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Article
Publication date: 17 August 2012

Li Junliang, Liao Ruiquan and Chen Xiaochun

In practical engineering, there are various sequences. The purpose of this paper is to improve and put forward a new model.

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Abstract

Purpose

In practical engineering, there are various sequences. The purpose of this paper is to improve and put forward a new model.

Design/methodology/approach

Based on the generalized accumulated generating operation, the paper improved the GM(1,1) cosine model and proposed the GAGM(1,1) cosine model.

Findings

It is found that the GAGM(1,1) cosine model can satisfy many kinds of periodic sequences and the precision of GAGM(1,1) cosine model is higher than the GM(1,1) model.

Originality/value

The paper shows that the GAGM(1,1) cosine model has important theoretic and practical significance.

Article
Publication date: 6 November 2017

Xinhai Kong, Peng Zhang and Xin Ma

The purpose of this paper is to improve the GM(1, 1) model based on concave sequences.

Abstract

Purpose

The purpose of this paper is to improve the GM(1, 1) model based on concave sequences.

Design/methodology/approach

First, the restored sequence of the GM(1, 1) model is proved to be convex, and the residual characters of the GM(1, 1) model for concave sequences are analyzed. Second, two symmetry transformations are introduced to transform an original concave sequence into a convex sequence, and then the GM(1, 1) model is established based on the convex sequence.

Findings

Compared with the traditional modeling method, the new method has high accuracy and is applicable for all concave sequence modeling.

Practical implications

Two cases are used to illustrate the superiority of this modeling method. Case A is to predict China’s per capita natural gas consumption, and case B is to predict the annual output of an oilfield.

Originality/value

The application scope of GM (1, 1) model is greatly extended.

Details

Grey Systems: Theory and Application, vol. 7 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 7 November 2016

Yuanjie Zhi, Dongmei Fu and Hanling Wang

The purpose of this paper is to present a new model which combines the non-equidistant GM(1,1) model with GCHM_WBO (generalized contra-harmonic mean (GCHM); weakening buffer…

Abstract

Purpose

The purpose of this paper is to present a new model which combines the non-equidistant GM(1,1) model with GCHM_WBO (generalized contra-harmonic mean (GCHM); weakening buffer operator (WBO)). The authors use the model to solve the deadlock that for a large number of non-equidistant corrosion rate, it is difficult to establish a reasonable prediction model and improve the prediction accuracy.

Design/methodology/approach

This research consists of three parts: non-equidistant GM(1,1) model, GCHM_WBO operator, and the optimization of morphing parameter (contained in GCHM, control the intensity of the weakening operator). The methodology is explained as follows. First, the authors built a non-equidistant GM(1,1) model with GCHM_WBO weakened data, of which morphing parameter was randomly selected. Next, the authors calculated the error between prediction data of model and the real data, and adjusted the morphing parameter according to the error and property of GCHM. Then, the authors generated a new non-equidistant GM(1,1) based on new morphing parameter, and repeated the previous step until the termination condition was satisfied. Finally, the model with appropriate morphing parameter was used to implement the prediction of new data.

Findings

This paper finds a property of GCHM, which is a monotonic increasing function of morphing parameter in some specific conditions. Based on the property and the fixed point axiom of WBO, an algorithm was designed to search an appropriate morphing parameter. The appropriate morphing parameter was implemented for the purpose of improving the accuracy of the model. The model was applied to predict the corrosion rate of six steels at Guangzhou experimental station. The results showed that the proposed method can get more accuracy in prediction capability compared to the models with the original data and AWBO weakened data. The method is applicable to long-term forecasts in case of data scarcity.

Practical implications

Corrosion will cause huge economic loss to a country; therefore, it is important to judge the remaining useful life of a material or equipment; the foundation for judgement of which is the prediction of material corrosion rate. However, the prediction of corrosion rate is very difficult because of corrosion data’s features, such as small sample size, non-equidistant, etc. The proposed method can be used to implement long-term forecast of corrosion data with only one sample and non-equidistant samples.

Originality/value

This paper presented a model which combines the non-equidistant GM(1,1) model with GCHM_WBO to handle the problem of long-term forecasting of corrosion data. In the modelling process, the proposed morphing parameter searched through algorithm can improve the prediction accuracy of the model. Therefore, the model can provide effective and reliable result when data are of a small sample size and non-equidistant.

Details

Grey Systems: Theory and Application, vol. 6 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 24 May 2022

Yufeng Lian, Wenhuan Feng, Pai Li, Qiang Lei, Haitao Ma, Hongliang Sun and Binglin Li

The purpose of this paper is to propose a fractional order optimization method based on perturbation bound and gamma function of a DGM(r,1).

Abstract

Purpose

The purpose of this paper is to propose a fractional order optimization method based on perturbation bound and gamma function of a DGM(r,1).

Design/methodology/approach

By analyzing and minimizing perturbation bound, the sub-optimal solution on fractional order interval is obtained through offline solving without iterative calculation. By this method, an optimized fractional order non-equidistant ROGM (OFONEROGM) is applied in fitting and prediction water quality parameters for a surface water pollution monitoring system.

Findings

This method can narrow fractional order interval in this work. In a surface water pollution monitoring system, the fitting and prediction performances of OFONEROGM are demonstrated comparing with integer order non-equidistant ROGM (IONEROGM).

Originality/value

A method of offline solving the sub-optimal solution on fractional order interval is proposed. It can narrow the optimized fractional order range of NEROGM without iterative calculation. A large number of calculations are eliminated. Besides that, optimized fractional order interval is only related to the number of original data, and convenient for practical application. In this work, an OFONEROGM is modeled for predicting water quality trend for preventing water pollution or stealing sewage discharge. It will provide guiding significance in water quality parameter fitting and predicting for water environment management.

Details

Grey Systems: Theory and Application, vol. 13 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 12 June 2017

Dalian Yang, Yilun Liu, Songbai Li, Jie Tao, Chi Liu and Jiuhuo Yi

The aim of this paper is to solve the problem of low accuracy of traditional fatigue crack growth (FCG) prediction methods.

Abstract

Purpose

The aim of this paper is to solve the problem of low accuracy of traditional fatigue crack growth (FCG) prediction methods.

Design/methodology/approach

The GMSVR model was proposed by combining the grey modeling (GM) and the support vector regression (SVR). Meanwhile, the GMSVR model parameter optimal selection method based on the artificial bee colony (ABC) algorithm was presented. The FCG prediction of 7075 aluminum alloy under different conditions were taken as the study objects, and the performance of the genetic algorithm, the particle swarm optimization algorithm, the n-fold cross validation and the ABC algorithm were compared and analyzed.

Findings

The results show that the speed of the ABC algorithm is the fastest and the accuracy of the ABC algorithm is the highest too. The prediction performances of the GM (1, 1) model, the SVR model and the GMSVR model were compared, the results show that the GMSVR model has the best prediction ability, it can improve the FCG prediction accuracy of 7075 aluminum alloy greatly.

Originality/value

A new prediction model is proposed for FCG combined the non-equidistant grey model and the SVR model. Aiming at the problem of the model parameters are difficult to select, the GMSVR model parameter optimization method based on the ABC algorithm was presented. the results show that the GMSVR model has better prediction ability, which increase the FCG prediction accuracy of 7075 aluminum alloy greatly.

Details

Engineering Computations, vol. 34 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 28 January 2011

Xinping Xiao and Kunkun Peng

The purpose of this paper is to establish a new model for non‐equidistance sequence and research affine properties of the new model.

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Abstract

Purpose

The purpose of this paper is to establish a new model for non‐equidistance sequence and research affine properties of the new model.

Design/methodology/approach

Generalized non‐equidistance GM(1,1) model is put forward based on generalized accumulated generating operation (AGO) theory, and particle swarm optimization is used to solve the parameters of the new model, then affine properties of the new model are researched based on matrix analysis.

Findings

The results are convincing: the simulation and prediction precisions of generalized non‐equidistance GM(1,1) model are raised greatly, and it is proved that the affine transformation sequence has the same simulative accuracy with the raw sequence for generalized non‐equidistance GM(1,1) model.

Practical implications

The method exposed in the paper can be used to model and predict for non‐equidistance sequence in the practical problem.

Originality/value

The paper succeeds in establishing a new non‐equidistance grey model and obtaining the affine properties of generalized non‐equidistance GM(1,1) model.

Details

Grey Systems: Theory and Application, vol. 1 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

Open Access
Article
Publication date: 14 August 2018

Xuemei Li, Ya Zhang and Kedong Yin

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can…

Abstract

Purpose

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues.

Design/methodology/approach

Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA).

Findings

To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability.

Originality/value

DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.

Details

Marine Economics and Management, vol. 1 no. 1
Type: Research Article
ISSN: 2516-158X

Keywords

Article
Publication date: 3 August 2015

Sifeng Liu, Bo Zeng, Jiefang Liu, Naiming Xie and Yingjie Yang

– The purpose of this paper is to provide a foundational reference and practical guidance for modelling small and poor data with incomplete information.

Abstract

Purpose

The purpose of this paper is to provide a foundational reference and practical guidance for modelling small and poor data with incomplete information.

Design/methodology/approach

The definitions of four basic models of GM(1, 1), such as Even Grey Model (EGM), Original Difference Grey Model (ODGM), Even Difference Grey Model (EDGM) and Discrete Grey Model (DGM), are put forward. The properties and characteristics of different models are studied and their equivalence are proved. The suitable sequences of different models are studied by simulation and analysis with homogeneous exponential sequences, nonhomogeneous exponential increasing sequences and vibration sequences.

Findings

The main conclusions have been obtained as follows: first, the three discrete models of ODGM, EDGM and DGM are suitable for homogeneous exponential sequences or sequences which close to a homogeneous exponential sequence; and second the EGM are suitable for nonhomogeneous exponential increasing sequences and vibration sequences.

Practical implications

The outcome obtained in this paper can be consulted for model selection in the course of practical modelling.

Originality/value

This paper systematically defined the four basic forms of model GM(1, 1) and studied their properties and characteristics, especially their suitable sequences. Although significant progress has been made in this field, such a systematic study on these models and their suitable sequences is still missing as far as we know. It can provide reference and basis for people to choose the correct model in the actual modelling process.

Details

Grey Systems: Theory and Application, vol. 5 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 3 April 2018

Lingling Pei, Qin Li and Zhengxin Wang

The purpose of this paper is to propose a new method based on nonlinear least squares (NLS) for solving the parameters of nonlinear grey Bernoulli model (NGBM(1,1)) and to verify…

Abstract

Purpose

The purpose of this paper is to propose a new method based on nonlinear least squares (NLS) for solving the parameters of nonlinear grey Bernoulli model (NGBM(1,1)) and to verify the proposed model using the case of employee demand prediction of high-tech enterprises in China.

Design/methodology/approach

First of all, minimising the square sum of fitting error of grey differential equation of NGBM(1,1) is taken as the optimisation target and the parameters of classic grey model (GM(1,1)) are set as the initial value of parameter vector. Afterwards, the structural parameters and power exponents are solved by using the Gauss-Newton iteration algorithm so as to calculate the parameters of NGBM(1,1) under given rules for ceasing the algorithm. Finally, by taking the employee demand of high-tech enterprises in the state-level high-tech industrial development zone in China as examples, the validity of the new method is verified.

Findings

The results show that the parameter estimation algorithm based on the NLS method can effectively identify the power exponents of NGBM(1,1) and therefore can favourably adapt to the nonlinear fluctuations of sequences. In addition, the algorithm is superior to the GM(1,1) model, grey Verhulst model, and Quadratic-Exponential smoothing algorithm in terms of the simulation and prediction accuracy.

Research limitations/implications

Under the framework of solving parameters based on NLS, various aspects of NGBM(1,1) remain to be further investigated including background value, initial condition and variable structural modelling methods.

Practical implications

The parameter estimation algorithm based on NLS can effectively identify the power exponent of NGBM(1,1) and therefore it can favourably adapt to the nonlinear fluctuation of sequences.

Originality/value

According to the basic principle of NLS, a new method for solving the parameters of NGBM(1,1) is proposed by using the Gauss-Newton iteration algorithm. Moreover, by conducting the modelling case about employees demand in high-tech enterprises in China, the effectiveness and superiority of the new method are verified.

Details

Grey Systems: Theory and Application, vol. 8 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 2 October 2018

Liang Zeng

High-tech industries play an important role in promoting economic and social development. The purpose of this paper is to accurately predict and analyze the output value of…

Abstract

Purpose

High-tech industries play an important role in promoting economic and social development. The purpose of this paper is to accurately predict and analyze the output value of high-tech products in Guangdong Province, China, by using a multivariable grey model.

Design/methodology/approach

Based on the principle of fractional order accumulation, this study proposes a multivariable grey prediction model. To further enhance the prediction ability and accuracy of the model, an optimized model is established by reconstructing the background value. The optimal parameters are solved by minimizing the average relative error of the system characteristic sequence with the constraint of parameter relationships.

Findings

The results from the study show that the two proposed models exhibit better simulation and prediction performance than the traditional models, while the optimized model can significantly improve the modelling precision. In addition, it is predicted that the output value of high-tech products is 12,269.443bn yuan in 2021, which will approximately double from 2016 to 2021.

Research limitations/implications

The two proposed models can be used to forecast the trend of the system and are grown as an effective extension and supplement of the traditional multivariable grey forecasting models.

Practical implications

The forecast and analysis of the development prospects of high-tech industries would be useful for the government departments of Guangdong Province and professional forecasters to grasp the future of high-tech industries and formulate decision planning.

Originality/value

A new multivariable grey prediction model based on fractional order accumulation and its optimized model obtained by reconstructing the background value, which can improve the modelling accuracy of the traditional model, is proposed in this paper.

Details

Kybernetes, vol. 48 no. 6
Type: Research Article
ISSN: 0368-492X

Keywords

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