DGM Model Research Articles

Adaptive backstepping control with grey signal predictor for nonlinear active suspension system matching mechanical elastic wheel

Abstract In order to stabilize the attitude and improve ride comfort of vehicles equipped with mechanical elastic wheel (MEW), an adaptive backstepping controller with grey signal predictor is presented for active suspension system, considering the uncertainty and nonlinearity of suspension and MEW. The MEW’s mathematical model is established through experiments firstly. Then the ideal suspension motions are generated according to a designed hybrid damping control. To track these ideal signals, Lyapunov theory and the thought of backstepping are used to estimate the nonlinearity of active suspension and obtain final control laws. Grey DGM (2,1) model is further applied to derive future motions of suspension, thus commands can be carried out in advance to realize control in time. The stability and convergence of whole scheme are also proved by Lyapunov-like lemma. Finally, simulations on two different road profiles (step and pulse) show that this strategy can effectively suppress the vertical motion of vehicle body by 19.7% and pitch motion by 9.5% respectively compared with that without control. And furthermore, the bounce of wheels is also decreased at the same time. The controller expands the application of MEW and establishes a good theoretical foundation for the novel wheels’ matching.

A Novel Method for Optimizing Fractional Grey Prediction Model

Aiming at the shortcoming that the classical FGM(1,1) model regards the gray action quantity as a fixed constant, the DGM(1,1) model is used to dynamically simulate and predict the gray action quantity, so that the gray action quantity can change dynamically with time. On this basis, a new FGM(1,1,b) model with dynamic gray quantity change with time is proposed, and the total primary energy consumption in the Middle East is taken as a numerical example for simulation prediction. The results show that the prediction accuracy of the dynamic FGM(1,1,b) model proposed in this paper is higher than that of the classical FGM(1,1) model, and the practicability and effectiveness of the FGM(1,1,b) model are verified. At the same time, it also provides relevant theoretical basis for the study of world energy development.

A Novel Dynamic Grey Action Quantity GM(1,1,b) Model and Its Application

The classical GM(1,1) model treats the grey action quantity as an invariant constant, but changes have occurred within the system as time and space change. If the fixed grey action quantity is still used for modeling, the model will have errors. Aiming at this shortcoming, this paper proposes a GM(1,1,b) model in which the grey action quantity can be dynamically changed. Starting from the background value formula, the model solves the grey action quantity at different time points by the development coefficient, and fits the sequence with the DGM(1,1) model, then brings the obtained time response sequence into the classical GM (1, 1) to replaces the grey action quantity constant, so as to establish a GM(1,1,b) model with dynamic change of grey action quantity. Finally, the model is applied to the example of China's rural residents' consumption index. The numerical example shows that the GM(1,1,b) model proposed in this paper effectively improves the prediction accuracy of the model and verifies the effectiveness and practicability of the improved model.

A novel energy consumption forecasting model combining an optimized DGM (1, 1) model with interval grey numbers

Since energy consumption (EC) is becoming an important issue for sustainable development in the world, it has a practical significance to predict EC effectively. However, there are two main uncertainty factors affecting the accuracy of a region's EC prediction. Firstly, with the ongoing rapid changes in society, the consumption amounts can be non-smooth or even fluctuating during a long time period, which makes it difficult to investigate the sequence's trend in order to forecast. Secondly, in a given region, it is difficult to express the consumption amount as a real number, as there are different development levels in the region, which would be more suitably described as interval numbers. Most traditional prediction models for energy consumption forecasting deal with long-term real numbers. It is seldom found to discover research that focuses specifically on uncertain EC data. To this end, a novel energy consumption forecasting model has been established by expressing ECs in a region as interval grey numbers combining with the optimized discrete grey model (DGM(1,1)) in Grey System Theory (GST). To prove the effectiveness of the method, per capita annual electricity consumption in southern Jiangsu of China is selected as an example. The results show that the proposed model reveals the best accuracy for the short data sequences (the average fitting error is only 2.19% and the average three-step forecasting error is less than 4%) compared with three GM models and four classical statistical models. By extension, any fields of EC, such as petroleum consumption, natural gas consumption, can also be predicted using this novel model. As the sustained growth in EC of China's, it is of great significance to predict EC accurately to manage serious energy security and environmental pollution problems, as well as formulating relevant energy policies by the government.

The application of trigonometric grey prediction model to average per capita natural gas consumption of households in China

PurposeDue to high efficiency and low carbon of natural gas, the consumption of natural gas is increasing rapidly, and the prediction of natural gas consumption has become the focus. The purpose of this paper is to employ a prediction technique by combining grey prediction model and trigonometric residual modification for predicting average per capita natural gas consumption of households in China.Design/methodology/approachThe GM(1,1) model is utilised to obtain the tendency term, then the generalised trigonometric model is used to catch the periodic phenomenon from the residual data of GM(1,1) model for improving predicting accuracy.FindingsThe case verified the view of Xie and Liu: “When the value of a is less, DGM model and GM(1,1) model can substitute each other.” The combination of the GM(1,1) and the trigonometric residual modification technique can observably improve the predicting accuracy of average per capita natural gas consumption of households in China. The mean absolute percentage errors of GM(1,1) model, DGM(1,1), unbiased grey forecasting model, and TGM model in ex post testing stage (from 2013 to 2015) are 32.5510, 33.5985, 36.9980, and 5.2996 per cent, respectively. The TGM model is suitable for the prediction of average per capita natural gas consumption of households in China.Practical implicationsAccording to the historical data of average per capita natural gas consumption of households in China, the authors construct GM(1,1) model, DGM(1,1) model, unbiased grey forecasting model, and GM(1,1) model with trigonometric residual modification. The accuracy of TGM is the best. TGM helps to improve the accuracy of GM(1,1).Originality/valueThis paper gives a successful practical application of grey model GM(1,1) with the trigonometric residual modification, where the cyclic variations exist in the residual series. The case demonstrates the effectiveness of trigonometric grey prediction model, which is helpful to understand the modeling mechanism of trigonometric grey prediction model.

Non-equidistance DGM(1,1) Model Based on the Concave Sequence and Its Application to Predict the China’s Per Capita Natural Gas Consumption

Abstract Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literatures show its performance could be further improved, such as for the DGM(1,1) model, based on a concave sequence, the modeling error will be larger. In this paper, firstly the definition of sequence convexity is given out, and it is proved that the output sequence of DGM(1,1) model is a convex sequence. Next, the residual change law of DGM(1,1) model based on the concave sequence is discussed, and the non-equidistance DGM(1,1) model is proposed. Finally, by introducing the symmetry transformation, a concave sequence is transformed into a convex sequence, called the symmetric sequence of the concave sequence, and then construct the non-equidistance DGM(1,1) model based on the convex sequence. The example results show that the novel method is more accurate than the direct modeling for a concave sequence.

Measurement of shock effect following change of one-child policy based on grey forecasting approach

PurposeThis paper aims to analyze general development trend of China’s population and to forecast China’s total population under the change of China’s family planning policy so as to measure shock disturbance effects on China’s population development.Design/methodology/approachChina has been the most populous country for hundreds of years. And this state will be sustained in the forthcoming decade. Obviously, China is confronted with greater pressure on controlling total scale of population than any other country. Meanwhile, controlling population will be beneficial for not only China but also the whole world. This paper first analyzes general development trend of China’s population total amount, sex ratio and aging ratio. The mechanism for measurement of the impact effect of a policy shock disturbance is proposed. Linear regression model, exponential curve model and grey Verhulst model are adopted to test accuracy of simulation of China’s total population. Then considering the policy shock disturbance on population, discrete grey model, DGM (1, 1), and grey Verhulst model were adopted to measure how China’s one-child policy affected its total population between 1978 and 2015. And similarly, the grey Verhulst model and scenario analysis of economic developing level were further used to forecast the effect of adjustment from China’s one-child policy to two-child policy.FindingsResults show that China has made an outstanding contribution toward controlling population; it was estimated that China prevented nearly 470 million births since the late 1970s to 2015. However, according to the forecast, with the adjustment of the one-child policy, the birth rate will be a little higher, China’s total population was estimated to reach 1,485.59 million in 2025. Although the scale of population will keep increasing, but it is tolerable for China and sex ratio and trend of aging will be relieved obviously.Practical implicationsThe approach constructed in the paper can be used to measure the effect of population change under the policy shock disturbance. It can be used for other policy effect measurement problems under shock events’ disturbance.Originality/valueThe paper succeeded in studying the mechanism for the measurement of the post-impact effect of a policy and the effect of changes in China’s population following the revision of the one-child policy. The mechanism is useful for solving system forecasting problems and can contribute toward improving the grey decision-making models.

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

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.

DGM (1, 1) model optimized by MVO (multi-verse optimizer) for annual peak load forecasting

A large number of renewable energies and uncertain power load accessing electric power system make the power load forecasting more complicated and face more new challenges. This paper presents a hybrid annual peak load forecasting model [namely MVO-DGM (1, 1)], which employs the latest optimization algorithm MVO (multi-verse optimizer) to determine two parameters of DGM (1, 1) model, and then uses the optimized DGM (1, 1) model to forecast annual peak load. The annual peak load of Shandong province in China from 2005 to 2014 is selected as the empirical example, and the analysis results demonstrate that the MVO algorithm for parameters’ determination of DGM (1, 1) model has significant superiority over the least square estimation method, particle swarm optimization and fruit fly optimization algorithm in terms of annual peak load forecasting. In addition, the proposed MVO-DGM (1, 1) peak load forecasting model has more excellent forecasting performance than other non-optimized forecasting techniques and other optimized DGM (1, 1) models due to its ascended local optima avoidance and better convergence speed. The hybrid MVO-DGM (1, 1) model proposed in this paper is feasible and effective in annual peak load forecasting, which can improve the forecasting accuracy.

A novel multi-variable grey forecasting model and its application in forecasting the amount of motor vehicles in Beijing

The structure defect of the GM(1,N) model is the major reason for its low simulation and prediction performance. To address this issue, a linear correction item h1(k−1) and a grey action quantity h2 are introduced into the GM(1,N) model to improve its structure in this paper. Specifically, the ‘h1(k−1)’ reflects the linear relations between the dependent variable and the independent variables, and the ‘h2’ shows the data change law of the dependent variable sequence. Based on this, a novel multi-variable grey forecasting model, NGM(1,1), is proposed. Furthermore, the NGM(1,N) model’s time-response expression and the final restored expression are proved, its initial value is optimized, and a MATLAB program for building the NGM(1,N) model is developed. Lastly the NGM(1,N) model is applied to simulate and forecast the amount of Beijing’s motor vehicles. The mean relative simulation and prediction percentage errors of the new model are only 0.009% and 1.149%, in comparison with the ones obtained from the traditional GM(1,N) model and the classical DGM(1,1) model, which are 4.680%, 10.685% and 4.411%, 11.167% respectively. The findings show that the new model has the best performance, which confirms the effectiveness of the structure improvement.

Evaluating Performance of the DGM(2,1) Model and Its Modified Models

The direct grey model (DGM(2,1)) is considered for fluctuation characteristics of the sampling data in Grey system theory. However, its applications are quite uncommon in the past literature. The improvement of the precision of the DGM(2,1) is only presented in few previous researches. Moreover, the evaluation of forecasted performance of the DGM(2,1) model and its applications was not conducted in previous studies. As the results, this study aims to evaluate forecasted performance of the DGM(2,1) and its three modified models, including the Markov direct grey model MDGM(2,1), the Fourier direct grey model FDGM(2,1), and the Fourier Markov direct grey model FMDGM(2,1) in order to determine the application of the DGM(2,1) model in practical applications and academic research. The results demonstrate that the DGM(2,1) model has lower precision than its modified models, while the forecasted precision of the FDGM(2,1) is better than that of MDGM(2,1). Additionally, the FMDGM(2,1) model presents the best performance among all of the modified models of DGM(2,1), which can effectively overcome the fluctuating of the data sample and minimize the predicted error of the DGM(2,1) model. The finding indicated that the FMDGM(2,1) model does not only have advantages with regard to the sample size requirement, but can also be flexibly applied to the large fluctuation and random sequences with a high quality of estimation.

Modelisation of Membrane Distillation: Mass and Heat Transfer in Air Gap Membrane Distillation

Membrane distillation (MD) is receiving recent attention as a technique to efficiently concentrate aqueous solution such as seawater. It has potential benefits of low temperature and pressure operation with high degrees of separation. In this work, the effect of the membrane thickness was studied to produce of the steam flow in the three different mass transfer mechanisms, and in the different possible combinations of its mechanisms in three different temperatures. The results have been carried using a polynomial approximation through MATLAB. A quite important increase in the flow in the model (DGM, Schofield, and KMPT) was observed with a decrease in the stream rating in the model (KMT). However, the Molecular model, DGM model, KMPT model, and Schofield model are not affected by the membrane’s thickness. After, we have studied the effect of this parameter (Thickness of the membrane) on the transfer of conduction heat and latent heat.

Predicting the Trend of Taiwan’s Electronic Paper Industry by an Effective Combined Grey Model

Electronic paper (e-paper) is a major sector of Taiwan’s Optoelectronic industry. It has paid much attention on the development of flexible displays. Even though the market is booming, the future is still unclear for business development. No research has yet forecasted the future market size of the e-paper industry. In addition, proposing an appropriate forecasting model to understand the trend of this industry plays a crucial role for market players and government’s authorities in formulating correct strategies. Therefore, in this paper, the future market size of Taiwan’s e-paper industry is predicted by an effective combined grey model. Two combinations of DGM(2,1) and Verhulst model with Fourier series and Markov chain, namely FM-Verhulst and FMDGM(2,1), were presented. Based on the annual data of Taiwan’s e-paper industry, the results show that the forecasting performances of two FM-Verhulst and FMDGM(2,1) models are highly accurate compared with other grey models. Precision is 96.36% and 97.77%, respectively. However, for long-term prediction, the FMDGM(2,1) model obtains the best performance in all proposed grey models. With obtained forecasting results in Taiwan’s e-paper industry by the FMDGM(2,1) model, it can be pointed out that the future market size of Taiwan’s e-paper would slowly increase in the next few years.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional non-homogenous discrete grey forecasting model (NDGM), the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence (MAPEM) and mean percent of interval sequence simulating value set covered (MPSVSC), are defined and, the procedure of the interval grey number sequence based the NDGM (IG-NDGM) is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM(1,1) model and GM(1,1) model.

The Prediction for Shanghai Business Climate Index by Grey Model

This study predicts Shanghai Business Climate Index from the third quarter of 2013 to the first quarter of 2014 by Grey Model. Business climate index (enterprise integrated production business index) is the judgments and expectations index to the development of an enterprise in the future. By comparing the forecasting accuracy of three grey models, i.e., GM (1, 1) model, Verhulst model and the DGM (2, 1) model, the results show that the forecasting accuracy of GM (1, 1) model is higher than Verhulst model and DGM (2, 1) model. And GM (1, 1) model is used to predict Shanghai business climate index in the next three quarters.

Using Grey Theory to Predict Shanghai Unit GDP Energy Consumption

Energy consumption per unit of GDP, reflecting the environmental costs of economic development, pointed out the direction for urban construction, environmental protection is our common responsibility. In real life, the impact of energy consumption per unit of GDP is complex and uncertain factors, according to a series of known and unknown information, we can predict the energy consumption per unit of GDP as a grey system, so you can use the grey system theory. Grey model requires only a limited amount of data to estimate the unknown system behavior. In this study, first of all, by using the known data we established GM (1, 1) model, Verhulst model and the DGM (2, 1) model predictive analysis. The results show that GM (1, 1) model’s prediction accuracy is higher than the prediction accuracy of Verhulst model and DGM (2, 1) model. Then, Shanghai next unit GDP energy consumption is predicted by GM (1, 1) model.

Forecast of Passenger and Freight Traffic Volume based on Elasticity Coefficient Method and Grey Model

The increase in passenger and freight traffic in a region reflects the development of railways, highways, waterways, aviation, and pipeline. With the growth of economy, China's transportation develops rapidly. However, the passenger and freight traffic present different growth features in different regions. Therefore, a reasonable forecast model for passenger and freight traffic and the analysis of relationship between regional transportation and economy are important for transportation planning. The elasticity coefficient between the passenger traffic volume, freight traffic volume and gross domestic product (GDP) is calculated based on the data from 2001 to 2010 in different regions in China. Then, the relationship between the change of regional traffic volume and regional economic development is obtained. With the analysis of the pros and cons for different forecast models, Elasticity Coefficient Method, GM (1, 1) model, and DGM model have been used to forecast passenger and freight traffic volumes from 2011 to 2015. In order to improve the accuracy of the forecast results, the combined models based on the variance reciprocal and the optimal weighting are applied to optimize the forecasting model. Among all the forecast models, the combined model with optimal weights outperforms other models with a relative error less than 0.006% for the freight traffic volume. The accuracy of forecast models on passenger and freight traffic volume has been improved, which provides a reasonable basis for the planning and development of the transportation system.

Unbiased Direct DGM(1,1) Model of Non-Homogeneous Exponential Sequence and its Application in Electric Load Forecasting

The traditional GM (1,1) has been used widely in the load forecasting, however, there are many defects in the GM (1,1). In order to overcome these defects and expand the application scope of the grey model in load forecasting, a new load forecasting method based on DDGM(1,1) is presented. First, the recursive solution of DDGM(1,1) is given. Then, based on the solution, the unbiased property for non-homogeneous exponential incremental sequence of this model is proved. It is applied to some load forecasting and is compared with the traditional GM (1,1) model.The results show that the presented forecasting method is superior obviously to traditional methods, and it can be used for the approximate non-homogeneous exponential incremental load forecasting generally.

Electrochemical performance characteristics and optimum design strategies of a solid oxide electrolysis cell system for carbon dioxide reduction

An analytical model is developed to study the electrochemical characteristics of a solid oxide electrolysis cell (SOEC) for carbon dioxide reduction, in which the activation overpotential, concentration overpotential, and ohmic overpotential are considered as the main sources of voltage losses. The Bulter-Volmer equation, DGM model, and Ohm's law are employed to characterize the three overpotentials, respectively. The theoretical model is validated by comparing the simulation results with the experimental data from the literature. The anode-supported configuration SOEC is found to be the most favorable design. The effects of the cathode inlet gas molar fraction on the cathode overpotential and the cell potential are discussed in detail. It is found that there exists an optimum molar fraction for the cathode inlet gas at which the cathode concentration overpotential attains its minimum for given operation conditions. Moreover, the effects of some importantly operating parameters such as the current density, temperature and pressure on the cell potential are discussed. Thermal-electrochemical analysis shows that the Joule heat generated from the irreversibilities in the SOEC may be larger than, equal to, or smaller than the thermal energy needed for the carbon dioxide reduction reaction, and consequently, a system layout with five different design strategies to implement the carbon dioxide electrolysis is put forward.

The Application of the Grey Disaster Model to Forecast Epidemic Peaks of Typhoid and Paratyphoid Fever in China

ObjectiveThe objectives of this study were to forecast epidemic peaks of typhoid and paratyphoid fever in China using the grey disaster model, to evaluate its feasibility of predicting the epidemic tendency of notifiable diseases.MethodsAccording to epidemiological features, the GM(1,1) model and DGM model were used to build the grey disaster model based on the incidence data of typhoid and paratyphoid fever collected from the China Health Statistical Yearbook. Model fitting accuracy test was used to evaluate the performance of these two models. Then, the next catastrophe date was predicted by the better model.ResultsThe simulation results showed that DGM model was better than GM(1,1) model in our data set. Using the DGM model, we predicted the next epidemic peak time will occur between 2023 to 2025.ConclusionThe grey disaster model can predict the typhoid and paratyphoid fever epidemic time precisely, which may provide valuable information for disease prevention and control.