A Probability Distribution of Surface Elevation for Wind Waves in Terms of the Gram-Charlier Series

Laboratory experiments are conducted to study the probability distribution of surface elevation for wind waves and the convergence is discussed of the Gram-Charlier series in describing the surface elevation distribution. Results show that the agreement between the Gram-Charlier series and the observed distribution becomes better and better as the truncated order of the series increases in a certain range, which is contrary to the phenomenon observed by Huang and Long (1980). It is also shown that the Gram-Charlier series is sensitive to the anomalies in the data set which will make the agreement worse if they are not preprocessed appropriately. Negative values of the probability distribution expressed by the Gram-Charlier series in some ranges of surface elevations are discussed, but the absolute values of the negative values as well as the ranges of their occurrence become smaller gradually as more and mote terms are included. Therefore the negative values will have no evident effect on the form of the whole surface elevation distribution when the series is truncated at higher orders. Furthermore, a simple recurrence formula is obtained to calculate the coefficients of the Gram-Charlier series in order to extend the Gram-Charlier series to high orders conveniently.

Research on Short-Term Load Forecasting of Distribution Stations Based on the Clustering Improvement Fuzzy Time Series Algorithm

An improved fuzzy time series algorithmbased on clustering is designed in this paper.The algorithm is successfully applied to short-term load forecasting in the distribution stations.Firstly,the K-means clustering method is used to cluster the data,and the midpoint of two adjacent clustering centers is taken as the dividing point of domain division.On this basis,the data is fuzzed to form a fuzzy time series.Secondly,a high-order fuzzy relation with multiple antecedents is established according to the main measurement indexes of power load,which is used to predict the short-term trend change of load in the distribution stations.Matlab/Simulink simulation results show that the load forecasting errors of the typical fuzzy time series on the time scale of one day and one week are[−50,20]and[−50,30],while the load forecasting errors of the improved fuzzy time series on the time scale of one day and one week are[−20,15]and[−20,25].It shows that the fuzzy time series algorithm improved by clustering improves the prediction accuracy and can effectively predict the short-term load trend of distribution stations.

Probability Distribution Characteristics of Strong Nonlinear Waves Under Typhoon Conditions in the Northern South China Sea

The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.

THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH(I)

This paper deals with the value distribution of random Dirichlet series whose coefficients are a martingale difference sequence, and which is of neutral growth.

THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH (Ⅱ)

This paper studies the value distribution of random analytic Dirichlet series f(s) = Zn()e-sn, where {Zn} is a sequence of independent random variables, n = 1 with moments zero, such that infE{Zn}/E1/2{Zn2≥ α > 0. Suppose [h*(σ)]2 = n converges for any α > 0, and diverges for = 0. It is shown that if = ρ E (0, ), then with probability one, where β is a constant depending only upon the constant α.

THE DISTRIBUTION OF VALUES OF TAYLOR SERIES

Clarify some classical results and their proofs on the distribution of values of simple Taylor series and extend them to multiple Taylor series.

Simulation Study on Series Capacitor Compensation to Improve the Voltage Quality of Rural Power Distribution Network

In order to improve the voltage quality of rural power distribution network, the series capacitor in distribution lines is proposed. The principle of series capacitor compensation technology to improve the quality of rural power distribution lines voltage is analyzed. The real rural power distribution network simulation model is established by Power System Power System Analysis Software Package (PSASP). Simulation analysis the effect of series capacitor compensation technology to improve the voltage quality of rural power distribution network, The simulation results show that the series capacitor compensation can effectively improve the voltage quality and reduce network losses and improve the transmission capacity of rural power distribution network.

Bivariate Zero-Inflated Power Series Distribution

Many researchers have discussed zero-inflated univariate distributions. These univariate models are not suitable, for modeling events that involve different types of counts or defects. To model several types of defects, multivariate Poisson model is one of the appropriate model. This can further be modified to incorporate inflation at zero and we can have multivariate zero-inflated Poisson distribution. In the present article, we introduce a new Bivariate Zero Inflated Power Series Distribution and discuss inference related to the parameters involved in the model. We also discuss the inference related to Bivariate Zero Inflated Poisson Distribution. The model has been applied to a real life data. Extension to k-variate zero inflated power series distribution is also discussed.

On the Equiconvergence of the Fourier Series and Integral of Distributions

We prove equiconvergence of the Bochner-Riesz means of the Fourier series and integral of distributions with compact support from the Liouville spaces.

Grey series time-delay predicting model in state estimation for power distribution networks

A new combined model is proposed to obtain predictive data value applied in state estimation for radial power distribution networks. The time delay part of the model is calculated by a recursive least squares algorithm of system identification, which can gradually forget past information. The grey series part of the model uses an equal dimension new information model (EDNIM) and it applies 3 points smoothing method to preprocess the original data and modify remnant difference by GM(1,1). Through the optimization of the coefficient of the model, we are able to minimize the error variance of predictive data. A case study shows that the proposed method achieved high calculation precision and speed and it can be used to obtain the predictive value in real time state estimation of power distribution networks.

Research on Low Voltage Series Arc Fault Prediction Method Based on Multidimensional Time-Frequency Domain Characteristics

The load types in low-voltage distribution systems are diverse.Some loads have current signals that are similar to series fault arcs,making it difficult to effectively detect fault arcs during their occurrence and sustained combustion,which can easily lead to serious electrical fire accidents.To address this issue,this paper establishes a fault arc prototype experimental platform,selects multiple commonly used loads for fault arc experiments,and collects data in both normal and fault states.By analyzing waveform characteristics and selecting fault discrimination feature indicators,corresponding feature values are extracted for qualitative analysis to explore changes in timefrequency characteristics of current before and after faults.Multiple features are then selected to form a multidimensional feature vector space to effectively reduce arc misjudgments and construct a fault discrimination feature database.Based on this,a fault arc hazard prediction model is built using random forests.The model’s multiple hyperparameters are simultaneously optimized through grid search,aiming tominimize node information entropy and complete model training,thereby enhancing model robustness and generalization ability.Through experimental verification,the proposed method accurately predicts and classifies fault arcs of different load types,with an average accuracy at least 1%higher than that of the commonly used fault predictionmethods compared in the paper.

Detecting DDoS Attacks against Web Server Using Time Series Analysis

Distributed Denial of Service （DDoS） attack is a major threat to the availability of Web service. The inherent presence of self-similarity in Web traffic motivates the applicability of time series analysis in the study of the burst feature of DDoS attack. This paper presents a method of detecting DDoS attacks against Web server by analyzing the abrupt change of time series data obtained from Web traffic. Time series data are specified in reference sliding window and test sliding window, and the abrupt change is modeled using Auto-Regressive （AR） process. By comparing two adjacent nonoverlapping windows of the time series, the attack traffic could be detected at a time point. Combined with alarm correlation and location correlation, not only the presence of DDoS attack, but also its occurring time and location can be deter mined. The experimental results in a test environment are illustrated to justify our method.

The Feature of Sedimentary，Structure and the Laws of Hydrocarbon Distribution in Erlian Basin

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DEFICIENT FUNCTIONS OF RANDOM DIRICHLET SERIES

In this article, the uniqueness theorem of Dirichlet series is proved. Then the random Dirichlet series in the right half plane is studied, and the result that the random Dirichlet series of finite order has almost surely（a.s.） no deficient functions is proved.

A Comparison of Four Precipitation Distribution Models Used in Daily Stochastic Models

Stochastic weather generators are statistical models that produce random numbers that resemble the observed weather data on which they have been fitted; they are widely used in meteorological and hydrologi- cal simulations. For modeling daily precipitation in weather generators, first-order Markov chain–dependent exponential, gamma, mixed-exponential, and lognormal distributions can be used. To examine the perfor- mance of these four distributions for precipitation simulation, they were fitted to observed data collected at 10 stations in the watershed of Yishu River. The parameters of these models were estimated using a maximum-likelihood technique performed using genetic algorithms. Parameters for each calendar month and the Fourier series describing parameters for the whole year were estimated separately. Bayesian infor- mation criterion, simulated monthly mean, maximum daily value, and variance were tested and compared to evaluate the fitness and performance of these models. The results indicate that the lognormal and mixed-exponential distributions give smaller BICs, but their stochastic simulations have overestimation and underestimation respectively, while the gamma and exponential distributions give larger BICs, but their stochastic simulations produced monthly mean precipitation very well. When these distributions were fitted using Fourier series, they all underestimated the above statistics for the months of June, July and August.

On Random Taylor Series

This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.

Modified Joint Distribution of Wave Heights and Periods

The modified versions of the linear theoretical model of Longuet-Higgins （1983） are derived in this work and also compared with the laboratory experiments carried out in MAR1NTEK. The main feature of modifications is to replace the mean frequency in the formulation with the peak frequency of the wave spectrum. These two alternative forms of joint distributions are checked in three typical random sea states characterized by the initial wave steepness. In order to further explore the properties ＆these models, the associated marginal distributions of wave heights and wave periods are also researched with the observed statistics and some encouraging results are obtained.

Information Worth of MinMaxEnt Models for Time Series

In this study, by starting from Maximum entropy (MaxEnt) distribution of time series, we introduce a measure that quantifies information worth of a set of autocovariances. The information worth of autocovariences is measured in terms of entropy difference of MaxEnt distributions subject to different autocovariance sets due to the fact that the information discrepancy between two distributions is measured in terms of their entropy difference in MaxEnt modeling. However, MinMaxEnt distributions (models) are obtained on the basis of MaxEnt distributions dependent on parameters according to autocovariances for time series. This distribution is the one which has minimum entropy and maximum information out of all MaxEnt distributions for family of time series constructed by considering one or several values as parameters. Furthermore, it is shown that as the number of autocovariances increases, the entropy of approximating distribution goes on decreasing. In addition, it is proved that information worth of each model defined on the basis of MinMaxEnt modeling about stationary time series is equal to sum of all possible information increments corresponding to each model with respect to preceding model starting with first model in the sequence of models. The fulfillment of obtained results is demonstrated on an example by using a program written in Matlab.

Improving the Performance of Fixed-Bed Catalytic Reactors by Innovative Catalyst Distribution

A comprehensive mathematical model is developed to simulate the interactions of the complex processes that take place in typical catalytic chemical reactors. This mathematical model includes correlations representing various modes of mass transport and chemical reactions. To illustrate the application and value of this approach for reactor optimizations, the model is applied to the case of series reactions with a desirable intermediate compound and the risk of degradation of this compound if the process conditions are not optimized. The modeling results show that in such cases, which are very common in practice, replacing the conventional uniform catalyst distribution with a novel non-uniform distribution will significantly improve the performance of the reactor and the production of the desirable compound. Various catalyst distribution options are compared, and a novel non-uniform loading of catalyst is identified that gives a much better performance compared to the conventional approach. The model is versatile and useful for both the design as well as the optimization of the catalytic fixed-bed reactors in a wide variety of reactor and reaction conditions.