In this paper,a grey Kalman filter model is proposed for lithium battery charge state estimation.Firstly,this paper establishes a recursive relation equation between the front and back terms through the grey model(GM)...In this paper,a grey Kalman filter model is proposed for lithium battery charge state estimation.Firstly,this paper establishes a recursive relation equation between the front and back terms through the grey model(GM).Secondly,the state space expression is constructed based on the recursive relationship equation.Next,the Kalman filter algorithm is integrated to form a grey Kalman filter model.Finally,the charge state is estimated based on public lithium battery data.In this paper,the state of charge is estimated from three different aspects,including different driving cycles,randomly mixed driving cycles,and the estimation of the state of charge by different temperatures under the same driving cycle conditions.On this basis,the model is applied to a life scenario using the charge state of 20 electric vehicles.The results show that the proposed model has good accuracy.展开更多
To create a new prediction model, the unbiased GM （1,1） model is optimized by the five-point slide method in this paper. Then, based on the occurrence areas of dce blast in Enshi District during 1995 -2004, the new ...To create a new prediction model, the unbiased GM （1,1） model is optimized by the five-point slide method in this paper. Then, based on the occurrence areas of dce blast in Enshi District during 1995 -2004, the new model and unbiased GM （1, 1 ） model are applied to predict the occurrence areas of rice blast during 2005 -2010. Predicting outcomes show that the prediction accuracy of five-point unbiased sliding optimized GM （1, 1 ） model is higher than the unbiased GM （1,1） model. Finally, combined with the prediction results, the author provides some suggestion for Enshi District in the prevention and control of rice blast in 2010.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
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
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
In order to describe the characteristics of some systems, such as the process of economic and product forecasting, a lot of discrete data may be used. Although they are discrete, the inside law can be founded by some ...In order to describe the characteristics of some systems, such as the process of economic and product forecasting, a lot of discrete data may be used. Although they are discrete, the inside law can be founded by some methods. For a series that the discrete degree is large and the integrated tendency is ascending, a new method for grey forecasting model group is given by the grey system theory. The method is that it firstly transforms original data, chooses some clique values and divides original data into groups by different clique values; then, it establishes non-equigap GM(1,1) model for different groups and searches forecasting area of original data by the solution of model. At the end of the paper, the result of reliability of forecasting value is obtained. It is shown that the method is feasible.展开更多
The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the origin...The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the original data,the fractional-order accumulation calculus could be used to do preprocessing. In this paper, the residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM(1,1) and improve the accuracy of predictor. The state space model of optimally modified GM(1,1)predictor is given and genetic algorithm(GA) is used to find the smallest relative error during the modeling step. Furthermore,the fractional form of continuous GM(1,1) is given to enlarge the content of prediction model. The simulation results illustrated that the fractional-order calculus could be used to depict the GM precisely with more degrees of freedom. Meanwhile, the ranges of the parameters and model application could be enlarged with better performance. The method of modified GM predictor using optimal fractional-order accumulation calculus is expected to be widely used in data processing, model theory, prediction control and related fields.展开更多
Based on PSR framework method, the land ecological security evaluation index system of 16 cities of Anhui Province was constructed. The land ecological security value of subsystem in Anhui Province from 2000 to 2011 w...Based on PSR framework method, the land ecological security evaluation index system of 16 cities of Anhui Province was constructed. The land ecological security value of subsystem in Anhui Province from 2000 to 2011 was calculated using the index weight which was determined by the entropy weight method, and land ecological security trend from 2012 to 2017 was forecasted using GM （1,1） model. The results indicated that, the land ecological security index in Anhui Province from 2000 to 2017 was rising on the whole, with the average value increasing from 0.442 in 2000 to 0.450 in 2017, and there was a huge difference among cities; at the same time, the state index and response index of each subsystem of land ecological security also rose. GM （ 1, 1 ） model had high simulation precision and was able to predict the land ecological security level and the de- velopment trend of each subsystem of Anhui Province from 2012 to 2017. The main factors that influenced the land ecological security of Anhui Prov- ince included per capita farmland area, population density, natural growth rate of population, urbanization level, soil coordination degree, agricultur- al mechanization degree, and the area proportion of nature reserve, which are the focus of land ecological security regulation in the future.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
The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-pr...The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.展开更多
In order to forecast the cotton output of China in the year 2011, Gray Metabolic Forecast Model is established based on both the Gray Forecast Model and the Metabolic Theory. According to the actual situation, forecas...In order to forecast the cotton output of China in the year 2011, Gray Metabolic Forecast Model is established based on both the Gray Forecast Model and the Metabolic Theory. According to the actual situation, forecast results of conventional GM (1, 1) Model and Metabolism GM (1, 1) Model are analyzed, showing that Metabolic Forecast Model has higher precision than the conventional forecast model. Therefore, Metabolism GM (1, 1) Model is used to forecast the cotton output of China in the year 2011, which is 614 968.3 thousand tons.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
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
The mixed model of improved exponential and power function and unequal interval gray GM(1,1)model have poor accuracy in predicting the maximum pull-out load of anchor bolts.An optimal combination model was derived usi...The mixed model of improved exponential and power function and unequal interval gray GM(1,1)model have poor accuracy in predicting the maximum pull-out load of anchor bolts.An optimal combination model was derived using the optimally weighted combination theory and the minimum sum of logarithmic squared errors as the objective function.Two typical anchor bolt pull-out engineering cases were selected to compare the performance of the proposed model with those of existing ones.Results showed that the optimal combination model was suitable not only for the slow P-s curve but also for the steep P-s curve.Its accuracy and stable reliability,as well as its prediction capability classification,were better than those of the other prediction models.Therefore,the optimal combination model is an effective processing method for predicting the maximum pull-out load of anchor bolts according to measured data.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
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
[Objective] Taken the Linjiang tourism as an example, tourism forecast system was established, difficulties related to the work of tourist area were solved. [Method] Dynamic predicted response model of Lijiang tourism...[Objective] Taken the Linjiang tourism as an example, tourism forecast system was established, difficulties related to the work of tourist area were solved. [Method] Dynamic predicted response model of Lijiang tourism market was established, through the gray correlation model GM (1, 1) and time-series method, using a computer simulation program for the actual model of operation, Lijiang tourism prospects were predicted and predicting results were evaluated. [Result] Total revenue of model gray parameter of Lijiang tourism a= 0.572 3 from 2009 to 2011, internal control parameters u=0.393 7, x(t+1) =-0.563 3exp(-0.572 3t)+0.688 0; total reception numbers of model gray parameter of Lijiang tourism a = 0.125 6, internal control parameters u = 344. 326 0, x(t+1)=3 102.483 5 exp(0.125 6 t)-2 741.283 5. Test results of two models showed that fitting degrees were good, and at the same time predicted that total revenue of Lijiang tourism reached 13 000 000 000, and total reception numbers reached 8 800 000. [Conclusion] This predicted system can carry out precision forecast for other tourist areas when cannot get all the information.展开更多
To establish a financial early-warning model with high accuracy of discrimination and achieve the aim of long-term prediction,principal component analysis(PCA),Fisher discriminant,together with grey forecasting models...To establish a financial early-warning model with high accuracy of discrimination and achieve the aim of long-term prediction,principal component analysis(PCA),Fisher discriminant,together with grey forecasting models are used at the same time.110 A-share companies listed on the Shanghai and Shenzhen stock exchange are selected as research samples.And 10 extractive factors with 89.746%of all the original information are determined by applying PCA,which obtains the goal of dimension reduction without information loss.Based on the index system,the early-warning model is constructed according to the Fisher rules.And then the GM(1,1)is adopted to predict financial ratios in 2004,according to 40 testing samples from 2000 to 2003.Finally,two different methods,a self-validated and a forecasting-validated,are used to test the validity of the financial crisis warning model.The empirical results show that the model has better predictability and feasibility,and GM(1,1)contributes to the ability to make long-term predictions.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
基金supported by the National Natural Science Foundation of China(92367301,72171116)the Fundamental Research Funds for the Central Universities(NK2023001,NP2024203)the“333 talent”project in Jiangsu Province.
文摘In this paper,a grey Kalman filter model is proposed for lithium battery charge state estimation.Firstly,this paper establishes a recursive relation equation between the front and back terms through the grey model(GM).Secondly,the state space expression is constructed based on the recursive relationship equation.Next,the Kalman filter algorithm is integrated to form a grey Kalman filter model.Finally,the charge state is estimated based on public lithium battery data.In this paper,the state of charge is estimated from three different aspects,including different driving cycles,randomly mixed driving cycles,and the estimation of the state of charge by different temperatures under the same driving cycle conditions.On this basis,the model is applied to a life scenario using the charge state of 20 electric vehicles.The results show that the proposed model has good accuracy.
基金Supported by Science Research Project of Department of Education of Hubei Province (B20092901)~~
文摘To create a new prediction model, the unbiased GM （1,1） model is optimized by the five-point slide method in this paper. Then, based on the occurrence areas of dce blast in Enshi District during 1995 -2004, the new model and unbiased GM （1, 1 ） model are applied to predict the occurrence areas of rice blast during 2005 -2010. Predicting outcomes show that the prediction accuracy of five-point unbiased sliding optimized GM （1, 1 ） model is higher than the unbiased GM （1,1） model. Finally, combined with the prediction results, the author provides some suggestion for Enshi District in the prevention and control of rice blast in 2010.
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.
文摘In order to describe the characteristics of some systems, such as the process of economic and product forecasting, a lot of discrete data may be used. Although they are discrete, the inside law can be founded by some methods. For a series that the discrete degree is large and the integrated tendency is ascending, a new method for grey forecasting model group is given by the grey system theory. The method is that it firstly transforms original data, chooses some clique values and divides original data into groups by different clique values; then, it establishes non-equigap GM(1,1) model for different groups and searches forecasting area of original data by the solution of model. At the end of the paper, the result of reliability of forecasting value is obtained. It is shown that the method is feasible.
基金supported by the National Natural Science Foundation of China(61174145)
文摘The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the original data,the fractional-order accumulation calculus could be used to do preprocessing. In this paper, the residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM(1,1) and improve the accuracy of predictor. The state space model of optimally modified GM(1,1)predictor is given and genetic algorithm(GA) is used to find the smallest relative error during the modeling step. Furthermore,the fractional form of continuous GM(1,1) is given to enlarge the content of prediction model. The simulation results illustrated that the fractional-order calculus could be used to depict the GM precisely with more degrees of freedom. Meanwhile, the ranges of the parameters and model application could be enlarged with better performance. The method of modified GM predictor using optimal fractional-order accumulation calculus is expected to be widely used in data processing, model theory, prediction control and related fields.
文摘Based on PSR framework method, the land ecological security evaluation index system of 16 cities of Anhui Province was constructed. The land ecological security value of subsystem in Anhui Province from 2000 to 2011 was calculated using the index weight which was determined by the entropy weight method, and land ecological security trend from 2012 to 2017 was forecasted using GM （1,1） model. The results indicated that, the land ecological security index in Anhui Province from 2000 to 2017 was rising on the whole, with the average value increasing from 0.442 in 2000 to 0.450 in 2017, and there was a huge difference among cities; at the same time, the state index and response index of each subsystem of land ecological security also rose. GM （ 1, 1 ） model had high simulation precision and was able to predict the land ecological security level and the de- velopment trend of each subsystem of Anhui Province from 2012 to 2017. The main factors that influenced the land ecological security of Anhui Prov- ince included per capita farmland area, population density, natural growth rate of population, urbanization level, soil coordination degree, agricultur- al mechanization degree, and the area proportion of nature reserve, which are the focus of land ecological security regulation in the future.
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 Natural Science Foundation of China(No.41874001 and No.41664001)Support Program for Outstanding Youth Talents in Jiangxi Province(No.20162BCB23050)National Key Research and Development Program(No.2016YFB0501405)。
文摘The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.
文摘In order to forecast the cotton output of China in the year 2011, Gray Metabolic Forecast Model is established based on both the Gray Forecast Model and the Metabolic Theory. According to the actual situation, forecast results of conventional GM (1, 1) Model and Metabolism GM (1, 1) Model are analyzed, showing that Metabolic Forecast Model has higher precision than the conventional forecast model. Therefore, Metabolism GM (1, 1) Model is used to forecast the cotton output of China in the year 2011, which is 614 968.3 thousand tons.
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The National Natural Science Foundation of China(No.51778485).
文摘The mixed model of improved exponential and power function and unequal interval gray GM(1,1)model have poor accuracy in predicting the maximum pull-out load of anchor bolts.An optimal combination model was derived using the optimally weighted combination theory and the minimum sum of logarithmic squared errors as the objective function.Two typical anchor bolt pull-out engineering cases were selected to compare the performance of the proposed model with those of existing ones.Results showed that the optimal combination model was suitable not only for the slow P-s curve but also for the steep P-s curve.Its accuracy and stable reliability,as well as its prediction capability classification,were better than those of the other prediction models.Therefore,the optimal combination model is an effective processing method for predicting the maximum pull-out load of anchor bolts according to measured data.
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.
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.
基金Supported by National Social Science Foundation of China(08BMZ042)~~
文摘[Objective] Taken the Linjiang tourism as an example, tourism forecast system was established, difficulties related to the work of tourist area were solved. [Method] Dynamic predicted response model of Lijiang tourism market was established, through the gray correlation model GM (1, 1) and time-series method, using a computer simulation program for the actual model of operation, Lijiang tourism prospects were predicted and predicting results were evaluated. [Result] Total revenue of model gray parameter of Lijiang tourism a= 0.572 3 from 2009 to 2011, internal control parameters u=0.393 7, x(t+1) =-0.563 3exp(-0.572 3t)+0.688 0; total reception numbers of model gray parameter of Lijiang tourism a = 0.125 6, internal control parameters u = 344. 326 0, x(t+1)=3 102.483 5 exp(0.125 6 t)-2 741.283 5. Test results of two models showed that fitting degrees were good, and at the same time predicted that total revenue of Lijiang tourism reached 13 000 000 000, and total reception numbers reached 8 800 000. [Conclusion] This predicted system can carry out precision forecast for other tourist areas when cannot get all the information.
文摘To establish a financial early-warning model with high accuracy of discrimination and achieve the aim of long-term prediction,principal component analysis(PCA),Fisher discriminant,together with grey forecasting models are used at the same time.110 A-share companies listed on the Shanghai and Shenzhen stock exchange are selected as research samples.And 10 extractive factors with 89.746%of all the original information are determined by applying PCA,which obtains the goal of dimension reduction without information loss.Based on the index system,the early-warning model is constructed according to the Fisher rules.And then the GM(1,1)is adopted to predict financial ratios in 2004,according to 40 testing samples from 2000 to 2003.Finally,two different methods,a self-validated and a forecasting-validated,are used to test the validity of the financial crisis warning model.The empirical results show that the model has better predictability and feasibility,and GM(1,1)contributes to the ability to make long-term predictions.
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.
