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
Trend forecasting is an important aspect in fault diagnosis and work state supervision. The principle, where Grey theory is applied in fault forecasting, is that the forecast system is considered as a Grey system; the...Trend forecasting is an important aspect in fault diagnosis and work state supervision. The principle, where Grey theory is applied in fault forecasting, is that the forecast system is considered as a Grey system; the existing known information is used to infer the unknown information's character, state and development trend in a fault pattern, and to make possible forecasting and decisions for future development. It involves the whitenization of a Grey process. But the traditional equal time interval Grey GM (1,1) model requires equal interval data and needs to bring about accumulating addition generation and reversion calculations. Its calculation is very complex. However, the non equal interval Grey GM (1,1) model decreases the condition of the primitive data when establishing a model, but its requirement is still higher and the data were pre processed. The abrasion primitive data of plant could not always satisfy these modeling requirements. Therefore, it establishes a division method suited for general data modeling and estimating parameters of GM (1,1), the standard error coefficient that was applied to judge accuracy height of the model was put forward; further, the function transform to forecast plant abrasion trend and assess GM (1,1) parameter was established. These two models need not pre process the primitive data. It is not only suited for equal interval data modeling, but also for non equal interval data modeling. Its calculation is simple and convenient to use. The oil spectrum analysis acted as an example. The two GM (1,1) models put forward in this paper and the new information model and its comprehensive usage were investigated. The example shows that the two models are simple and practical, and worth expanding and applying in plant fault diagnosis.展开更多
To predict the annual total yields of Chinese aquatic products in future five years ( 2011-2015) ,based on the theory and method of gray system,this paper firstly establishes a conventional GM ( 1,1) model and a gray ...To predict the annual total yields of Chinese aquatic products in future five years ( 2011-2015) ,based on the theory and method of gray system,this paper firstly establishes a conventional GM ( 1,1) model and a gray metabolic GM ( 1,1) model respectively to predict the annual total yields of Chinese aquatic products in 2006-2009 and compare the prediction accuracy between these two models. Then,it selects the model with higher accuracy to predict the annual total yields of Chinese aquatic products in future five years. The comparison indicates that gray metabolic GM ( 1,1) model has higher prediction accuracy and smaller error,thus it is more suitable for prediction of annual total yields of aquatic products. Therefore,it adopts the gray metabolic GM ( 1,1) model to predict annual total yields of Chinese aquatic products in 2011-2015. The prediction results of annual total yields are 55. 32,57. 46,59. 72,62. 02 and 64. 43 million tons respectively in future five years with annual average increase rate of about 3. 7% ,much higher than the objective of 2. 2% specified in the Twelfth Five-Year Plan of the National Fishery Development ( 2011 to 2015) . The results of this research show that the gray metabolic GM ( 1,1) model is suitable for prediction of yields of aquatic products and the total yields of Chinese aquatic products in 2011-2015 will totally be able to realize the objective of the Twelfth Five-Year Plan.展开更多
Grey prediction is vital in statistical prediction with wide applications.However,most grey prediction methods focus on annual predictions of the monotonic time series instead of the seasonal time series.The paper use...Grey prediction is vital in statistical prediction with wide applications.However,most grey prediction methods focus on annual predictions of the monotonic time series instead of the seasonal time series.The paper uses the extended model of the grey GM(1,1)model to predict the seasonal time series.Some improvements have been made in two aspects to improve the prediction accuracy of the model.1)We introduce seasonal multiple factors to transform the original time series,which improves the adaptability of the seasonal data to the model.The transformed series conforms to the law presented by the model.2)The seasonal data are in superimposed sine and cosine fluctuations with tendencies.Therefore,the paper extends the grey action quantity of the traditional GM(1,1)model.The newly extended grey model is called the GM(1,1,exp×sin,exp×cos)model,which is provided with the parameter optimization methods and time response equations.According to the proposed modeling method,we establish a GM(1,1,exp×sin,exp×cos)model for China's quarterly gross domestic product(GDP)with high accuracy.展开更多
To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) ...To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.展开更多
Evaluation of ecological carrying capacity is an important method of analyzing regional sustainable development, study on ecological carrying capacity is to settle the contradictions between resource and environment, ...Evaluation of ecological carrying capacity is an important method of analyzing regional sustainable development, study on ecological carrying capacity is to settle the contradictions between resource and environment, and it is a significant basis for realizing regional sustainable development. This paper, on the basis of the academician Sun Tiehang's "unification of three" for the eco-city construction, established ecological carrying capacity evaluation indexes for the traditional industrial and mining city—Huainan City; and applied GM–BP neural network coupling model for the dynamic evolution and prediction of ecological carrying capacity of Huainan City in the future decade. The results showed that ecological carrying capacity index of Huainan would be 2.13 by 2025, higher than the loadable state 1, so the ecological carrying capacity would keep in the over-loaded level, but the over-loaded degree would be lower than the current. Carrying capacity of arable land, energy and water resources contribute greatly to the improvement of ecological carrying capacity, thus it is imperative to adjust this unreasonable and unsustainable ecological consumption relationship, enhance environmental protection awareness and high-efficiency utilization of resources, and take an energy-saving and intensive development path.展开更多
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
The data on the coal production and consumption in Jilin Province for the last ten years were collected,and the Grey System GM( 1,1) model and unary linear regression model were applied to predict the coal consumption...The data on the coal production and consumption in Jilin Province for the last ten years were collected,and the Grey System GM( 1,1) model and unary linear regression model were applied to predict the coal consumption of Jilin Production in 2014 and 2015. Through calculation,the predictive value on the coal consumption of Jilin Province was attained,namely consumption of 2014 is 114. 84 × 106 t and of 2015 is 117. 98 ×106t,respectively. Analysis of error data indicated that the predicted accuracy of Grey System GM( 1,1) model on the coal consumption in Jilin Province improved 0. 21% in comparison to unary linear regression model.展开更多
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Trend forecasting is an important aspect in fault diagnosis and work state supervision. The principle, where Grey theory is applied in fault forecasting, is that the forecast system is considered as a Grey system; the existing known information is used to infer the unknown information's character, state and development trend in a fault pattern, and to make possible forecasting and decisions for future development. It involves the whitenization of a Grey process. But the traditional equal time interval Grey GM (1,1) model requires equal interval data and needs to bring about accumulating addition generation and reversion calculations. Its calculation is very complex. However, the non equal interval Grey GM (1,1) model decreases the condition of the primitive data when establishing a model, but its requirement is still higher and the data were pre processed. The abrasion primitive data of plant could not always satisfy these modeling requirements. Therefore, it establishes a division method suited for general data modeling and estimating parameters of GM (1,1), the standard error coefficient that was applied to judge accuracy height of the model was put forward; further, the function transform to forecast plant abrasion trend and assess GM (1,1) parameter was established. These two models need not pre process the primitive data. It is not only suited for equal interval data modeling, but also for non equal interval data modeling. Its calculation is simple and convenient to use. The oil spectrum analysis acted as an example. The two GM (1,1) models put forward in this paper and the new information model and its comprehensive usage were investigated. The example shows that the two models are simple and practical, and worth expanding and applying in plant fault diagnosis.
基金Supported by Special Project for Construction of Modern Agricultural Industrial Technology System(Grant No.:CARS-46-05)Scientific and Technological Project of Huazhong Agricultural University(Grant No.:52902-0900206038)National Natural Science Foundation of China(Grant No:31201719)
文摘To predict the annual total yields of Chinese aquatic products in future five years ( 2011-2015) ,based on the theory and method of gray system,this paper firstly establishes a conventional GM ( 1,1) model and a gray metabolic GM ( 1,1) model respectively to predict the annual total yields of Chinese aquatic products in 2006-2009 and compare the prediction accuracy between these two models. Then,it selects the model with higher accuracy to predict the annual total yields of Chinese aquatic products in future five years. The comparison indicates that gray metabolic GM ( 1,1) model has higher prediction accuracy and smaller error,thus it is more suitable for prediction of annual total yields of aquatic products. Therefore,it adopts the gray metabolic GM ( 1,1) model to predict annual total yields of Chinese aquatic products in 2011-2015. The prediction results of annual total yields are 55. 32,57. 46,59. 72,62. 02 and 64. 43 million tons respectively in future five years with annual average increase rate of about 3. 7% ,much higher than the objective of 2. 2% specified in the Twelfth Five-Year Plan of the National Fishery Development ( 2011 to 2015) . The results of this research show that the gray metabolic GM ( 1,1) model is suitable for prediction of yields of aquatic products and the total yields of Chinese aquatic products in 2011-2015 will totally be able to realize the objective of the Twelfth Five-Year Plan.
基金Supported by National Natural Science Foundation of China (11401418)。
文摘Grey prediction is vital in statistical prediction with wide applications.However,most grey prediction methods focus on annual predictions of the monotonic time series instead of the seasonal time series.The paper uses the extended model of the grey GM(1,1)model to predict the seasonal time series.Some improvements have been made in two aspects to improve the prediction accuracy of the model.1)We introduce seasonal multiple factors to transform the original time series,which improves the adaptability of the seasonal data to the model.The transformed series conforms to the law presented by the model.2)The seasonal data are in superimposed sine and cosine fluctuations with tendencies.Therefore,the paper extends the grey action quantity of the traditional GM(1,1)model.The newly extended grey model is called the GM(1,1,exp×sin,exp×cos)model,which is provided with the parameter optimization methods and time response equations.According to the proposed modeling method,we establish a GM(1,1,exp×sin,exp×cos)model for China's quarterly gross domestic product(GDP)with high accuracy.
基金The 11th Five-Year Plan for Key Constructing Academic Subject of Hunan Province(No.XJT2006180)Natural Science Foundation of Hunan Province (No.07JJ3093)Hunan Province Foundation Research Program (No.2007FJ3030,2007GK3058)
文摘To overcome the deficiencies of the existing Verhulst GM(1,1) model, based on the existing grey theory, a non-equal-interval direct optimum Verhulst GM(1,1) model is built which chooses a modified n-th component x(n) of X(0) as the starting condition of the grey differential model. It optimizes a modified β value and the background value, and takes two times fitting optimization. The new model extends equal intervals to non-equal-intervals and is suitable for general data modelling and estimating parameters of the direct Verhulst GM(1,1). The new model does not need to pre-process the primitive data, nor accumulate generating operation (AGO) and inverse accumulated generating operation (IAGO). It is not only suitable for equal interval data modelling, but also for non-equal interval data modelling. As the new information is fully used and two times fitting optimization is taken, the fitting accuracy is the highest in all existing models. The example shows that the new model is simple and practical. The new model is worth expanding on and applying in data processing or on-line monitoring for tests, social sciences and other engineering sciences.
基金Sponsored by National Natural Science Foundation of China(41101566)
文摘Evaluation of ecological carrying capacity is an important method of analyzing regional sustainable development, study on ecological carrying capacity is to settle the contradictions between resource and environment, and it is a significant basis for realizing regional sustainable development. This paper, on the basis of the academician Sun Tiehang's "unification of three" for the eco-city construction, established ecological carrying capacity evaluation indexes for the traditional industrial and mining city—Huainan City; and applied GM–BP neural network coupling model for the dynamic evolution and prediction of ecological carrying capacity of Huainan City in the future decade. The results showed that ecological carrying capacity index of Huainan would be 2.13 by 2025, higher than the loadable state 1, so the ecological carrying capacity would keep in the over-loaded level, but the over-loaded degree would be lower than the current. Carrying capacity of arable land, energy and water resources contribute greatly to the improvement of ecological carrying capacity, thus it is imperative to adjust this unreasonable and unsustainable ecological consumption relationship, enhance environmental protection awareness and high-efficiency utilization of resources, and take an energy-saving and intensive development path.
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 project of National Natural Science Foundation of China(No.41272360)
文摘The data on the coal production and consumption in Jilin Province for the last ten years were collected,and the Grey System GM( 1,1) model and unary linear regression model were applied to predict the coal consumption of Jilin Production in 2014 and 2015. Through calculation,the predictive value on the coal consumption of Jilin Province was attained,namely consumption of 2014 is 114. 84 × 106 t and of 2015 is 117. 98 ×106t,respectively. Analysis of error data indicated that the predicted accuracy of Grey System GM( 1,1) model on the coal consumption in Jilin Province improved 0. 21% in comparison to unary linear regression model.
