Grey System Model Research Articles

A novel multivariate grey system model with conformable fractional derivative and its applications

To further improve the effectiveness and precision of multivariate time series forecasting, a conformable fractional derivative multivariate grey system model is proposed in this work. Firstly, the general solution of the model is deduced by the grey theory, the definition of the conformable fractional derivative, the theory of ordinary differential equations and the two-point trapezoidal approximation formula. Then the ordinary least squares estimation method is utilized to derive linear system parameters, and the ant lion optimizer algorithm is used to search the optimal fractional order. Finally the newly constructed model is applied to forecast the urban consumption per capita of China. The total mean absolute percentage error of the new model is only 0.6434%, in comparison with ones obtained from GM(1,1), DGM(1,1), CFGM(1,1), CFNGM(1,1,k,c), CFGM(1,1,D), MLR, GMCT(1,N), RDGM(1,N), FGMC(1,N) and GMC(r,N), which are 4.0334%, 4.0837%, 3.4751%, 3.6629%, 2.2129%, 1.0487%, 784.1107%, 1.0168%, 0.7655% and 0.7954% respectively. The results show the new model has a better performance compared with other models.

Predicting the trend of infectious diseases using grey self-memory system model: a case study of the incidence of tuberculosis

ObjectivesThe prediction and early warning of infectious diseases is an important work in the field of public health. This study constructed the grey self-memory system model to predict the incidence trend of infectious diseases affected by many uncertain factors. Study designThe design of this study is a combination of the prediction method and empirical analysis. MethodsBy organically coupling the self-memory algorithm with the mean GM(1,1) model, the tuberculosis incidence statistics of China from 2004 to 2018 were selected for prediction analysis. Meanwhile, by comparing with the other traditional prediction methods, three representative accuracy check indexes (MSE, AME, MAPE) were conducting for error analysis. ResultsOwing to the multiple time-points initial fields, which replace the single time-points, the limitation of the traditional grey prediction model, which is sensitive to the initial value, is overcome in the self–memory equation. Consequently, compared with the mean GM model and other statistical methods, the grey self-memory model shows significant forecasting advantages, and its single-step rolling prediction accuracy is superior to other prediction methods. Therefore, the incidence of tuberculosis in China in the next year can be predicted as 55.30 (unit: 1/105). ConclusionsThe grey self-memory system model can closely capture the individual random fluctuation in the whole evolution trend of the uncertain system. It is appropriate for predicting the future incidence trend of infectious diseases and is worth popularizing to other similar public health prediction problems.

Forecasting Natural Gas Consumption in the US Power Sector by a Randomly Optimized Fractional Grey System Model

Natural gas is one of the main energy resources for electricity generation. Reliable forecasting is vital to make sensible policies. A randomly optimized fractional grey system model is developed in this work to forecast the natural gas consumption in the power sector of the United States. The nonhomogeneous grey model with fractional-order accumulation is introduced along with discussions between other existing grey models. A random search optimization scheme is then introduced to optimize the nonlinear parameter of the grey model. And the complete forecasting scheme is built based on the rolling mechanism. The case study is executed based on the updated data set of natural gas consumption of the power sector in the United States. The comparison of results is analyzed from different step sizes, different grey system models, and benchmark models. They all show that the proposed method has significant advantages over the other existing methods, which indicates the proposed method has high potential in short-term forecasting for natural gas consumption of the power sector in United States.

Generalized fractional grey system models: The memory effects perspective

In recent years, grey models based on fractional-order accumulation and/or derivatives have attracted considerable research interest because they offer better performance in handling limited samples with uncertainty than integer-order grey models; however, there remains room for improvement. This paper considers a more flexible and general structure for the fractional grey model by incorporating a generalized fractional-order derivative (GFOD) that complies by memory effects, resulting in the development of a generalized fractional grey model (denoted as GFGM(1,1)). Specifically, we comprehensively analyse the modelling mechanism of the proposed GFGM(1,1) model, involving model parameter estimation and time response function derivation, and discuss the link between the proposed approach and existing special cases. Then, to further improve the efficacy of the proposed approach, four mainstream metaheuristic algorithms are employed to ascertain the orders of fractional accumulation and derivatives. Finally, we carry out a series of simulation studies and a real-world application case to demonstrate the applicability and advantage of the our approach. The numerical results show that GFGM(1,1) outperforms other benchmarks, and some significant insights are obtained from the numerical experiments.

A novel neural grey system model with Bayesian regularization and its applications

Most machine learning models are essentially “Black-box” models, of which the performance heavily relies on large scale data sets. In this work the idea of “Grey-box” modelling is adopted in order to take most advantage of known information represented by deterministic structure, and then the neural grey system model is developed. Levenberg-Marquardt algorithm is used to train the proposed model, and the Bayesian regularization is used to tune the regularized parameter automatically. Six real world case studies are presented to show the performance of the proposed model, comparing to 6 existing machine learning models and 17 grey system models. The results show that the proposed model can significantly overperform the other models and has very good generality, illustrating its high potential in a wide variety of real world applications and the efficiency of the proposed modelling method.

Improvement of Grey System Model using Particle Swarm Optimization

An improvement of the traditional grey system model, GM(1,1), to enhance forecast accuracy, has been realized using the particle swarm optimization (PSO) algorithm. Unlike the GM(1,1) which uses a fixed adjacent neighbor weight for all data sets, the proposed PSO-improved model, PSO-GM(1,1), determines an optimal adjacent neighbor weight, based on the presented data set. This optimal adjacent neighbor weight so determined is the principal factor that enhances forecast accuracy. The performance of the proposed model was evaluated using generated monotonic increasing and decreasing data sets as well as measured energy consumption data for a laptop computer, desktop computer, printer, and photocopier. The performance of PSO-GM(1,1) was compared with that of GM(1,1), and two other models in literature that sought to improve the performance of GM(1,1). The PSO-GM(1,1) outperformed the traditional model and the two other models. For the monotonic increasing data, the mean absolute percentage error (MAPE) for the proposed model was 0.007% as against a MAPE value of 20.383% for the GM(1,1). For the monotonic decreasing data, the PSO-GM(1,1) again outperformed GM(1,1), yielding a MAPE of 0.057% compared to a value of 13.407% for the traditional model. For the measured laptop computer energy data, the obtained MAPE for the PSO-GM(1,1) was 0.675% while the values for the two models were 4.052% and 2.991%. For the measured desktop computer energy data, the obtained MAPE for the PSO-GM(1,1) was 0.0018% while the values for the two models were 0.0018% and 1.163%. For the data associated with the printer, the MAPEs were 8.414% for the PSO-GM(1,1), 20.957% for the first model and 9.080% for the second model. For the measured photocopier energy data, the obtained MAPE for the PSO-GM(1,1) was 0.901% while the values for the two models were 3.799% and 0.943%. Thus, the proposed PSO-GM(1,1) greatly improves forecast accuracy and is recommended for adoption, for forecasting.

Forecasting U.S. Maritime Incidents using the Grey-Markov Model

Vessel incidents periodically occur in the waterways of the United States, but some types of commercial vessels have shown a downward trend in the number of incidents in recent years. One of the missions of the United States Coast Guard (USCG) is to develop regulations to mitigate and potentially prevent maritime incidents. In this paper, the USCG gathered data on more than 117,000 incidents that involved U.S.-flag vessels in U.S. waterways for the period 2001 through 2018. We applied the Grey System theory or model and Grey-Markov forecasting model to predict the future number of vessel incidents for four different vessel types from 2019 through 2030. Incident data can vary considerably from year to year and often can be incomplete. The Grey-Markov model, which is a combination of the Grey model and the Markov chain process, is suitable for this purpose because of its predictive ability. From our results, we found that the Grey-Markov model performed exceptionally well and showed the predicted values of the number of incidents to be remarkably similar to the actual values with acceptable mean relative errors ranging from 5.2% to 8.2%. We expect that these results will benefit decision makers in formulating sound policies thereby improving the maritime safety of vessels operating in waterways of the United States.

Improved grey system models for predicting traffic parameters

In transportation applications such as real-time route guidance, ramp metering, congestion pricing and special events traffic management, accurate short-term traffic flow prediction is needed. For this purpose, this paper proposes several novel online Grey system models (GM): GM(1,1|cos(ωt)), GM(1,1|sin(ωt),cos(ωt)), and GM(1,1|e-at,sin(ωt),cos(ωt)). To evaluate the performance of the proposed models, they are compared against a set of benchmark models: GM(1,1) model, Grey Verhulst models with and without Fourier error corrections, linear time series model, and nonlinear time series model. The evaluation is performed using loop detector and probe vehicle data from California, Virginia, and Oregon. Among the benchmark models, the error corrected Grey Verhulst model with Fourier outperformed the GM(1,1) model, linear time series, and non-linear time series models. In turn, the three proposed models, GM(1,1|cos(ωt)), GM(1,1|sin(ωt),cos(ωt)), and GM(1,1|e-at,sin(ωt),cos(ωt)), outperformed the Grey Verhulst model in prediction by at least 65%, 16% and 11%, in terms of Root Mean Squared Error, and by 82%, 58% and 42%, in terms of Mean Absolute Percentage Error, respectively. It is observed that the proposed Grey system models are more adaptive to location (e.g., perform well for all roadway types) and traffic parameters (e.g., speed, travel time, occupancy, and volume), and they do not require as many data points for training (4 observations are found to be sufficient).

Gray Water Recovery System Model by Solar Photocatalysis with TiO<sub>2</sub> Nanoparticles for Crop Irrigation

Gray Water Recovery System Model by Solar Photocatalysis with TiO<sub>2</sub> Nanoparticles for Crop Irrigation

Application of Grey System Model to Forecast the Natural Gas Imports in China

China’s natural gas imports will keep an upward trend in the future due to its increasing demands. A comparatively accurate prediction of natural gas imports will help the Chinese government make appropriate decisions when formulating energy policies. In this paper, a new grey predication model, GPM_NGI model, was proposed to forecast China’s natural gas imports. Compared with GM (1, 1) and DGM (1, 1) model, the proposed new model performed better in the simulation process and bore smaller mean relative percentage error when used in simulating China’s natural gas imports from 2011 to 2019. Then, the new model was employed to forecast China’s natural gas imports from 2020 to 2022. The results showed that China’s natural gas imports would continue to grow rapidly over the next three years. Therefore, in order to strike a balance between the natural gas supply and demand in the future and avoid overdependence on imports, the Chinese government should take effective measures from both the supply and demand ends, such as making better use of shale gas, wind, and solar energy as well as reducing the industrial dependence on natural gas.

Prediction of Coalbed Methane Production in China Based on an Optimized Grey System Model

Coalbed methane (CBM) is one of the three major sources of unconventional natural gas. Accurate prediction of CBM production is an important basis for the governmental decision-making in the exploi...

Application of a novel time-delayed power-driven grey model to forecast photovoltaic power generation in the Asia-Pacific region

Photovoltaic engineering is one of the most important ways for utilizing solar energy. With fast development and large investment, the photovoltaic market has become more complex, leading to less reasonable samples for accurate forecasting. In this work, a time-delayed power effect with high flexibility is considered to develop a new grey system model, which can be more efficient in dealing with small and complex time series and shares a more general formulation. The Grey Wolf Optimizer is used to select the optimal nonlinear parameter. Three real-world cases in energy forecasting are used to validate the new model, showing its significant advantages over eight existing grey system models. The cumulative installed capacity of photovoltaic in Asia-Pacific from 2009 to 2018 is used to assess the effectiveness of the new model. Results indicate that high accuracy forecasts can be obtained by using the new model, showing its high potential in installed capacity of photovoltaic forecasting, which may be very useful in photovoltaic marketing and policy making.

A novel ensemble learning-based grey model for electricity supply forecasting in China

<abstract><p>Electricity consumption is one of the most important indicators reflecting the industrialization of a country. Supply of electricity power plays an import role in guaranteeing the running of a country. However, with complex circumstances, it is often difficult to make accurate forecasting with limited reliable data sets. In order to take most advantages of the existing grey system model, the ensemble learning is adopted to provide a new stratagy of building forecasting models for electricity supply of China. The nonhomogeneous grey model with different types of accumulation is firstly fitted with multiple setting of acculumation degrees. Then the majority voting is used to select and combine the most accurate and stable models validated by the grid search cross validation. Two numerical validation cases are taken to validate the proposed method in comparison with other well-known models. Results of the real-world case study of forecasting the electricity supply of China indicate that the proposed model outperforms the other 15 exisiting grey models, which illustrates the proposed model can make much more accurate and stable forecasting in such real-world applications.</p></abstract>

A Novel Optimized Grey Model with Quadratic Polynomials Term and its Application

A grey forecasting model NGM(1,1,k2) with quadratic polynomials bt2+ct+d as grey action time is proposed based on the theory of grey system modeling in this paper. It is found that GM(1,1) model, NGM(1,1,k) model, SAIGM model, GM(1,1,k2) model are the special forms of NGM(1,1,k2) with different parameters. Moreover, the characteristics of NGM(1,1,k2) and its effect on the modeling precision are evaluated under the contractive transformation. We further analyze the error of NGM(1,1,k2) model and propose a new model called BNGM(1,1,k2) model, which is obtained by optimizing the background value based on Simpson formula, so as to improve the prediction precision of the model. Three numerical cases show that BNGM(1,1,k2) is significantly superior to the other grey models. Finally, three examples indicate that the practicability of the BNGM(1,1,k2) model is very good.

Parameter Optimization on the Three-Parameter Whitenization Grey Model and Its Application in Simulation and Prediction of Gross Enrollment Rate of Higher Education in China

The gray prediction model, based on the GM(1,1) method, is an important branch of gray theory with the most active research and the most fruitful results, and it is the most widely used because of its small sample size, simple modeling process, and easy to use. Such advantages have been successfully applied in many fields such as transportation, agriculture, energy, medicine, and environment and have been gradually developed into a mainstream predictive modeling method. This study combines the Three-parameter Whitenization Grey Model (TWGM(1,1)), which fits the inhomogeneous exponential law sequence, and the Particle Swarm Algorithm (PSA) to optimize the order and background value coefficients under the condition of the minimum sum of squares of simulation errors, and hence, to solve the problem that the cumulative order is fixed to “1” and the background value coefficient value is fixed to “0.5.” As a result, a parameter-optimized gray system model with flexibility, adaptability, and dynamic adjustment is designed to simulate and predict China’s higher education gross enrollment rate. The application shows that the model has better overall simulation and prediction performance than others. On the one hand, the parametric optimization model significantly improves its own performance, and on the other hand, its intelligent and adjustable adaptivity improves the accuracy and further extends its application.

Parameter estimation for grey system models: A nonlinear least squares perspective

Grey system models can be viewed as a special class of dynamic data analysis tools, in which the continuous-time dynamics (differential equations or integral equations) are used to define the implicit regression formula. This communication investigates the parameter estimation of grey system models from noisy observations. Based on the state-space representation, the parameter estimation of dynamics is converted to a nonlinear regression and four optimization criteria are induced under a measurement error environment. Then, nonlinear least squares is utilized to estimate parameters and quantify the uncertainty on the estimates. Under different sample size and noise level combinations, simulations are conducted on the models (with and without exogenous variables) to compare the parameter estimation approaches. The results show that nonlinear least squares has multiple advantages over the conventional integral matching in terms of accuracy and robustness to noise, especially when the observations are irregularly-spaced.

Research and application of novel Euler polynomial-driven grey model for short-term PM10 forecasting

PurposePM10 is one of the most dangerous air pollutants which is harmful to the ecological system and human health. Accurate forecasting of PM10 concentration makes it easier for the government to make efficient decisions and policies. However, the PM10 concentration, particularly, the emerging short-term concentration has high uncertainties as it is often impacted by many factors and also time varying. Above all, a new methodology which can overcome such difficulties is needed.Design/methodology/approachThe grey system theory is used to build the short-term PM10 forecasting model. The Euler polynomial is used as a driving term of the proposed grey model, and then the convolutional solution is applied to make the new model computationally feasible. The grey wolf optimizer is used to select the optimal nonlinear parameters of the proposed model.FindingsThe introduction of the Euler polynomial makes the new model more flexible and more general as it can yield several other conventional grey models under certain conditions. The new model presents significantly higher performance, is more accurate and also more stable, than the six existing grey models in three real-world cases and the case of short-term PM10 forecasting in Tianjin China.Practical implicationsWith high performance in the real-world case in Tianjin China, the proposed model appears to have high potential to accurately forecast the PM10 concentration in big cities of China. Therefore, it can be considered as a decision-making support tool in the near future.Originality/valueThis is the first work introducing the Euler polynomial to the grey system models, and a more general formulation of existing grey models is also obtained. The modelling pattern used in this paper can be used as an example for building other similar nonlinear grey models. The practical example of short-term PM10 forecasting in Tianjin China is also presented for the first time.

Analysis and Optimization of Influencing Factors of Zhuhai Marine Tourism Economic Development

Li, D. and Yu, Y., 2020. Analysis and optimization of influencing factors of Zhuhai marine tourism economic development. In: Gong, D.; Zhang, M., and Liu, R. (eds.), Advances in Coastal Research: Engineering, Industry, Economy, and Sustainable Development. Journal of Coastal Research, Special Issue No. 106, pp. 101–104. Coconut Creek (Florida), ISSN 0749-0208.An important part of the marine economy of Zhuhai, China, is the marine tourism industry, not only the development trend, but also how it affects the development of the whole city's marine economy. Although Zhuhai has rich marine tourism resources, the level and quality of its tourism industry, mining, and development still need to be improved. On this basis, it is necessary to analyze and optimize the influencing factors of marine tourism economic development in Zhuhai. This study investigates the significance of the development of marine tourism in Zhuhai, analyzes the grey system model of the economic development of marine tourism, and creates a quantitative analysis and optimization of the influencing factors of the economic development of marine tourism in Zhuhai.

Research on the computer evaluation of land price in Urban-rural Fringe Based on RS and GIS

Urban-rural fringe land prices is the weak spot in the study of land prices, rapid and healthy development of land market demands on the land price evaluation. Under the guidance of the concept of sustainable development, this paper discusses the composition of land value in the rural-urban fringe, which is divided into three parts: the value of quality, the value of the environment and the value of existence. The value of quality is evaluated by revenue reduction method, but at present, when using this method to evaluate the land price, the actual pure income is used to replace the expected pure income, resulting in the unreasonable land price. This study systematically demonstrated the feasibility of using grey system modeling to predict the expected net income of land, and analyzed the whole modeling process. Finally, the model was applied to the land valuation of urban and rural areas in our city.

Identifying Acetylation Protein by Fusing Its PseAAC and Functional Domain Annotation.

Acetylation is one of post-translational modification (PTM), which often reacts with acetic acid and brings an acetyl radical to an organic compound. It is helpful to identify acetylation protein correctly for understanding the mechanism of acetylation in biological systems. Although many acetylation sites have been identified by high throughput experimental studies via mass spectrometry, there still are lots of acetylation sites need to be discovered. Computational methods have showed their power for identifying acetylation sites with informatics techniques which usually reduce experiment cost and improve the effectiveness and efficiency. In fact, if there is an approach can distinguish the acetylated proteins from the non-acetylated ones, it is no doubt a very meaningful and effective method for this issue. Here, we proposed a novel computational method for identifying acetylation proteins by extracting features from the conservation information of sequence via gray system model and KNN scores based on the information of functional domain annotation and subcellular localization. The authors have performed the 5-fold cross-validation on three datasets along with much analysis of features and the Relief feature selection algorithm. The obtained accuracies are all satisfactory, as the mean performance, the accuracy is 77.10%, the Matthew's correlation coefficient is 0.5457, and the AUC value is 0.8389. These works might provide useful insights for the related experimental validation, and further studies of other PTM process. For the convenience of related researchers, the web-server named “iACetyP” was established and is accessible at http://www.jci-bioinfo.cn/iAcetyP.