This paper present a simulation study of an evolutionary algorithms, Particle Swarm Optimization PSO algorithm to optimize likelihood function of ARMA（1, 1） model, where maximizing likelihood function is equivalent ...This paper present a simulation study of an evolutionary algorithms, Particle Swarm Optimization PSO algorithm to optimize likelihood function of ARMA（1, 1） model, where maximizing likelihood function is equivalent to maximizing its logarithm, so the objective function ＇obj.fun＇ is maximizing log-likelihood function. Monte Carlo method adapted for implementing and designing the experiments of this simulation. This study including a comparison among three versions of PSO algorithm “Constriction coefficient CCPSO, Inertia weight IWPSO, and Fully Informed FIPSO”, the experiments designed by setting different values of model parameters al, bs sample size n, moreover the parameters of PSO algorithms. MSE used as test statistic to measure the efficiency PSO to estimate model. The results show the ability of PSO to estimate ARMA＇ s parameters, and the minimum values of MSE getting for COPSO.展开更多
Electricity demand forecasting plays an important role in smart grid expansion planning.In this paper,we present a dynamic GM(1,1) model based on grey system theory and cubic spline function interpolation principle.Us...Electricity demand forecasting plays an important role in smart grid expansion planning.In this paper,we present a dynamic GM(1,1) model based on grey system theory and cubic spline function interpolation principle.Using piecewise polynomial interpolation thought,this model can dynamically predict the general trend of time series data.Combined with low-order polynomial,the cubic spline interpolation has smaller error,avoids the Runge phenomenon of high-order polynomial,and has better approximation effect.Meanwhile,prediction is implemented with the newest information according to the rolling and feedback mechanism and fluctuating error is controlled well to improve prediction accuracy in time-varying environment.Case study using the living electricity consumption data of Jiangsu province in 2008 is presented to demonstrate the effectiveness of the proposed model.展开更多
The basic difference non-equal interval model GM(1,1) in grey theory was used to fit and forecast data series with non-equal lengths and different inertias, acquired from oil monitoring of internal combustion engines....The basic difference non-equal interval model GM(1,1) in grey theory was used to fit and forecast data series with non-equal lengths and different inertias, acquired from oil monitoring of internal combustion engines. The fitted and forecasted results show that the length or inertia of a sequence affects its precision very much, i.e. the bigger the inertia of a sequence is, or the shorter the length of a series is, the less the errors of fitted and forecasted results are. Based on the research results, it is suggested that short series should be applied to be fitted and forecasted; for longer series, the newer datum should be applied instead of the older datum to be analyzed by non- equalinterval GM(1,1) to improve the forecasted and fitted precision, and that data sequence should be verified to satisfy the conditions of grey forecasting.展开更多
In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.B...In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.展开更多
文摘This paper present a simulation study of an evolutionary algorithms, Particle Swarm Optimization PSO algorithm to optimize likelihood function of ARMA（1, 1） model, where maximizing likelihood function is equivalent to maximizing its logarithm, so the objective function ＇obj.fun＇ is maximizing log-likelihood function. Monte Carlo method adapted for implementing and designing the experiments of this simulation. This study including a comparison among three versions of PSO algorithm “Constriction coefficient CCPSO, Inertia weight IWPSO, and Fully Informed FIPSO”, the experiments designed by setting different values of model parameters al, bs sample size n, moreover the parameters of PSO algorithms. MSE used as test statistic to measure the efficiency PSO to estimate model. The results show the ability of PSO to estimate ARMA＇ s parameters, and the minimum values of MSE getting for COPSO.
基金This work has been supported by the National 863 Key Project Grant No. 2008AA042901, National Natural Science Foundation of China Grant No.70631003 and No.90718037, Foundation of Hefei University of Technology Grant No. 2010HGXJ0083.
文摘Electricity demand forecasting plays an important role in smart grid expansion planning.In this paper,we present a dynamic GM(1,1) model based on grey system theory and cubic spline function interpolation principle.Using piecewise polynomial interpolation thought,this model can dynamically predict the general trend of time series data.Combined with low-order polynomial,the cubic spline interpolation has smaller error,avoids the Runge phenomenon of high-order polynomial,and has better approximation effect.Meanwhile,prediction is implemented with the newest information according to the rolling and feedback mechanism and fluctuating error is controlled well to improve prediction accuracy in time-varying environment.Case study using the living electricity consumption data of Jiangsu province in 2008 is presented to demonstrate the effectiveness of the proposed model.
文摘The basic difference non-equal interval model GM(1,1) in grey theory was used to fit and forecast data series with non-equal lengths and different inertias, acquired from oil monitoring of internal combustion engines. The fitted and forecasted results show that the length or inertia of a sequence affects its precision very much, i.e. the bigger the inertia of a sequence is, or the shorter the length of a series is, the less the errors of fitted and forecasted results are. Based on the research results, it is suggested that short series should be applied to be fitted and forecasted; for longer series, the newer datum should be applied instead of the older datum to be analyzed by non- equalinterval GM(1,1) to improve the forecasted and fitted precision, and that data sequence should be verified to satisfy the conditions of grey forecasting.
基金supported by the National Natural Science Foundation of China(7084001290924022)the Ph.D.Thesis Innovation and Excellent Foundation of Nanjing University of Aeronautics and Astronautics(2010)
文摘In grey system theory,the studies in the field of grey prediction model are focused on real number sequences,rather than grey number ones.Hereby,a prediction model based on interval grey number sequences is proposed.By mining the geometric features of interval grey number sequences on a two-dimensional surface,all the interval grey numbers are converted into real numbers by means of certain algorithm,and then the prediction model is established based on those real number sequences.The entire process avoids the algebraic operations of grey number,and the prediction problem of interval grey number is usefully solved.Ultimately,through an example＇s program simulation,the validity and practicability of this novel model are verified.
