Interval prediction of wind power,which features the upper and lower limits of wind power at a given confidence level,plays a significant role in accurate prediction and stability of the power grid integrated with win...Interval prediction of wind power,which features the upper and lower limits of wind power at a given confidence level,plays a significant role in accurate prediction and stability of the power grid integrated with wind power.However,the conventional methods of interval prediction are commonly based on a hypothetic probability distribution function,which neglects the correlations among various variables,leading to the decrease of prediction accuracy.Therefore,we improve the multi-objective interval prediction based on the conditional copula function,through which we can fully utilize the correlations among variables to improve prediction accuracy without an assumed probability distribution function.We use the multi-objective optimization method of nondominated sorting genetic algorithm-II(NSGA-II)to obtain the optimal solution set.The particular best solution is weighted by the prediction interval average width(PIAW)and prediction interval coverage probability(PICP)to pick the optimized solution in practical examples.Finally,we apply the proposed method to three wind power plants in different cities in China as examples forvalidation and obtain higher prediction accuracy compared with other methods,i.e.,relevance vector machine(RVM),artificial neural network(ANN),and particle swarm optimization kernel extreme learning machine(PSO-KELM).These results demonstrate the superiority and practicability of this method in interval prediction of wind power.展开更多
The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copul...The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.展开更多
Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict o...Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.展开更多
Draxler and Zessin [1] derived the power function for a class of conditional tests of assumptions of a psychometric model known as the Rasch model and suggested an MCMC approach developed by Verhelst [2] for the numer...Draxler and Zessin [1] derived the power function for a class of conditional tests of assumptions of a psychometric model known as the Rasch model and suggested an MCMC approach developed by Verhelst [2] for the numerical approximation of the power of the tests. In this contribution, the precision of the Verhelst approach is investigated and compared with an exact sampling procedure proposed by Miller and Harrison [3] for which the discrete probability distribution to be sampled from is exactly known. Results show no substantial differences between the two numerical procedures and quite accurate power computations. Regarding the question of computing time the Verhelst approach will have to be considered much more efficient.展开更多
基金supported by the National Natural Science Foundation of China(No.51507141)Key research and development plan of Shaanxi Province(No.2018ZDCXL-GY-10-04)+1 种基金the National Key Research and Development Program of China(No.2016YFC0401409)the Shaanxi provincial education office fund(No.17JK0547).
文摘Interval prediction of wind power,which features the upper and lower limits of wind power at a given confidence level,plays a significant role in accurate prediction and stability of the power grid integrated with wind power.However,the conventional methods of interval prediction are commonly based on a hypothetic probability distribution function,which neglects the correlations among various variables,leading to the decrease of prediction accuracy.Therefore,we improve the multi-objective interval prediction based on the conditional copula function,through which we can fully utilize the correlations among variables to improve prediction accuracy without an assumed probability distribution function.We use the multi-objective optimization method of nondominated sorting genetic algorithm-II(NSGA-II)to obtain the optimal solution set.The particular best solution is weighted by the prediction interval average width(PIAW)and prediction interval coverage probability(PICP)to pick the optimized solution in practical examples.Finally,we apply the proposed method to three wind power plants in different cities in China as examples forvalidation and obtain higher prediction accuracy compared with other methods,i.e.,relevance vector machine(RVM),artificial neural network(ANN),and particle swarm optimization kernel extreme learning machine(PSO-KELM).These results demonstrate the superiority and practicability of this method in interval prediction of wind power.
基金supported by the Science Fund for Creative Research Groups of the National Natural ScienceFoundation of China (Grant No. 51021004)the National High Technology Research and DevelopmentProgram of China (863 Program, Grants No. 2012AA112509 and 2012AA051702)
文摘The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.
文摘Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.
文摘Draxler and Zessin [1] derived the power function for a class of conditional tests of assumptions of a psychometric model known as the Rasch model and suggested an MCMC approach developed by Verhelst [2] for the numerical approximation of the power of the tests. In this contribution, the precision of the Verhelst approach is investigated and compared with an exact sampling procedure proposed by Miller and Harrison [3] for which the discrete probability distribution to be sampled from is exactly known. Results show no substantial differences between the two numerical procedures and quite accurate power computations. Regarding the question of computing time the Verhelst approach will have to be considered much more efficient.
