On novel grey forecasting model based on non-homogeneous index sequence

Xie, Naiming; Liu, Sifeng; Yang, Yingjie; Yuan, Chaoqing

doi:10.1016/j.apm.2012.10.037

Cited by 141 publications

(63 citation statements)

References 11 publications

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“…However, the discrete gray model, like the classical GM(1, 1), can only solve the problem of exponential growth order, and sequences with exponential growth are very rare in real life; comparatively speaking, more original sequence data conform to nonexponential growth laws. The discrete gray model of the approximate nonhomogenous exponential sequence extends the application range of the discrete model to approximate nonhomogenous exponential sequences [34], which enhances the applicability of the discrete gray model.…”

Section: Introductionmentioning

confidence: 99%

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Forecasting the Short-Term Traffic Flow in the Intelligent Transportation System Based on an Inertia Nonhomogenous Discrete Gray Model

2017

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The traffic-flow system has basic dynamic characteristics. This feature provides a theoretical basis for constructing a reasonable and effective model for the traffic-flow system. The research on short-term traffic-flow forecasting is of wide interest. Its results can be applied directly to advanced traffic information systems and traffic management, providing real-time and effective traffic information. According to the dynamic characteristics of traffic-flow data, this paper extends the mechanical properties, such as distance, acceleration, force combination, and decomposition, to the traffic-flow data vector. According to the mechanical properties of the data, this paper proposes four new models of structural parameters and component parameters, inertia nonhomogenous discrete gray models (referred to as INDGM), and analyzes the important properties of the model. This model examines the construction of the inertia nonhomogenous discrete gray model from the mechanical properties of the data, explaining the classic NDGM modeling mechanism in the meantime. Finally, this paper analyzes the traffic-flow data of Whitemud Drive in Canada and studies the relationship between the inertia model and the traffic-flow state according to the data analysis of the traffic-flow state. A simulation accuracy and prediction accuracy of up to 0.0248 and 0.0273, respectively, are obtained.

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Section: Introductionmentioning

confidence: 99%

“…define the first-order gray system-prediction model including a variable, referred to as the NDGM(1, 1) [34]. Then the recurrence function is defined as follows:…”

Section: Nonhomogenous Discrete Gray Model (Ndgm)mentioning

confidence: 99%

Forecasting the Short-Term Traffic Flow in the Intelligent Transportation System Based on an Inertia Nonhomogenous Discrete Gray Model

2017

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“…However, the real world is full of complexity and uncertainty, and a sequence with approximately exponential growth is only a special case. More systematic behaviour sequences exhibit the characteristic of approximately inhomogeneous exponential growth [25,26]. In this case, if the GM(1,1) model is used to simulate or forecast the approximate inhomogeneous exponential growth sequence, the inherent modelling mechanism and model structure will lead to unsatisfactory simulation and prediction accuracy.…”

Section: Introductionmentioning

confidence: 99%

Forecasting the Energy Consumption of China’s Manufacturing Using a Homologous Grey Prediction Model

2017

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Abstract:With the rapid development of China's manufacturing, energy consumption has increased rapidly, and this has become a major bottleneck affecting the sustainable development of China's economy. This paper deduces and constructs a homologous grey prediction model with one variable and one first order equation (HGEM(1,1)) for forecasting the total energy consumption of China's manufacturing based on the Grey system theory. Both parameter estimation (PE) and the deduction of the final restored expression (FRE) of the HGEM(1,1) model are all from the time response expression of the whitenization differential equation, which solves the 'non-homologous' defects of PE and FRE with traditional grey prediction models. HGEM(1,1) has good performance and can unbiasedly simulate a homogeneous/non-homogeneous exponential function sequence and a linear function sequence. Then, the HGEM(1,1)model is used to simulate and forecast the total energy consumption of China's energy manufacturing, and the results show that the comprehensive performance of this model is much better than that of the classic Grey Model with one variable and single order equation, GM(1,1) for short and the frequently-used Discrete Grey Model with one variable and single order equation, DGM(1,1) for short. Finally, we forecast the total energy consumption of China's manufacturing industry during the years 2018-2024. The results show that the total energy consumption in China's manufacturing is slowing down but is still too large. For this, some measures, such as optimizing the manufacturing structure and speeding up the development and promotion of energy saving and emission reduction technologies, to ensure the effective supply of energy in China's manufacturing industry are suggested.

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“…NDGM model increased the applicability of discrete grey model. According to improve simulation and prediction accuracies, there were some the results [22,23] of 2 Mathematical Problems in Engineering nonhomogeneous discrete grey model. However, these models had a higher requirement for data; when the data did not meet the requirements, the errors of both model-fitting and prediction were larger.…”

Section: Introductionmentioning

confidence: 99%

Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

Duan

Shao

Xiao

et al. 2017

Mathematical Problems in Engineering

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The grey forecasting model has been successfully applied in numerous fields since it was proposed. The nonhomogeneous discrete grey model (NDGM) was approximately constructed based on the nonhomogeneous index trend; it increased the applicability of discrete grey model. However, the NDGM required accurate data and better effect when the original data did not meet the conditions and fitting and prediction errors were larger. For this, the NDGM with the fractional order accumulating operator (abbreviated as NDGM 푝/푞 ) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGM 푝/푞 and the NDGM 푝/푞 can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGM 푝/푞 was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGM 푝/푞 and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGM 푝/푞 was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.

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On novel grey forecasting model based on non-homogeneous index sequence

Cited by 141 publications

References 11 publications

Forecasting the Short-Term Traffic Flow in the Intelligent Transportation System Based on an Inertia Nonhomogenous Discrete Gray Model

Forecasting the Short-Term Traffic Flow in the Intelligent Transportation System Based on an Inertia Nonhomogenous Discrete Gray Model

Forecasting the Energy Consumption of China’s Manufacturing Using a Homologous Grey Prediction Model

Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

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