A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In th...A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization （PSO）. The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.展开更多
Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problem...Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization(PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste(MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.展开更多
基金supported by the National Natural Science Foundation of China (10872030)
文摘A rational approximation method of the fractional-order derivative and integral operators is proposed. The turning fre- quency points are fixed in each frequency interval in the standard Oustaloup approximation. In the improved Oustaloup method, the turning frequency points are determined by the adaptive chaotic particle swarm optimization （PSO）. The average velocity is proposed to reduce the iterations of the PSO. The chaotic search scheme is combined to reduce the opportunity of the premature phenomenon. Two fitness functions are given to minimize the zero-pole and amplitude-phase frequency errors for the underlying optimization problems. Some numerical examples are compared to demonstrate the effectiveness and accuracy of this proposed rational approximation method.
基金supported by the National Natural Science Foundation of China (51479151,61403288)。
文摘Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization(PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste(MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.
