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
Recently, fault or health condition prediction of complex systems becomes an interesting research topic. However, it is difficult to establish precise physical model for complex systems, and the time series properties...Recently, fault or health condition prediction of complex systems becomes an interesting research topic. However, it is difficult to establish precise physical model for complex systems, and the time series properties are often necessary to be incorporated for the prediction in practice. Currently, the LS-SVR is widely adopted for prediction of systems with time series data. In this paper, in order to improve the prediction accuracy, accumulated generating operation （AGO） is carried out to improve the data quality and regularity of raw time series data based on grey system theory; then, the inverse accumulated generating operation （IAGO） is performed to obtain the prediction results. In addition, due to the reason that appropriate kernel function plays an important role in improving the accuracy of prediction through LS-SVR, a modified Gaussian radial basis function （RBF） is proposed. The requirements of distance functions-based kernel functions are satisfied, which ensure fast damping at the place adjacent to the test point and a moderate damping at infinity. The presented model is applied to the analysis of benchmarks. As indicated by the results, the proposed method is an effective prediction one with good precision.展开更多
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.
基金supported by National Natural Science Foundation(NNSF)of China under Grant No.61371024Aviation Science Fund of China under Grant No.2013ZD53051+1 种基金Aerospace Technology Support Fund of Chinathe Industry-Academy-Research Project of AVIC(cxy2013XGD14)
文摘Recently, fault or health condition prediction of complex systems becomes an interesting research topic. However, it is difficult to establish precise physical model for complex systems, and the time series properties are often necessary to be incorporated for the prediction in practice. Currently, the LS-SVR is widely adopted for prediction of systems with time series data. In this paper, in order to improve the prediction accuracy, accumulated generating operation （AGO） is carried out to improve the data quality and regularity of raw time series data based on grey system theory; then, the inverse accumulated generating operation （IAGO） is performed to obtain the prediction results. In addition, due to the reason that appropriate kernel function plays an important role in improving the accuracy of prediction through LS-SVR, a modified Gaussian radial basis function （RBF） is proposed. The requirements of distance functions-based kernel functions are satisfied, which ensure fast damping at the place adjacent to the test point and a moderate damping at infinity. The presented model is applied to the analysis of benchmarks. As indicated by the results, the proposed method is an effective prediction one with good precision.
