文章以幂函数变换为研究对象,从背景值误差和还原误差的角度分析了幂函数变换对GM(1,1)模型建模精度的影响,论证了幂函数变换的GM(1,1)模型(PFNGM(1,1)模型)具有逼近无偏性,能在可忽略的误差范围内实现对白指数序列的预测无偏性。实例...文章以幂函数变换为研究对象,从背景值误差和还原误差的角度分析了幂函数变换对GM(1,1)模型建模精度的影响,论证了幂函数变换的GM(1,1)模型(PFNGM(1,1)模型)具有逼近无偏性,能在可忽略的误差范围内实现对白指数序列的预测无偏性。实例应用结果表明,其建模精度和预测效果均优于无偏GM(1,1)模型和离散GM(1,1)模型。为将适宜建模序列拓展至近似非齐次指数序列和季节波动序列,同时保留幂函数变换可以有效降低背景值误差对建模精度影响的优势,将幂函数变换与平移变换相结合构建了PFNGM(1,1)模型,将幂函数变换与季节性GM(1,1)模型(SGM(1,1)模型)相结合构建了PFSGM(1,1)模型。实例应用结果表明,PFNGM(1,1)模型的建模精度和预测效果均优于背景值改进的NGM(1,1, k )模型和ONGM(1,1, k,c )模型,PFSGM(1,1)模型的建模精度和预测效果均优于SGM(1,1)模型,验证了两种模型的有效性。展开更多
Firstly, the research progress of grey model GM （1,1） is summarized, which is divided into three development stages： assimilation, alienation and melting stages. Then, the matrix analysis theory is used to study th...Firstly, the research progress of grey model GM （1,1） is summarized, which is divided into three development stages： assimilation, alienation and melting stages. Then, the matrix analysis theory is used to study the modeling mechanism of GM （1,1）, which decomposes the modeling data matrix into raw data transformation matrix, accumulated generating operation matrix and background value selection matrix. The changes of these three matrices are the essential reasons affecting the modeling and the accuracy of GM （1,1）. Finally, the paper proposes a generalization grey model GGM （1,1）, which is a extended form of GM （1,1） and also a unified form of model GM （1,1）, model GM （1,1,α）, stage grey model, hopping grey model, generalized accumulated model, strengthening operator model, weakening operator model and unequal interval model. And the theory and practical significance of the extended model is analyzed.展开更多
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
As a kind of mathematical model, grey systems predi ct ion model has been widely applied to economy, management and engineering technol ogy. In 1982, Professor Deng Ju-long presented GM prediction model. Then some o t...As a kind of mathematical model, grey systems predi ct ion model has been widely applied to economy, management and engineering technol ogy. In 1982, Professor Deng Ju-long presented GM prediction model. Then some o ther scholars made improvements on GM model. Of course, much still should be don e to develop it. What the scholars have done is to take the first component of X (1) as the starting conditions of the grey differential model. It occ urs that the new information can not be used enough. This paper is addressed to choose the nth component of X (1) as the starting conditions to improv e the models. The main results of the paper is given in Theorem 2: The time response function of the grey differential equation x (0)(k)+az (1)(k)=b is given by x (1)(k)=x (1)(n)-ba e -a(k-n )+ba. and Theorem4: The time response of the grey Verhulst model is given by (1)(k) =ax (1)(n)bx (1)(n)+(a-bx (1)(n))ae a(k-n). As the new information is fully used, the accuracy of prediction is improved gre atly. Therefore, the new model with a certain theoretical and practical value.展开更多
This paper expresses the efficient outputs of decisionmaking unit（DMU） as the sum of ＂average outputs＂ forecasted by a GM（1,N） model and ＂increased outputs＂ which reflect the difficulty to realize efficient ou...This paper expresses the efficient outputs of decisionmaking unit（DMU） as the sum of ＂average outputs＂ forecasted by a GM（1,N） model and ＂increased outputs＂ which reflect the difficulty to realize efficient outputs.The increased outputs are solved by linear programming using data envelopment analysis efficiency theories,wherein a new sample is introduced whose inputs are equal to the budget in the issue No.n ＋ 1 and outputs are forecasted by the GM（1,N） model.The shortcoming in the existing methods that the forecasted efficient outputs may be less than the possible actual outputs according to developing trends of input-output rate in the periods of pre-n is overcome.The new prediction method provides decision-makers with more decisionmaking information,and the initial conditions are easy to be given.展开更多
Over the past century,the safety of dams has gradually attracted attention from all parties.Research on the dynamic response and damage evolution of dams under extreme loads is the basis of dam safety issues.In recent...Over the past century,the safety of dams has gradually attracted attention from all parties.Research on the dynamic response and damage evolution of dams under extreme loads is the basis of dam safety issues.In recent decades,scholars have studied the responses of dams under earthquake loads,but there is still much room for improvement in experimental and theoretical research on small probability loads such as explosions.In this paper,a 50-m-high concrete gravity dam is used as a prototype dam,and a water explosion model test of a 2.5-m-high concrete gravity dam is designed.The water pressure and the acceleration response of the dam body in the test are analysed.The pressure characteristics and dynamic response of the dam body are assessed.Taking the dam damage test as an example,a numerical model of concrete gravity dam damage is established,and the damage evolution of the dam body is analysed.By combining experiments and numerical simulations,the damage characteristics of the dam body under the action of different charge water explosions are clarified.The integrity of the dam body is well maintained under the action of a small-quantity water explosion,and the dynamic response of the dam body is mainly caused by the shock wave.Both the shock wave and the bubble pulsation cause the dam body to accelerate,and the peak acceleration of the dam body under the action of the bubble pulsation is only one percent of the peak acceleration of the dam body under the action of the shock wave.When subjected to explosions in large quantities of water,the dam body is seriously damaged.Under the action of a shock wave,the dam body produces a secondary acceleration response,which is generated by an internal interaction after the dam body is damaged.The damage evolution process of the dam body under the action of a large-scale water explosion is analysed,and it is found that the shock wave pressure of the water explosion causes local damage to the dam body facing the explosion.After the peak value of the shock wave,the impulse continues to act on the dam body,causing cumulative damage and damage inside the dam body.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 this paper, we develope a timodependent, nonlinear, photochemical-dynamical 2-D model which is composed of 3 models: dynamical gravity wave model, middle atmospheric photochemical model, and airglow layer photochem...In this paper, we develope a timodependent, nonlinear, photochemical-dynamical 2-D model which is composed of 3 models: dynamical gravity wave model, middle atmospheric photochemical model, and airglow layer photochemical model. We use the model to study the effect of the gravity wave propagation on the airglow layer. The comparison between the effects of the different wavelength gravity wave on the airglow emission distributions is made. When the vertical wavelength of the gravity wave is close to or is shorter than the thickness of the airglow layer, the gravity wave can make complex structure of the airglow layer, such as the double and multi-peak structures of the airglow layer. However, the gravity wave that has long vertical wavelength can make large scale perturbation of the airglow emission distribution.展开更多
Since grey system theory was established by prof. Deng, GM models and their improvements have all taken the first vector of the original sequence as the initialization, which resulted to deficiency in making use of th...Since grey system theory was established by prof. Deng, GM models and their improvements have all taken the first vector of the original sequence as the initialization, which resulted to deficiency in making use of the latest information. Based on the principle, which new information should be used fully, we think it is scientific to pay more attention to the new information or endow them a more weigh. So, this paper deals with the GM improvement by taking the n-th vector as the initialization, and gets great improvement in forecasting precision. Last, we validate the practicability and reliability of the models with examples.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
文摘文章以幂函数变换为研究对象,从背景值误差和还原误差的角度分析了幂函数变换对GM(1,1)模型建模精度的影响,论证了幂函数变换的GM(1,1)模型(PFNGM(1,1)模型)具有逼近无偏性,能在可忽略的误差范围内实现对白指数序列的预测无偏性。实例应用结果表明,其建模精度和预测效果均优于无偏GM(1,1)模型和离散GM(1,1)模型。为将适宜建模序列拓展至近似非齐次指数序列和季节波动序列,同时保留幂函数变换可以有效降低背景值误差对建模精度影响的优势,将幂函数变换与平移变换相结合构建了PFNGM(1,1)模型,将幂函数变换与季节性GM(1,1)模型(SGM(1,1)模型)相结合构建了PFSGM(1,1)模型。实例应用结果表明,PFNGM(1,1)模型的建模精度和预测效果均优于背景值改进的NGM(1,1, k )模型和ONGM(1,1, k,c )模型,PFSGM(1,1)模型的建模精度和预测效果均优于SGM(1,1)模型,验证了两种模型的有效性。
基金supported by the National Natural Science Foundation of China(70971103)the Specialized Research Fund for the Doctora Program of Higher Education(20120143110001)
文摘Firstly, the research progress of grey model GM （1,1） is summarized, which is divided into three development stages： assimilation, alienation and melting stages. Then, the matrix analysis theory is used to study the modeling mechanism of GM （1,1）, which decomposes the modeling data matrix into raw data transformation matrix, accumulated generating operation matrix and background value selection matrix. The changes of these three matrices are the essential reasons affecting the modeling and the accuracy of GM （1,1）. Finally, the paper proposes a generalization grey model GGM （1,1）, which is a extended form of GM （1,1） and also a unified form of model GM （1,1）, model GM （1,1,α）, stage grey model, hopping grey model, generalized accumulated model, strengthening operator model, weakening operator model and unequal interval model. And the theory and practical significance of the extended model is analyzed.
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.
文摘As a kind of mathematical model, grey systems predi ct ion model has been widely applied to economy, management and engineering technol ogy. In 1982, Professor Deng Ju-long presented GM prediction model. Then some o ther scholars made improvements on GM model. Of course, much still should be don e to develop it. What the scholars have done is to take the first component of X (1) as the starting conditions of the grey differential model. It occ urs that the new information can not be used enough. This paper is addressed to choose the nth component of X (1) as the starting conditions to improv e the models. The main results of the paper is given in Theorem 2: The time response function of the grey differential equation x (0)(k)+az (1)(k)=b is given by x (1)(k)=x (1)(n)-ba e -a(k-n )+ba. and Theorem4: The time response of the grey Verhulst model is given by (1)(k) =ax (1)(n)bx (1)(n)+(a-bx (1)(n))ae a(k-n). As the new information is fully used, the accuracy of prediction is improved gre atly. Therefore, the new model with a certain theoretical and practical value.
基金supported by the Research Start Funds for Introducing High-level Talents of North China University of Water Resources and Electric Power
文摘This paper expresses the efficient outputs of decisionmaking unit（DMU） as the sum of ＂average outputs＂ forecasted by a GM（1,N） model and ＂increased outputs＂ which reflect the difficulty to realize efficient outputs.The increased outputs are solved by linear programming using data envelopment analysis efficiency theories,wherein a new sample is introduced whose inputs are equal to the budget in the issue No.n ＋ 1 and outputs are forecasted by the GM（1,N） model.The shortcoming in the existing methods that the forecasted efficient outputs may be less than the possible actual outputs according to developing trends of input-output rate in the periods of pre-n is overcome.The new prediction method provides decision-makers with more decisionmaking information,and the initial conditions are easy to be given.
文摘Over the past century,the safety of dams has gradually attracted attention from all parties.Research on the dynamic response and damage evolution of dams under extreme loads is the basis of dam safety issues.In recent decades,scholars have studied the responses of dams under earthquake loads,but there is still much room for improvement in experimental and theoretical research on small probability loads such as explosions.In this paper,a 50-m-high concrete gravity dam is used as a prototype dam,and a water explosion model test of a 2.5-m-high concrete gravity dam is designed.The water pressure and the acceleration response of the dam body in the test are analysed.The pressure characteristics and dynamic response of the dam body are assessed.Taking the dam damage test as an example,a numerical model of concrete gravity dam damage is established,and the damage evolution of the dam body is analysed.By combining experiments and numerical simulations,the damage characteristics of the dam body under the action of different charge water explosions are clarified.The integrity of the dam body is well maintained under the action of a small-quantity water explosion,and the dynamic response of the dam body is mainly caused by the shock wave.Both the shock wave and the bubble pulsation cause the dam body to accelerate,and the peak acceleration of the dam body under the action of the bubble pulsation is only one percent of the peak acceleration of the dam body under the action of the shock wave.When subjected to explosions in large quantities of water,the dam body is seriously damaged.Under the action of a shock wave,the dam body produces a secondary acceleration response,which is generated by an internal interaction after the dam body is damaged.The damage evolution process of the dam body under the action of a large-scale water explosion is analysed,and it is found that the shock wave pressure of the water explosion causes local damage to the dam body facing the explosion.After the peak value of the shock wave,the impulse continues to act on the dam body,causing cumulative damage and damage inside the dam body.
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 Science Foundation of China (40225011, 40336054)National Research Project (G2000078407)project of CAS (KZCX3-SW-217)International Collaboration Research Team Program of the Chinese Academy of SciencesChina-Russia Joint Research Center on Space Weather,Chinese Academy of Sciences
文摘In this paper, we develope a timodependent, nonlinear, photochemical-dynamical 2-D model which is composed of 3 models: dynamical gravity wave model, middle atmospheric photochemical model, and airglow layer photochemical model. We use the model to study the effect of the gravity wave propagation on the airglow layer. The comparison between the effects of the different wavelength gravity wave on the airglow emission distributions is made. When the vertical wavelength of the gravity wave is close to or is shorter than the thickness of the airglow layer, the gravity wave can make complex structure of the airglow layer, such as the double and multi-peak structures of the airglow layer. However, the gravity wave that has long vertical wavelength can make large scale perturbation of the airglow emission distribution.
基金This project was supported by Specially-Employed Professor Foundation of NUAA( 1009-260812)Ph. D Foundation of Na-tional Department of Education(20020287001)+1 种基金Natural Science Foundation of Jiangsu Province(BK2003211) Ph. D Foundation of Nanjing Unive
文摘Since grey system theory was established by prof. Deng, GM models and their improvements have all taken the first vector of the original sequence as the initialization, which resulted to deficiency in making use of the latest information. Based on the principle, which new information should be used fully, we think it is scientific to pay more attention to the new information or endow them a more weigh. So, this paper deals with the GM improvement by taking the n-th vector as the initialization, and gets great improvement in forecasting precision. Last, we validate the practicability and reliability of the models with examples.
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.
