s):  
Distribution Function ◽  
Density Distribution ◽  
Probability Density ◽  
Wind Power ◽  
Rapid Development ◽  
Probability Density Distribution ◽  
Power Fluctuation ◽  
Function Model ◽  
New Model ◽  
Fireworks Algorithm

With the rapid development of grid-connected wind power, analysing and describing the probability density distribution characteristics of wind power fluctuation has always been a hot and difficult problem in the wind power field. In traditional methods, a single distribution function model is used to fit the probability density distribution of wind power output fluctuation; however, the results are unsatisfying. Therefore, a new distribution function model is proposed in this work for fitting the probability density distribution to replace a single distribution function model. In form, the new model includes only four parameters which make it easier to implement. Four statistical index models are used to evaluate the distribution function fits with the measured probability data. Simulations are designed to compare the new model with the Gaussian mixture model, and results illustrate the effectiveness and advantages of the newly developed model in fitting the wind power fluctuation probability density distribution. Besides, the fireworks algorithm is adopted for determining the optimal parameters in the distribution function model. The comparison experiments of the fireworks algorithm with the particle swarm optimization (PSO) algorithm and the genetic algorithm (GA) are carried out, which shows that the fireworks algorithm has faster convergence speed and higher accuracy than the two common intelligent algorithms, so it is useful for optimizing parameters in power systems.

Non-Equilibrium Statistical Theory of Void Microstructure Evolution in Irradiated Metals

2013 ◽  
Vol 364 ◽  
pp. 568-572
Author(s):  
Xiang Hui Guo ◽  
Hai Yun Hu
Keyword(s):  
Distribution Function ◽  
Statistical Theory ◽  
Density Distribution ◽  
Probability Density ◽  
Microstructure Evolution ◽  
Void Growth ◽  
Probability Density Distribution ◽  
Density Distribution Function ◽  
Void Evolution ◽  
Non Equilibrium

The non-equilibrium statistical theory was used as a theoretical approach to modeling and predicting void evolution in metal materials. Fokker-Plank equation was introduced as the kinetic equation for the void evolution, from which the probability density distribution function of voids could be obtained. From the micro-mechanism of metal's irradiation damage, void growth rate equation was obtained using spherical Weilv model and control diffusion theory, and then was simplified based on appropriate assumptions. According to the probability density distribution function of void, a series of macro-mechanical characteristics caused by void growth can be calculated, such as: the critical radius of the void nucleation, the average radius of void. Thus the correlation between the void microstructure evolution and the macroscopic properties of metals can be achieved.

Theoretical and experimental investigation of the function of the wall flow deflecting ring. A generalized mathematical model for the case of a large number of deflecting rings

1987 ◽  
Vol 52 (6) ◽  
pp. 1440-1453 ◽  
Author(s):  
Krumm Semkov ◽  
Nikolai Kolev ◽  
Vladimír Staněk ◽  
Pavel Moravec
Keyword(s):  
Mathematical Model ◽  
Probability Theory ◽  
Experimental Investigation ◽  
Distribution Function ◽  
Density Distribution ◽  
Probability Density ◽  
Packed Bed ◽  
Probability Density Distribution ◽  
Density Distribution Function ◽  
Wall Flow

Based on the probability theory considerations a probability density distribution function has been derived for the radius on which the liquid, upon hiting the wall flow deflectiong ring, or an element of packing resting on it, is deflected and proceeds descending in a trickle bed column. The obtained probability density distribution function has been used in turn in the model describing the distribution of liquid in columns equipped with the wall flow deflecting rings. The ultimate goal is a reliable theory for optimization of the size and spacing of the wall flow deflecting rings in packed bed columns.

scholarly journals Production decline analysis of shale gas based on a probability density distribution function

2020 ◽  
Vol 17 (2) ◽  
pp. 365-376 ◽  
Author(s):  
Yingzhong Yuan ◽  
Zhilin Qi ◽  
Zhangxing Chen ◽  
Wende Yan ◽  
Zhiheng Zhao
Keyword(s):  
Distribution Function ◽  
Density Distribution ◽  
Probability Density ◽  
Shale Gas ◽  
Distribution Model ◽  
Probability Density Distribution ◽  
Density Distribution Function ◽  
Gas Reservoir ◽  
Shale Gas Reservoir ◽  
Better Than

Abstract Production decline analysis is a simple and efficient method to forecast production dynamics of shale gas. The traditional Arps decline model is also widely used in the production decline analysis of shale gas, but an obvious error is often generated. Based on the Weibull and χ2 probability density distribution function, the monotonic decreasing production prediction equations of shale gas are established. It is deduced that recently, the widely used Duong model is essentially a Weibull probability density distribution model. Decline analysis results of production data from actual shale gas well and numerical simulations indicate that the fitting results of the Weibull (Duong) model and χ2 distribution model are better than the Arps model whose deviation of early data is large. For a shale gas reservoir with very low permeability, pressure conformance area is small and it is obviously influenced by fractures. Early shale gas production rate mainly contributed to by fractures declines quickly and the later production rate mainly contributed to by the matrix declines slowly over time. The production decline curve has obvious long-tail distribution characteristics and it is a better fit to the data with a χ2 distribution model. As for the increase of permeability, the fitting accuracy of the Weibull (Duong) model gradually becomes better than the χ2 distribution model. Research results provide theoretical guidance for choosing a reasonable production decline model of a shale gas reservoir with a different permeability.

Short-Term Forecasting and Uncertainty Analysis of Wind Power

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
Gu Bo ◽  
Luo Keke ◽  
Zhang Hongtao ◽  
Zhang Jinhua ◽  
Huang Hui
Keyword(s):  
Density Distribution ◽  
Probability Density ◽  
Wind Power ◽  
Training Sample ◽  
Support Vector ◽  
Probability Density Distribution ◽  
Distribution Characteristics ◽  
Short Term ◽  
Forecasting Accuracy ◽  
Sample Set

Abstract Accurate forecasting is the key factor in promoting wind power consumption and improving the stable operation of power systems. A short-term wind power forecasting (WPF) and uncertainty analysis method based on whale optimization algorithm (WOA), least squares support vector machine (LSSVM), and nonparametric kernel density estimation (NPKDE) was proposed in this paper. The advantages of WOA (fast convergence speed and high convergence accuracy) were used to optimize the penalty factor and kernel function width of the LSSVM model, and the calculation speed and forecasting accuracy of the LSSVM model were improved. The training sample set is classified according to the wind speed interval, and the WOA-LSSVM forecasting model is trained by subclass after classification to further improve the accuracy of short-term WPF. The NPKDE method is used to accurately calculate the probability density distribution characteristics of the forecasting error of wind power, and the confidence interval of the WPF is accurately calculated based on the probability density distribution characteristics. The calculation results show that the forecasting accuracy of the WOA-LSSVM model is higher than those of the LSSVM, long short-term memory (LSTM), and particle swarm optimization and least squares support vector machine (PSO-LSSVM) models, and the forecasting accuracy of the WOA-LSSVM model can be further improved after classifying the training sample set. The coverage of the confidence intervals in different time scales is higher than the corresponding confidence level, indicating that the NPKDE method can accurately describe the probability density distribution characteristics of the WPF errors.

scholarly journals Influence Assessment of the Information Concerning the Bearing Type of Axle Box of Cars on the Automatic Classification Accuracy of Heated Boxes

2021 ◽  
pp. 5-14
Author(s):  
V. V Burchenkov
Keyword(s):  
Density Distribution ◽  
Probability Density ◽  
Heating Temperature ◽  
Threshold Value ◽  
Probability Density Distribution ◽  
Practical Implementation ◽  
System Of Equations ◽  
Average Value ◽  
Optimal Thresholds ◽  
Different Types

Purpose. The main purpose of the work is to determine and classify the heated cars’ boxes based on the probability of appearance of roller and cassette type boxes in the classes of heated and overheated boxes, as well as the laws of probability density distribution of the recognition signs of normally heated and overheated roller and cassette type boxes. Methodology. The operation features of freight cars with cassette type axle boxes with increased operating heating have been investigated. The methodology of assessing the probability of recognition errors was proposed, which takes into account the fact that sets of normally heated and overheated boxes consist of subsets of boxes with different types of bearings. A system of equations is obtained, the roots of which represent еру values that minimize the recognition probability of the errors of the heated boxes. Findings. It was found out that with some methods of determining the bearing type, for example, by the average value of the ranges of thermal image for each car, the probability of erroneous selection may depend on the probability density distribution of the sign for bearings of different types and the threshold value of this sign. The optimal thresholds for detecting the overheated roller boxes in comparison with the optimal thresholds for detecting overheated cassette boxes were determined. It has been established that the pass of an overheated cassette bearing, provided that the type of bearing is determined correctly, is less likely to lead to an accident than if the cassette box is classified as a roller box. The rejection criteria of axle boxes according to their heating temperature difference on one of the wheel set axis for three variants of settings of the alarm system according to an arrangement of multipurpose complexes of technical means (CTM) were formulated. The practical implementation of this method of adjusting the CTM settings for the Minsk branch of the Belarusian Railways was demonstrated. Originality. A system of equations is obtained, which allows finding the optimal values of temperature thresholds for the detection of overheated roller and cassette boxes under the assumption that the error probabilities in the selection of boxes by their types are known and constant. Practical value. The developed method of adjusting the alarm settings of CTM makes it possible to significantly reduce unjustified train delays and the number of car uncouplings.

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