Based on the optimization method, a new modified GM (1,1) model is presented, which is characterized by more accuracy prediction for the grey modeling.
For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the backgrou...For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the background value as a variable related to k.At the same time,the initial value is set as a variable,and the corresponding optimal parameter and the time response formula are determined according to the minimum value of mean relative error(MRE).Combined with the domestic natural gas annual consumption data,the classical model and the improved GM(1,1)model are applied to the calculation and error comparison respectively.It proves that the improved model is better than any other models.展开更多
A new method to improve prediction precision of GM（1,1） model with unequal time interval is presented.The grey derivative is multiplied by a parameter to guarantee the time response function satisfying approximately...A new method to improve prediction precision of GM（1,1） model with unequal time interval is presented.The grey derivative is multiplied by a parameter to guarantee the time response function satisfying approximately exponential function distribution.To simplify the process of parametric estimation,an approximate value is taken for the multiplied parameter.Then the estimators of coefficient of development and grey action quantity can be derived.At the same time,the principle of the new information priority is also considered.We take the last item of the first-order accumulated generation operator（1-AGO） on raw data sequence as the initial condition in the time response function.Then the new information can be taken full advantage of through the improved initial condition.Some properties of this new model are also discussed.The presented method is actually a combination of improvement of grey derivative and improvement of the initial condition.The results of an example indicate that the proposed method can improve prediction precision prominently.展开更多
The grey forecasting model has been successfully applied to many fields. However, the precision of GM(1,1) model is not high. In order to remove the seasonal fluctuations in monitoring series before building GM(1,1) m...The grey forecasting model has been successfully applied to many fields. However, the precision of GM(1,1) model is not high. In order to remove the seasonal fluctuations in monitoring series before building GM(1,1) model, the forecasting series of GM(1,1) was built, and an inverse process was used to resume the seasonal fluctuations. Two deseasonalization methods were presented , i.e., seasonal index-based deseasonalization and standard normal distribution-based deseasonalization. They were combined with the GM(1,1) model to form hybrid grey models. A simple but practical method to further improve the forecasting results was also suggested. For comparison, a conventional periodic function model was investigated. The concept and algorithms were tested with four years monthly monitoring data. The results show that on the whole the seasonal index-GM(1,1) model outperform the conventional periodic function model and the conventional periodic function model outperform the SND-GM(1,1) model. The mean Absolute error and mean square error of seasonal index-GM(1,1) are 30.69% and 54.53% smaller than that of conventional periodic function model, respectively. The high accuracy, straightforward and easy implementation natures of the proposed hybrid seasonal index-grey model make it a powerful analysis technique for seasonal monitoring series.展开更多
GM(1,1)models have been widely used in various fields due to their high performance in time series prediction.However,some hypotheses of the existing GM(1,1)model family may reduce their prediction performance in some...GM(1,1)models have been widely used in various fields due to their high performance in time series prediction.However,some hypotheses of the existing GM(1,1)model family may reduce their prediction performance in some cases.To solve this problem,this paper proposes a self-adaptive GM(1,1)model,termed as SAGM(1,1)model,which aims to solve the defects of the existing GM(1,1)model family by deleting their modeling hypothesis.Moreover,a novel multi-parameter simultaneous optimization scheme based on firefly algorithm is proposed,the proposed multi-parameter optimization scheme adopts machine learning ideas,takes all adjustable parameters of SAGM(1,1)model as input variables,and trains it with firefly algorithm.And Sobol’sensitivity indices are applied to study global sensitivity of SAGM(1,1)model parameters,which provides an important reference for model parameter calibration.Finally,forecasting capability of SAGM(1,1)model is illustrated by Anhui electricity consumption dataset.Results show that prediction accuracy of SAGM(1,1)model is significantly better than other models,and it is shown that the proposed approach enhances the prediction performance of GM(1,1)model significantly.展开更多
Three forecasting models are set up: the auto\|regressive moving average model, the grey forecasting model for the rate of qualified products P t, and the grey forecasting model for time intervals of the quality cata...Three forecasting models are set up: the auto\|regressive moving average model, the grey forecasting model for the rate of qualified products P t, and the grey forecasting model for time intervals of the quality catastrophes. Then a combined forewarning system for the quality of products is established, which contains three models, judgment rules and forewarning state illustration. Finally with an example of the practical production, this modeling system is proved fairly effective.展开更多
To improve prediction accuracy of strip thickness in hot rolling, a kind of Dempster/Shafer(D_S) information reconstitution prediction method(DSIRPM) was presented. DSIRPM basically consisted of three steps to impleme...To improve prediction accuracy of strip thickness in hot rolling, a kind of Dempster/Shafer(D_S) information reconstitution prediction method(DSIRPM) was presented. DSIRPM basically consisted of three steps to implement the prediction of strip thickness. Firstly, iba Analyzer was employed to analyze the periodicity of hot rolling and find three sensitive parameters to strip thickness, which were used to undertake polynomial curve fitting prediction based on least square respectively, and preliminary prediction results were obtained. Then, D_S evidence theory was used to reconstruct the prediction results under different parameters, in which basic probability assignment(BPA) was the key and the proposed contribution rate calculated using grey relational degree was regarded as BPA, which realizes BPA selection objectively. Finally, from this distribution, future strip thickness trend was inferred. Experimental results clearly show the improved prediction accuracy and stability compared with other prediction models, such as GM(1,1) and the weighted average prediction model.展开更多
文摘Based on the optimization method, a new modified GM (1,1) model is presented, which is characterized by more accuracy prediction for the grey modeling.
基金supported by the National Natural Science Foundation of China (71871106)the Blue and Green Project in Jiangsu Provincethe Six Talent Peaks Project in Jiangsu Province (2016-JY-011)
文摘For the classical GM(1,1)model,the prediction accuracy is not high,and the optimization of the initial and background values is one-sided.In this paper,the Lagrange mean value theorem is used to construct the background value as a variable related to k.At the same time,the initial value is set as a variable,and the corresponding optimal parameter and the time response formula are determined according to the minimum value of mean relative error(MRE).Combined with the domestic natural gas annual consumption data,the classical model and the improved GM(1,1)model are applied to the calculation and error comparison respectively.It proves that the improved model is better than any other models.
基金supported by the National Natural Science Foundation of China (7090103471071077)+2 种基金the National Educational Sciences Planning Key Project of Ministry of Education (DFA090215)the Fundamental Research Funds for the Central Universities (JUSRP21146JUSRP31107)
文摘A new method to improve prediction precision of GM（1,1） model with unequal time interval is presented.The grey derivative is multiplied by a parameter to guarantee the time response function satisfying approximately exponential function distribution.To simplify the process of parametric estimation,an approximate value is taken for the multiplied parameter.Then the estimators of coefficient of development and grey action quantity can be derived.At the same time,the principle of the new information priority is also considered.We take the last item of the first-order accumulated generation operator（1-AGO） on raw data sequence as the initial condition in the time response function.Then the new information can be taken full advantage of through the improved initial condition.Some properties of this new model are also discussed.The presented method is actually a combination of improvement of grey derivative and improvement of the initial condition.The results of an example indicate that the proposed method can improve prediction precision prominently.
文摘The grey forecasting model has been successfully applied to many fields. However, the precision of GM(1,1) model is not high. In order to remove the seasonal fluctuations in monitoring series before building GM(1,1) model, the forecasting series of GM(1,1) was built, and an inverse process was used to resume the seasonal fluctuations. Two deseasonalization methods were presented , i.e., seasonal index-based deseasonalization and standard normal distribution-based deseasonalization. They were combined with the GM(1,1) model to form hybrid grey models. A simple but practical method to further improve the forecasting results was also suggested. For comparison, a conventional periodic function model was investigated. The concept and algorithms were tested with four years monthly monitoring data. The results show that on the whole the seasonal index-GM(1,1) model outperform the conventional periodic function model and the conventional periodic function model outperform the SND-GM(1,1) model. The mean Absolute error and mean square error of seasonal index-GM(1,1) are 30.69% and 54.53% smaller than that of conventional periodic function model, respectively. The high accuracy, straightforward and easy implementation natures of the proposed hybrid seasonal index-grey model make it a powerful analysis technique for seasonal monitoring series.
基金supported by the National Natural Science Foundation of China(72171116,71671090)the Fundamental Research Funds for the Central Universities(NP2020022)+1 种基金the Key Research Projects of Humanities and Social Sciences in Anhui Education Department(SK2021A1018)Qinglan Project for Excellent Youth or Middlea ged Academic Leaders in Jiangsu Province,China.
文摘GM(1,1)models have been widely used in various fields due to their high performance in time series prediction.However,some hypotheses of the existing GM(1,1)model family may reduce their prediction performance in some cases.To solve this problem,this paper proposes a self-adaptive GM(1,1)model,termed as SAGM(1,1)model,which aims to solve the defects of the existing GM(1,1)model family by deleting their modeling hypothesis.Moreover,a novel multi-parameter simultaneous optimization scheme based on firefly algorithm is proposed,the proposed multi-parameter optimization scheme adopts machine learning ideas,takes all adjustable parameters of SAGM(1,1)model as input variables,and trains it with firefly algorithm.And Sobol’sensitivity indices are applied to study global sensitivity of SAGM(1,1)model parameters,which provides an important reference for model parameter calibration.Finally,forecasting capability of SAGM(1,1)model is illustrated by Anhui electricity consumption dataset.Results show that prediction accuracy of SAGM(1,1)model is significantly better than other models,and it is shown that the proposed approach enhances the prediction performance of GM(1,1)model significantly.
文摘Three forecasting models are set up: the auto\|regressive moving average model, the grey forecasting model for the rate of qualified products P t, and the grey forecasting model for time intervals of the quality catastrophes. Then a combined forewarning system for the quality of products is established, which contains three models, judgment rules and forewarning state illustration. Finally with an example of the practical production, this modeling system is proved fairly effective.
基金Projects(61174115,51104044)supported by the National Natural Science Foundation of ChinaProject(L2010153)supported by Scientific Research Project of Liaoning Provincial Education Department,China
文摘To improve prediction accuracy of strip thickness in hot rolling, a kind of Dempster/Shafer(D_S) information reconstitution prediction method(DSIRPM) was presented. DSIRPM basically consisted of three steps to implement the prediction of strip thickness. Firstly, iba Analyzer was employed to analyze the periodicity of hot rolling and find three sensitive parameters to strip thickness, which were used to undertake polynomial curve fitting prediction based on least square respectively, and preliminary prediction results were obtained. Then, D_S evidence theory was used to reconstruct the prediction results under different parameters, in which basic probability assignment(BPA) was the key and the proposed contribution rate calculated using grey relational degree was regarded as BPA, which realizes BPA selection objectively. Finally, from this distribution, future strip thickness trend was inferred. Experimental results clearly show the improved prediction accuracy and stability compared with other prediction models, such as GM(1,1) and the weighted average prediction model.
