A generalization of the GM(1,1) direct modeling method with a step by step optimizing grey derivative's whiten values and its applications

Wang, Yinao; Chen, Zhijie; Zhiqiang, Gao; Mian-yun, Chen

doi:10.1108/03684920410514391

Cited by 20 publications

(7 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In actual calculation, it can be omitted. In step 6, the actual initial condition x(1) is not directly chosen as the initial condition of the differential equation, but the method majorizing further the model coefficient is chosen, which is introduced by Yinao et al (2001). It is equivalent to the circumstance that the initial condition of the differential equation model is majorized further.…”

Section: Gm(11) Direct Modeling Methods With a Step By Step Majorizing Grey Derivative's Whitening Valuesmentioning

confidence: 99%

“…Note 3. When the initial data is equal time interval, the above modeling method is GM(1,1) direct modeling with a step by step majorizing grey derivative's whitening values put forward by Yinao et al (2001), so it is the generalization of the model mentioned in the work of Yinao et al (2001).…”

Section: Gm(11) Direct Modeling Methods With a Step By Step Majorizing Grey Derivative's Whitening Valuesmentioning

confidence: 99%

“…Grey system is a "poor" information system The GM(1,1) model is a kind of grey system model which has been applied extensively. For the equal time interval grey exponential sequence {xðt k Þ j t k [ R; k [ K}; Yinao et al (2001) introduced a method for building nonhomogeneous exponential modelx…”

Section: Introductionmentioning

confidence: 99%

“…To establish model (3), we whiten grey derivative first. For original data (1), Yinao et al (2001) takes the background value 0:5½xðkÞ þ xðk þ 1Þ; and establishes majorizing model (3), with a step by step majorizing derivative value corresponding to the background value, similarly, for original data (4), we can establish majorizing model (3). Theorem 1.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A generalization of the GM(1,1) direct modeling method with a step by step optimizing grey derivative's whiten values and its applications

Wang

Chen²,

Zhiqiang³

et al. 2004

Kybernetes

Self Cite

View full text Add to dashboard Cite

This paper generalises the GM(1,1) direct modeling method with a step by step majorizing grey derivative's whiten values to unequal time interval sequence modeling, and proves that the new method still has linear transformation consistency of the old method. The example indicates that the new method still has gradual approaching white exponential law coincidence property. With this new method, we then model the high precision soft foundation settlement.

show abstract

Section: Gm(11) Direct Modeling Methods With a Step By Step Majorizing Grey Derivative's Whitening Valuesmentioning

confidence: 99%

Section: Gm(11) Direct Modeling Methods With a Step By Step Majorizing Grey Derivative's Whitening Valuesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A generalization of the GM(1,1) direct modeling method with a step by step optimizing grey derivative's whiten values and its applications

Wang

Chen²,

Zhiqiang³

et al. 2004

Kybernetes

Self Cite

View full text Add to dashboard Cite

show abstract

“…Xiao and Li (2009) studied the ill-conditioned problem for the non-equigap GM (1,1) control model by using the method of multiple transformations. Yinao et al (2004) generalised the GM (1,1) direct modeling method with a step by step majorizing grey derivative's whiten values to unequal time interval sequence modeling and proves that the new method still has linear transformation consistency of the old method. Xie and Liu (2009a) proposed a novel NGM (1,1,k) prediction model discrete grey forecasting model termed DGM model and a series of optimized models of DGM.…”

Section: Introductionmentioning

confidence: 95%

Study on parameters characteristics of NGM (1,1,k) prediction model with multiplication transformation

Cui

Zeng

2012

Grey Systems: Theory and Application

View full text Add to dashboard Cite

Purpose -The purpose of this paper is to study the properties of the NGM (1,1,k) prediction model with multiplication transformation and reduce its modeling complexity. Design/methodology/approach -The authors improved this model by putting forward a formula to solve its parameters, building an algorithm for optimizing the NGM (1,1,k) model in terms of the least modeling error and designing a key technology for the implementation of this algorithm. The optimized NGM (1,1,k) model is built accordingly. The parameter characteristics of the two models under multiple transformations and its effect of the simulation value and forecasting value are analyzed by studying the properties of multiple transformation of the two models. Findings -The research finding shows that the modeling accuracies of the NGM (1,1,k) model and the optimized NGM (1,1,k) model are all in no relation to multiple transformations. Practical implications -The above results imply that the data level can be reduced; the process of building the NGM (1,1,k) model and the optimized NGM (1,1,k) model can be simplified; but the simulative and predictive accuracy of the two models remain unchanged. Originality/value -The paper succeeds in realising the properties of NGM (1,1,k) model and the optimized NGM (1,1,k) model by using the method of multiplication transformation, which is helpful for understanding the modeling mechanism and expanding the application range of the NGM (1,1,k) model.

show abstract

Research on Optimum Weighted Combination GM(1,1) Model with Different Initial Value

Qiu-mei

Jin

2015

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. In this paper, a new method of GM(1,1) model based on optimum weighted combination with different initial value is put forward. The new proposed model is comprised of weighted combination models with different initial value of raw data. Weighted coefficients of every model in the combination are derived from a method of minimizing error summation of square. The optimum weighted combination can express the principle of new information priority emphasized on in grey systems theory fully. The result of a numerical example indicates that optimum weighted combination GM (1,1) model presented in this paper can obtain a better prediction performance than that from the original GM(1,1) model.

show abstract

A generalization of the GM(1,1) direct modeling method with a step by step optimizing grey derivative's whiten values and its applications

Cited by 20 publications

References 1 publication

A generalization of the GM(1,1) direct modeling method with a step by step optimizing grey derivative's whiten values and its applications

A generalization of the GM(1,1) direct modeling method with a step by step optimizing grey derivative's whiten values and its applications

Study on parameters characteristics of NGM (1,1,k) prediction model with multiplication transformation

Research on Optimum Weighted Combination GM(1,1) Model with Different Initial Value

Contact Info

Product

Resources

About