A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimiza...A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.展开更多
Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in...Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in GIS does not obey the normal distribution but the p-norm distribution with a determinate parameter. Assuming that the error is random and has the same statistical properties, the probability density function of the normal distribution, Laplace distribution and p-norm distribution are derived based on the arithmetic mean axiom, median axiom and p-median axiom, which means that the normal distribution is only one of these distributions but not the least one. Based on this ideal distribution fitness tests such as Skewness and Kurtosis coefficient test, Pearson chi-square chi(2) test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys the p-norm distribution whose parameter is close to 1.60. A least p-norm estimation and the least square estimation of digitized data are further analyzed, showing that the least p-norm adjustment is better than the least square adjustment for digitized data processing in GIS.展开更多
基金supported by the National Natural Science Fundation of China(61273127)the Specialized Research Fund of the Doctoral Program in Higher Education(20106118110009+2 种基金20116118110008)the Scientific Research Plan Projects of Shaanxi Education Department(12JK0524)the Young Teachers Scientific Research Fund of Xi’an University of Posts and Telecommunications(1100434)
文摘A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.
文摘Traditionally, it is widely accepted that measurement error usually obeys the normal distribution. However, in this paper a new idea is proposed that the error in digitized data which is a major derived data source in GIS does not obey the normal distribution but the p-norm distribution with a determinate parameter. Assuming that the error is random and has the same statistical properties, the probability density function of the normal distribution, Laplace distribution and p-norm distribution are derived based on the arithmetic mean axiom, median axiom and p-median axiom, which means that the normal distribution is only one of these distributions but not the least one. Based on this ideal distribution fitness tests such as Skewness and Kurtosis coefficient test, Pearson chi-square chi(2) test and Kolmogorov test for digitized data are conducted. The results show that the error in map digitization obeys the p-norm distribution whose parameter is close to 1.60. A least p-norm estimation and the least square estimation of digitized data are further analyzed, showing that the least p-norm adjustment is better than the least square adjustment for digitized data processing in GIS.
