Grey System Model Research Articles

A Hybrid Grey System Model Based on Stacked Long Short-Term Memory Layers and Its Application in Energy Consumption Forecasting

Accurate energy consumption prediction is crucial for addressing energy scheduling problems. Traditional machine learning models often struggle with small-scale datasets and nonlinear data patterns. To address these challenges, this paper proposes a hybrid grey model based on stacked LSTM layers. This approach leverages neural network structures to enhance feature learning and harnesses the strengths of grey models in handling small-scale data. The model is trained using the Adam algorithm with parameter optimization facilitated by the grid search algorithm. We use the latest annual data on coal, electricity, and gasoline consumption in Henan Province as the application background. The model’s performance is evaluated against nine machine learning models and fifteen grey models based on four performance metrics. Our results show that the proposed model achieves the smallest prediction errors across all four metrics (RMSE, MAE, MAPE, TIC, U1, U2) compared with other 15 grey system models and 9 machine learning models during the testing phase, indicating higher prediction accuracy and stronger generalization performance. Additionally, the study investigates the impact of different LSTM layers on the model’s prediction performance, concluding that while increasing the number of layers initially improves prediction performance, too many layers lead to overfitting.

Grey System Model GM (1,1) for Predicting Student Performance

The purpose of this study is to predict student quiz assignments in the General Physics I course during one semester using the Grey system GM (1,1) model. The prediction model integrates the first-order two-variable grey differential equation model from the Grey system theory. Additionally, a MATLAB program for the GM (1,1) prediction model was developed. The predicted results were compared with the original GM (1,1) model, showing good agreement.

The general conformable fractional grey system model and its applications

As a mathematical instrument, the fractional order grey system model can be employed to characterize uncertain real-world data. This paper presents new definitions for the generalized conformable fractional accumulation (GCFA) and the generalized conformable fractional difference (GCFD). For the first time, complex network theory explains the modelling mechanisms of accumulation. Then a novel generalized conformable fractional grey model (GCFGM(1,1)) is proposed based on the GCFA and GCFD, and the particle swarm optimizer (PSO) method is employed to optimize its fractional order. In this study, the proposed model is applied to the prediction of China’s overall energy consumption, natural gas consumption, and gross domestic product. Our research reveals that our proposed model achieves mean absolute percentage error (MAPE) values of less than 5% on real datasets from 9 different regions, outperforming other comparative models. These key empirical findings demonstrate the superiority of our model in accurately predicting relevant variables.

A novel fractional neural grey system model with discrete q-derivative

The challenge of predicting time series with limited data has evolved over time due to nonlinearity, complexity, and limited information. It can be perceived as a mapping of dynamical systems in one-dimensional space. This article proposes a neural grey system to tackle this challenge. The system enhances its ability to fit nonlinearity by employing polynomials, captures complexity through a fractional-order cumulant operator, and resolves information-poor uncertainty by utilizing grey system modeling techniques. The model effectively integrates research findings from neural computing, uncertainty theory, and complexity theory at a theoretical level. It accurately describes dynamic processes of complex systems. Additionally, we have reduced the complexity of calculations in the algorithm design. We selected a dataset of total retail sales of consumer goods to test the model’s validity and applicability. Our experiments demonstrate that the newly proposed grey forecasting model can effectively forecast time series with small samples, offering good forecasting outcomes and generalization ability.

Potential yields of two staple cereal crops worldwide under global warming

Most studies on model-estimated yield potential of crop under climate change are based on the principle of production function, for specific variety, from static biological dimension and at local or regional level, while few theoretically are based on time-series approach for world crop from dynamic evolutionary angle and on global scale. Therefore we conducted following research in 2019 to 2023 at Guiyang City of China: potential yields of rice and wheat worldwide by 2030 are projected creatively using Auto-regressive Integrated Moving Average and Trend-regressed model based on their history since 1961, in which the projections are tested by actual yields in recent two years and further validated by Gray System model; the impacts of global warming on past production of rice and wheat worldwide since 1961 are analyzed using binary regression model in which global mean temperature is treated as the independent variable while the crop yield as the dependent variable. Our results show that: in the future between 2022 and 2030, average yield of world rice is projected to be from 4876 kg/ha to 5195 kg/ha whereas that of world wheat from 3548 kg/ha to 3817 kg/ha; top (national) yield of world rice is projected to be from 10148 kg/ha to 10269 kg/ha whereas that of world wheat from 9914 kg/ha to 10042 kg/ha; or the ratio between average and top yields of world rice will be from 48.05% to 50.59% whereas that of world wheat from 35.79% to 38.01%; since 1961, global warming exerts a negative impact on average yield of world rice less than on its top, and a positive effect on average yield of world wheat while a negative one on its top, which partially drives the gap between average and top yields of world rice slightly narrowed and that of world wheat gradually closed. These findings indicate that: given that top yield is considered potential limit of average yield, to improve global production of these two staple cereal crops by 2030, the priorities should be given to rice as well as wheat worldwide in their both high and low yield countries.

Prediction of Enterprise Human Resource Demand Based on Iot and Data Mining Technology

This paper analyzes the prediction model of enterprise human resource demand based on Internet of Things (IoT) technology and data mining technology. It also analyzes the impact of the company’s growth scale and other key factors on the demand for human resources, tries to establish a coupling factor model of enterprise development and economic benefits, and then analyzes and forecasts the enterprise’s personnel structure and quality structure. The experimental results show that the optimized human resource demand forecasting model integrates the advantages of the grey system model in data processing, can mine the inherent laws of unorganized data information, and provides a certain convenience for forecasting. Through the linear mapping and processing of sample data, the input and output reflect a kind of correlation, thus changing the fault tolerance of information, making the prediction in the calculation process more accurate, and its comprehensive accuracy can exceed 92.5%.

From resettlement to revitalization: Examining the water resource environment carrying capacity of ecological migrant resettlement areas in China

Identifying the threshold and leverage point of water resource environment carrying capacity (WRECC) is crucial for effectively adjusting the industrial structure, population migration, and regional planning. This study has introduced the concept of leverage points and employed both the gray system model and the system dynamic (SD) model to reveal the threshold of WRECC and capture the coupling relationship between the population growth system and the WRECC system in Hongsibao County, China. Three typical scenarios were designed for distinct purposes and simulated by the constructed SD model in Hongsibao County from 2021 to 2030. The results indicate that the quantity of water resource carrying capacity, rather than the quality, is a critical shortcoming hindering socio-economic sustainability in Hongsibao County. Threshold and leverage point analysis showed that the increased development speed scenario performed the worst in terms of WRECC (28.02 × 104 persons in 2021) and leverage point (23.65 × 104 persons in 2026). The steady development scenario is considerably more effective for improving WRECC and boosting system recovery and conditioning, and the steady development scenario performs the best in both aspects. To achieve stable development, priority actions are necessary. Firstly, it is imperative to improve agricultural water-saving irrigation rates while addressing soil salinization in Hongsibao County. Secondly, efforts should be directed toward developing the grape industry, breeding industry, and wolfberry industry to stimulate economic growth while avoiding excessive water consumption. Finally, promoting the establishment of comprehensive sewage disposal infrastructure in rural areas is vital for protecting the water environment.

A novel discrete conformable fractional grey system model for forecasting carbon dioxide emissions

A novel discrete conformable fractional grey system model for forecasting carbon dioxide emissions

A Novel Rolling and Fractional-ordered Grey System Model and Its Application for Predicting Industrial Electricity Consumption

A Novel Rolling and Fractional-ordered Grey System Model and Its Application for Predicting Industrial Electricity Consumption

Application of grey system model with intelligent parameters in predicting regional electricity consumption

PurposeGiven the regional heterogeneity of economic development, electricity consumption in various regions exhibits a discrepant growth pattern. The purpose of this study is to construct a grey system forecasting model with intelligent parameters for predicting provincial electricity consumption in China.Design/methodology/approachFirst, parameter optimization and structural expansion are simultaneously integrated into a unified grey system prediction framework, enhancing its adaptive capabilities. Second, by setting the minimum simulation percentage error as the optimization goal, the authors apply the particle swarm optimization (PSO) algorithm to search for the optimal grey generation order and background value coefficient. Third, to assess the performance across diverse power consumption systems, the authors use two electricity consumption cases and select eight other benchmark models to analyze the simulation and prediction errors. Further, the authors conduct simulations and trend predictions using data from all 31 provinces in China, analyzing and predicting the development trends in electricity consumption for each province from 2021 to 2026.FindingsThe study identifies significant heterogeneity in the development trends of electricity consumption systems among diverse provinces in China. The grey prediction model, optimized with multiple intelligent parameters, demonstrates superior adaptability and dynamic adjustment capabilities compared to traditional fixed-parameter models. Outperforming benchmark models across various evaluation indicators such as root mean square error (RMSE), average percentage error and Theil’s index, the new model establishes its robustness in predicting electricity system behavior.Originality/valueAcknowledging the limitations of traditional grey prediction models in capturing diverse growth patterns under fixed-generation orders, single structures and unadjustable background values, this study proposes a fractional grey intelligent prediction model with multiple parameter optimization. By incorporating multiple parameter optimizations and structure expansion, it substantiates the model’s superiority in forecasting provincial electricity consumption.

How does climate change affect potential yields of four staple grain crops worldwide by 2030?

Global food security basically depends on potential yields of staple grain crops worldwide, especially under climate change. However, most scholars use various models of production function in which climatic factors are often considered to estimate crop yield mostly at local or regional level. Therefore, in this paper: Potential yields of rice, wheat, maize and soybean worldwide by 2030 are projected creatively using Auto-regressive Integrated Moving Average and Trend Regressed (ARIMA-TR) model in which actual yields in recent two years are used for testing the reliability of projection and Gray System (GS) model for validating the test; Especially individual impacts of climate change on the productions of rice, wheat, maize and soybean worldwide since 1961 are analyzed by using unary regression model in which global mean temperature and land precipitation are independent variable while the yield of crop being dependent one, respectively. Results show that: by 2030, the ratio between average and top yields of world rice is projected to be 50.6% increasing, while those of world wheat, world maize and world soybean are projected to be 38.0% increasing, 14.7% decreasing and 72.5% increasing, respectively. Since 1961 global warming has exerted a negative impact on average yield of world rice less than on its top, a positive effect on average yield of world wheat while a negative impact on its top, a positive effect on average yield of world maize less than on its top, and a positive influence on average yield of world soybean while a negative one on its top, which might be slightly mitigated by 'Carbon Peak' target. The fluctuation of global rainfall contributes to the productions of these crops much less than global warming during same period. Our findings indicate that: to improve global production of four staple grain crops by 2030, the priorities of input should be given to either rice or wheat in both high and low yield countries, whereas to maize in high yield countries and to soybean in low yield countries. These insights highlight some difference from previous studies, and provide academia with innovative comprehension and policy-decision makers with supportive information on sustainable production of these four staple grain crops for global food security under climate change in the future.

Prediction of GDP per Capita in Fuqing City Based on GM Grey System Model

Prediction of GDP per Capita in Fuqing City Based on GM Grey System Model

A novel kernel ridge grey system model with generalized Morlet wavelet and its application in forecasting natural gas production and consumption

Natural gas production (NGP) and consumption (NGC) always exhibit high nonlinearity, posing challenges for accurate small-sample forecasting. In this work, a novel kernel ridge grey system model with an extended parametric Morlet wavelet (GMW-KRGM) is proposed by integrating the kernel ridge regularization and grey system modelling within a partially linear regression framework and trained by the conjugate gradient method to mitigate the ill-posed problem. Besides, a weighted multi-objective optimization strategy is designed for model hyperparameter optimization and solved by the grey wolf optimizer (GWO). Six real-world NGP and NGC forecasting cases are carried out and empirical results demonstrate that the proposed GMW-KRGM model with optimal hyperparameters solved by GWO always yields superior forecasting performance than the other 2 machine learning models and 7 conventional grey system benchmarks with out-of-sample mean average percentage error (MAPE) improved in 7.4245%–91.8392% and 14.7303%–42.67% on average, respectively and yields more precise forecasting accuracy with fast and stable convergence than the other 5 optimization algorithms with improved MAPE range from 9.5608% to 48.2584%, indicating that the proposed model holds the capability to effectively deal with the nonlinear complex system and has great potential in nonlinear small sample forecasting.

Study on Economic Data Forecasting Based on Hybrid Intelligent Model of Artificial Neural Network Optimized by Harris Hawks Optimization

To use different models for forecasting economic data suitably, three main basic models (the grey system model, time series analysis model, and artificial neural network (ANN) model) are analyzed and compared comprehensively. Based on the analysis results of forecasting models, one new hybrid intelligent model based on the ANN model and Harris hawks optimization (HHO) has been proposed. In this hybrid model, HHO is used to select the hyperparameters of the ANN and also to optimize the linking weights and thresholds of the ANN. At last, by using four economic data cases including two simple data sets and two complex ones, the analysis of the basic models and the proposed hybrid model have been verified comprehensively. The results show that the grey system model can suitably analyze exponential data sequences, the time series analysis model can analyze random sequences, and the ANN model can be applied to any kind of data sequence. Moreover, when compared with the basic models, the new hybrid model can be suitably applied for both simple data sets and complex ones, and its forecasting performance is always very suitable. In comparison with other hybrid models, not only for computing accuracy but also for computing efficiency, the performance of the new hybrid model is the best. For the least initial parameters used in the new hybrid model, which can be determined easily and simply, the application of the new hybrid model is the most convenient too.

Grey Systems Model to Assess Water Quality in Mantaro River in Peru

The section of the Mantaro River that flows through the department of Huancavelica, Peru, has been affected by toxic wastes and mineral residues from industrial and mining activities, which have directly impacted the water quality. In this work, a grey system model, based on the grey clustering method, was used to assess water quality. The grey clustering method was applied using the central point of triangular whitening weight functions (CTWF). In addition, the Prati index and the Environmental Quality Standards for water from the Peru government were revised and used for this study. In the case study, six physicochemical parameters, pH, DO, BOD, Cd, As, and Pb, at nine monitoring points were assessed along the Mantaro River. The results showed that the sixth monitoring point (P6), which is influenced by mining activity, was highly contaminated, while the other points were classified as noncontaminated. Finally, the results obtained by applying the grey clustering method can be useful to competent authorities, for decision making on water management in this watershed.

A novel fractional Hausdorff grey system model and its applications

Grey system models have proven to be effective techniques in diverse fields and are crucial to global decision science. Amongst the various approaches of grey theory, the fractional-order grey model is fundamental and extends the cumulative generation method used in grey theory. Fractional-order cumulative generating operator offers numerous significant benefits, especially in educational funding that is often influenced by economic policies. However, their computational complexity complicates the generalization of fractional-order operators in real-world scenarios. In this paper, an enhanced fractional-order grey model is proposed based on a new fractional-order accumulated generating operator. The newly introduced model estimates parameters by utilizing the method of least squares and determines the order of the model through the implementation of metaheuristic algorithms. Our results show that, after conducting both Monte Carlo simulations and practical case analyses, the newly proposed model outperforms both existing grey prediction models and machine learning models in small sample environments, thus demonstrating superior forecast accuracy. Moreover, our experiments reveal that the proposed model has a simpler structure than previously developed grey models and achieves greater prediction accuracy.

Forecasting the Natural Gas Supply and Consumption in China Using a Novel Grey Wavelet Support Vector Regressor

Natural gas is playing an important role in the reconstruction of the energy system of China. Natural gas supply and consumption indicators forecasting is an important decision-making support for the government and energy companies, which has attracted considerable interest from researchers in recent years. In order to deal with the more complex features of the natural gas datasets in China, a Grey Wavelet Support Vector Regressor is proposed in this work. This model integrates the primary framework of the grey system model with the kernel representation employed in the support vector regression model. Through a series of mathematical transformations, the parameter optimization problem can be solved using the sequential minimal optimization algorithm. The Grey Wolf Optimizer is used to optimize its hyperparameters with the nested cross-validation scheme, and a complete computational algorithm is built. The case studies are conducted with real-world datasets from 2003–2020 in China using the proposed model and 15 other models. The results show that the proposed model presents a significantly higher performance in out-of-sample forecasting than all the other models, indicating the high potential of the proposed model in forecasting the natural gas supply and consumption in China.

Application of a novel hybrid accumulation grey model to forecast total energy consumption of Southwest Provinces in China

PurposeConsidering the small sample size and non-linear characteristics of historical energy consumption data from certain provinces in Southwest China, the authors propose a hybrid accumulation operator and a hybrid accumulation grey univariate model as a more accurate and reliable methodology for forecasting energy consumption. This method can provide valuable decision-making support for policy makers involved in energy management and planning.Design/methodology/approachThe hybrid accumulation operator is proposed by linearly combining the fractional-order accumulation operator and the new information priority accumulation. The new operator is then used to build a new grey system model, named the hybrid accumulation grey model (HAGM). An optimization algorithm based on the JAYA optimizer is then designed to solve the non-linear parameters θ, r, and γ of the proposed model. Four different types of curves are used to verify the prediction performance of the model for data series with completely different trends. Finally, the prediction performance of the model is applied to forecast the total energy consumption of Southwest Provinces in China using the real world data sets from 2010 to 2020.FindingsThe proposed HAGM is a general formulation of existing grey system models, including the fractional-order accumulation and new information priority accumulation. Results from the validation cases and real-world cases on forecasting the total energy consumption of Southwest Provinces in China illustrate that the proposed model outperforms the other seven models based on different modelling methods.Research limitations/implicationsThe HAGM is used to forecast the total energy consumption of the Southwest Provinces of China from 2010 to 2020. The results indicate that the HAGM with HA has higher prediction accuracy and broader applicability than the seven comparative models, demonstrating its potential for use in the energy field.Practical implicationsThe HAGM(1,1) is used to predict energy consumption of Southwest Provinces in China with the raw data from 2010 to 2020. The HAGM(1,1) with HA has higher prediction accuracy and wider applicability compared with some existing models, implying its high potential to be used in energy field.Originality/valueTheoretically, this paper presents, for the first time, a hybrid accumulation grey univariate model based on a new hybrid accumulation operator. In terms of application, this work provides a new method for accurate forecasting of the total energy consumption for southwest provinces in China.

Evaluation and prediction of earth pressure balance shield performance in complex rock strata: A case study in Dalian, China

This research explores the potential for the evaluation and prediction of earth pressure balance shield performance based on a gray system model. The research focuses on a shield tunnel excavated for Metro Line 2 in Dalian, China. Due to the large error between the initial geological exploration data and real strata, the project construction is extremely difficult. In view of the current situation regarding the project, a quantitative method for evaluating the tunneling efficiency was proposed using cutterhead rotation ( R ), advance speed ( S ), total thrust ( F ) and torque ( T ). A total of 80 datasets with three input parameters and one output variable ( F or T ) were collected from this project, and a prediction framework based gray system model was established. Based on the prediction model, five prediction schemes were set up. Through error analysis, the optimal prediction scheme was obtained from the five schemes. The parametric investigation performed indicates that the relationships between F and the three input variables in the gray system model harmonize with the theoretical explanation. The case shows that the shield tunneling performance and efficiency are improved by the tunneling parameter prediction model based on the gray system model.

Forecasting education expenditure with a generalized conformable fractional-order nonlinear grey system model

As an important human capital investment, education is an effective means to improve the comprehensive quality of people. Education expenditure is an important material guarantee for the development of educational undertakings. Education expenditure data is highly susceptible to numerous economic and social factors that complicate its nonlinear structure. In order to model the complex nonlinear problems of the system, this paper proposes a generalized conformable fractional-order nonlinear grey prediction model for the first time by analyzing the traditional time series-based modeling method in a nonlinear grey domain. The proposed model expands on the classical grey Bernoulli model by introducing the generalized conformable fractional accumulation as a new accumulation generator and utilizes error minimization principles in the modeling process. By altering the optimal order of the model and the cumulative generation operator, this model can adapt to various time series and reduce errors. Finally, the model is applied to education expenditure forecasting, and it is proved that the proposed model achieved good results and has higher accuracy than other models.