A variable-order fractional discrete grey model and its application

2021 ◽  
pp. 1-14
Author(s):  
Huang Meixin ◽  
Liu Caixia
Keyword(s):  
Electricity Consumption ◽  
Grey Model ◽  
Liaoning Province ◽  
Model Parameters ◽  
Variable Order ◽  
Matrix Perturbation ◽  
Application Range ◽  
Whale Optimization ◽  
Grey Models ◽  
The Stability

Fractional order grey model is effective in describing the uncertainty of the system. In this paper, we propose a novel variable-order fractional discrete grey model (short for VOFDGM(1,1)) by combining the discrete grey model and variable-order fractional accumulation, which is a more general form of the DGM(1,1). The detailed modeling procedure of the presented model is first systematically studied, in particular, matrix perturbation theory is used to prove the validity in terms of the stability of the model, and then, the model parameters are optimized by the whale optimization algorithm. The accuracy of the proposed model is verified by comparing it with classical models on six data sequences with different forms. Finally, the model is applied to predict the electricity consumption of Beijing and Liaoning Province of China, and the results show that the model has a better prediction performance compared with the other four commonly-used grey models. To the best of our knowledge, this is the first time that the variable-order fractional accumulation is introduced into the discrete grey model, which greatly increases the prediction accuracy of the DGM(1,1) and extends the application range of grey models.

A novel fractional discrete grey model with an adaptive structure and its application in electricity consumption prediction

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yitong Liu ◽  
Yang Yang ◽  
Dingyu Xue ◽  
Feng Pan
Keyword(s):  
Fractional Order ◽  
Electricity Consumption ◽  
Grey Model ◽  
The Novel ◽  
Raw Data ◽  
Content Type ◽  
Power Load ◽  
Grey Models ◽  
Novel Model ◽  
Consumption Prediction

PurposeElectricity consumption prediction has been an important topic for its significant impact on electric policies. Due to various uncertain factors, the growth trends of electricity consumption in different cases are variable. However, the traditional grey model is based on a fixed structure which sometimes cannot match the trend of raw data. Consequently, the predictive accuracy is variable as cases change. To improve the model's adaptability and forecasting ability, a novel fractional discrete grey model with variable structure is proposed in this paper.Design/methodology/approachThe novel model can be regarded as a homogenous or non-homogenous exponent predicting model by changing the structure. And it selects the appropriate structure depending on the characteristics of raw data. The introduction of fractional accumulation enhances the predicting ability of the novel model. And the relative fractional order r is calculated by the numerical iterative algorithm which is simple but effective.FindingsTwo cases of power load and electricity consumption in Jiangsu and Fujian are applied to assess the predicting accuracy of the novel grey model. Four widely-used grey models, three classical statistical models and the multi-layer artificial neural network model are taken into comparison. The results demonstrate that the novel grey model performs well in all cases, and is superior to the comparative eight models.Originality/valueA fractional-order discrete grey model with an adaptable structure is proposed to solve the conflict between traditional grey models' fixed structures and variable development trends of raw data. In applications, the novel model has satisfied adaptability and predicting accuracy.

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

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Huiming Duan ◽  
Kailiang Shao ◽  
Xinping Xiao ◽  
Jinwei Yang
Keyword(s):  
Fractional Order ◽  
Estimation Method ◽  
Original Data ◽  
Grey Model ◽  
Prediction Errors ◽  
Matrix Perturbation ◽  
Perturbation Bound ◽  
Grey Forecasting ◽  
The Matrix ◽  
The Stability

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 NDGMp/q) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGMp/q and the NDGMp/q can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGMp/q was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGMp/q and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGMp/q was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.

Fuzzy grey forecasting model optimized by moth-flame optimization algorithm for short time electricity consumption

2021 ◽  
pp. 1-10
Author(s):  
Ceyda Tanyolaç Bilgiç ◽  
Boğaç Bilgiç ◽  
Ferhan Çebi
Keyword(s):  
Optimization Algorithm ◽  
Electricity Consumption ◽  
Grey Model ◽  
Forecasting Model ◽  
Model Parameters ◽  
Forecasting Accuracy ◽  
Forecasting Models ◽  
True Value ◽  
Proposed Model ◽  
Moth Flame Optimization Algorithm

It is significant that the forecasting models give the closest result to the true value. Forecasting models are widespread in the literature. The grey model gives successful results with limited data. The existing Triangular Fuzzy Grey Model (TFGM (1,1)) in the literature is very useful in that it gives the maximum, minimum and average value directly in the data. A novel combined forecasting model named, Moth Flame Optimization Algorithm optimization of Triangular Fuzzy Grey Model, MFO-TFGM (1,1), is presented in this study. The existing TFGM (1,1) model parameters are optimized by a new nature- inspired heuristic algorithm named Moth-Flame Optimization algorithm which is inspired by the moths flying path. Unlike the studies in the literature, in order to improve the forecasting accuracy, six parameters (λL, λM, λR, α, β and γ) were optimized. After the steps of the model is presented, a forecasting implementation has been made with the proposed model. Turkey’s hourly electricity consumption data is utilized to show the success of the prediction model. Prediction results of proposed model is compared with TFGM (1,1). MFO-TFGM (1,1) performs higher forecasting accuracy.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Da Yang ◽  
Liling Zhu ◽  
Yun Pu
Keyword(s):  
Traffic Flow ◽  
Heterogeneous Traffic ◽  
Model Parameters ◽  
Optimal Velocity ◽  
Stability Functions ◽  
Car Following Model ◽  
Traffic Wave ◽  
The Stability ◽  
Different Characteristics ◽  
Stationary Velocity

Although traffic flow has attracted a great amount of attention in past decades, few of the studies focused on heterogeneous traffic flow consisting of different types of drivers or vehicles. This paper attempts to investigate the model and stability analysis of the heterogeneous traffic flow, including drivers with different characteristics. The two critical characteristics of drivers, sensitivity and cautiousness, are taken into account, which produce four types of drivers: the sensitive and cautious driver (S-C), the sensitive and incautious driver (S-IC), the insensitive and cautious driver (IS-C), and the insensitive and incautious driver (IS-IC). The homogeneous optimal velocity car-following model is developed into a heterogeneous form to describe the heterogeneous traffic flow, including the four types of drivers. The stability criterion of the heterogeneous traffic flow is derived, which shows that the proportions of the four types of drivers and their stability functions only relating to model parameters are two critical factors to affect the stability. Numerical simulations are also conducted to verify the derived stability condition and further explore the influences of the driver characteristics on the heterogeneous traffic flow. The simulations reveal that the IS-IC drivers are always the most unstable drivers, the S-C drivers are always the most stable drivers, and the stability effects of the IS-C and the S-IC drivers depend on the stationary velocity. The simulations also indicate that a wider extent of the driver heterogeneity can attenuate the traffic wave.

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

scholarly journals A Theoretical Model for the Transmission Dynamics of the Buruli Ulcer with Saturated Treatment

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ebenezer Bonyah ◽  
Isaac Dontwi ◽  
Farai Nyabadza
Keyword(s):  
Human Population ◽  
Reproduction Number ◽  
Buruli Ulcer ◽  
Coupled System ◽  
Model Parameters ◽  
The Public ◽  
Treatment Function ◽  
Medical Facilities ◽  
The Stability ◽  
Saturated Treatment

The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.

scholarly journals A Study on the Generalized Approximation Modeling Method Based on Fitting Sensitivity for Prediction of Engine Performance

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Lin Lin ◽  
Fang Wang ◽  
Shisheng Zhong
Keyword(s):  
Engine Performance ◽  
Grey Model ◽  
Model Parameters ◽  
Bayesian Regularization ◽  
Safety Engineering ◽  
The Novel ◽  
Mean Square ◽  
Approximation Model ◽  
Mean Square Errors ◽  
Fitting Accuracy

Prediction technology for aeroengine performance is significantly important in operational maintenance and safety engineering. In the prediction of engine performance, to address overfitting and underfitting problems with the approximation modeling technique, we derived a generalized approximation model that could be used to adjust fitting precision. Approximation precision was combined with fitting sensitivity to allow the model to obtain excellent fitting accuracy and generalization performance. Taking the Grey model (GM) as an example, we discussed the modeling approach of the novel GM based on fitting sensitivity, analyzed the setting methods and optimization range of model parameters, and solved the model by using a genetic algorithm. By investigating the effect of every model parameter on the prediction precision in experiments, we summarized the change regularities of the root-mean-square errors (RMSEs) varying with the model parameters in novel GM. Also, by analyzing the novel ANN and ANN with Bayesian regularization, it is concluded that the generalized approximation model based on fitting sensitivity can achieve a reasonable fitting degree and generalization ability.

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