Discrete Grey Model Research Articles

Prediction of Energy-Related Carbon Emissions in East China Using a Spatial Reverse-Accumulation Discrete Grey Model

In order to better analyze and predict energy-related carbon emissions in East China to address climate change, this paper enhances the predictive capabilities of grey models in spatial joint prediction by creating the reverse-accumulation spatial discrete grey model RSDGM (1,1,m) and accumulation spatial discrete grey breakpoint model RSDGBM (1,1,m,t), which took the impact of system shocks into consideration. The efficiency of the models is confirmed by calculating the energy-related carbon emissions in East China from 2010 to 2022. Future emissions are predicted, and the spatial spillover effect of emissions in East China is discussed. The conclusions are as follows: (1) The RSDGM (1,1,m) theoretically avoids errors in background values and parameter calculations, reducing computational complexity. Empirically, the model exhibits high performance and reflects the priority of new information in spatial joint analysis. (2) The RSDGBM (1,1,m,t) captures the impact of shocks on system development, improving the reliability of carbon emissions prediction. (3) Jiangsu and Shandong are positively affected by spatial factors in terms of carbon emissions, while Shanghai and Zhejiang are negatively affected. (4) It is estimated that carbon emissions in East China will increase by approximately 23.8% in 2030 compared to the level in 2022, with the levels in Zhejiang and Fujian expected to increase by 45.2% and 39.7%, respectively; additionally, the level in Shanghai is projected to decrease. Overall, East China still faces significant pressure to reduce emissions.

A novel grey seasonal model with time power for energy prediction

The fluctuation of seasonal time series has attracted considerable attention. However, the complexity of socio-economic development and the variability of influencing factors make accurate predictions of seasonal time series more difficult. A new discrete grey seasonal model, namely DGSTPM(1,1), is established, which employs the time power term based on the cultural algorithm to effectively deal with the time sequences characterized by nonlinear tendency and periodic fluctuations. Firstly, the operating mechanism of the DGSTPM(1,1) model is expounded by combining the time power item with the traditional grey seasonal model to enhance the forecasting capability. Then, the optimal time power index of the model can be determined by incorporating the cultural algorithm. Subsequently, several properties are thoroughly discussed to illustrate the superiority and uniformity of the new model. Finally, two energy-related cases with different data features and sample sizes are applied to identify the efficacy and robustness of the DGSTPM(1,1) model, referring to monthly crude oil production in the United States and quarterly coke production in China. Based on the various error criteria, SPA and DM tests, the results indicate that the DGSTPM(1,1) outperforms its competitors both in simulation and prediction phases, including DGSTM(1,1), SGM(1,1), SDTGM, FTGM, SARIMA, LSSVM, BPNN, and LSTM models. Meanwhile, the new model can effectively address seasonal time series with nonlinear characteristics owing to its dynamic time power item with the support of the cultural algorithm.

Application of a high-performance grey prediction model to predict the cardiovascular disease mortality in elderly Chinese residents

With the acceleration of urbanization and aging process, an increasing number of Chinese senior citizens are suffering from cardiovascular diseases (CVDs). Therefore, reducing the prevalence and mortality of CVD has become one of the priorities of the public health department. And the scientific prediction of CVD morality is of great significance in the prevention and treatment of CVD among the elderly. Given the characteristics of “small sample, complex causes and long duration” of CVD among the senior citizens, grey prediction models which aim at handling the data with “small sample, poor information” are more feasible in forecasting its developing trend. In this paper, a new discrete grey prediction model is designed to forecast the CVD morality among Chinese senior citizens, in which a non-linear function is introduced to expand the model structure and the order and background value coefficient are optimized. In all the three sets of experiments, the errors of the new model are close to but smaller than those of the other three mainstream grey prediction models, indicating that the simulation and prediction performance of the new model is more accurate and stable. The research provides a new modelling approach to predicting the CVD mortality among Chinese senior citizens, which is conducive to the prevention of CVD prevalence and the sustainable development of public health.

Reduced-order reconstruction of discrete grey forecasting model and its application

Discrete grey forecasting models based on an accumulative operator have been widely used in many practical fields. With the development of grey forecasting models, it is a problem to be solved to further analyze internal mechanisms and unify the structures. This paper aims to reconstruct the model from a perspective of sequence characteristics and simplify the modeling steps under the condition of ensuring the accuracy of the model. First, this paper analyzes dynamic sequence evolution hidden and mines relationship between the structure and original sequence features contained in discrete grey forecasting model. Then, the reconstruction is carried out to prove the equivalence and quantitative relation between reduced-order model and original model. Under order recursive estimation, new parameters are addressed. Finally, theoretical correctness is verified by large-scale numerical simulation. Moreover, the reduced-order model is applied for prediction on the peak of battery incremental capacity and capacity degradation. Results show the effectiveness and superior prediction performance of the reduced-order model, where MAPEs of grey forecasting models have controlled under 4%.

Forecasting China's renewable energy consumption using a novel dynamic fractional-order discrete grey multi-power model

Accurately predicting renewable energy consumption is crucial for sustainable social and economic development, especially in China during its energy transition. This research introduces a novel dynamic fractional-order discrete grey multi-power model (DFDGMM(1,1,N)) to enable accurate forecasting of renewable energy consumption in China. The proposed method introduces a fractional-order accumulation operator and three power exponents that not only ensure the priority of new information, but also accurately capture the nonlinear traits of system data. It also incorporates a dynamic time delay function to account for the time lag between energy and economic development, enhancing the model's flexibility. Additionally, the study combines the whale optimization algorithm and the double-error idea to optimal parameter search. The proposed model is versatile and can be simplified into 14 other grey models. The case study demonstrates the model's impressive predictive accuracy, with a fitting error of 4.02 % and a test error of 0.89 %. The model is then employed to forecast renewable energy consumption in China, predicting a rapid annual growth rate of 17.25 % from 2022 to 2030. Overall, this article successfully constructs a dynamic prediction model in theory and scientifically provides valuable data support for the nation's energy development planning in practice.

Forecasting Oil Production and Consumption Using the Time-delayed Fractional Discrete Grey Model with Multiple Fractional Order

Forecasting Oil Production and Consumption Using the Time-delayed Fractional Discrete Grey Model with Multiple Fractional Order

Prediction of servo industry development in China by an optimized reverse Hausdorff fractional discrete grey power model

Prediction of servo industry development in China by an optimized reverse Hausdorff fractional discrete grey power model

Rolling discrete grey periodic power model with interaction effect under dual processing and its application

Time series characterized by periodic fluctuations are widespread in reality behavioural systems, and accurate forecasting of them has important practical application value. In this paper, based on the idea of discrete grey model, dual interaction effects and the nonlinear characteristics of the system are considered under the perspective of dual processing, and the fluctuating trend of the periodic sequence is portrayed through the introduction of the periodic dummy variable, and at the same time, combined with the extended periodic rolling time window method, the rolling discrete grey periodic power model with the interaction effect under dual processing is proposed, namely DIE-RDGM(1,1,T)α model. Differential evolution algorithm (DE) are employed to determine the optimum power index. Finally, the new model was compared with nine other forecasting models by three instances and applied to the problem of agricultural drought forecasting in Zhoukou City and Anyang City, Henan Province. The results show: (1) The new model has demonstrated strong competitiveness, confirming its rationality, validity, and superiority. (2) The DE is suitable for power index optimization search. (3) The new model can better describe the periodic change rule of seasonal-scale soil moisture in the two cities, and the forecast results are consistent with the actual drought conditions.

A novel structure adaptive discrete grey Bernoulli model and its application in renewable energy power generation prediction

Currently, the renewable energy power generation industry has entered a new stage, and accurate renewable energy power generation prediction is of great significance for the strategic planning of energy systems. However, renewable energy power generation data is characterized by nonlinearity and poor information, which brings challenges to accurately predict its development trend. Thus, this paper proposes a novel discrete grey Bernoulli model based on the spiral structure accumulated generating operator to deal with this problem. The spiral structure accumulated generating operator is introduced into the grey model to realize the effective utilization of renewable energy data information. Meanwhile, with the introduction of time delay structure, periodic structure and Bernoulli structure, the novel model can effectively characterize the nonlinearity, volatility, and time lag information between economic growth and energy development of renewable energy data. In addition, using the Differential Evolution optimization (DE) algorithm for nonlinear parameter optimization can effectively improve the stability and accuracy of the model, and also makes the model have the ability of structural self-adaptation. Finally, the new model was used to predict the bioenergy and wind power generation data. Based on comparative experiments and grey correlation analysis, the predictive performance of the novel model is verified, and the prediction results are highly correlated with those of authoritative organization. The experimental results show that the novel model is an effective predictive tool for renewable energy generation, which is an important reference value for energy development decision-making.

Forecasting the potential of global marine shipping carbon emission under artificial intelligence based on a novel multivariate discrete grey model

PurposeTo achieve sustainable development in shipping, accurately identifying the impact of artificial intelligence on shipping carbon emissions and predicting these emissions is of utmost importance.Design/methodology/approachA multivariable discrete grey prediction model (WFTDGM) based on weakening buffering operator is established. Furthermore, the optimal nonlinear parameters are determined by Grey Wolf optimization algorithm to improve the prediction performance, enhancing the model’s predictive performance. Subsequently, global data on artificial intelligence and shipping carbon emissions are employed to validate the effectiveness of our new model and chosen algorithm.FindingsTo demonstrate the applicability and robustness of the new model in predicting marine shipping carbon emissions, the new model is used to forecast global marine shipping carbon emissions. Additionally, a comparative analysis is conducted with five other models. The empirical findings indicate that the WFTDGM (1, N) model outperforms other comparative models in overall efficacy, with MAPE for both the training and test sets being less than 4%, specifically at 0.299% and 3.489% respectively. Furthermore, the out-of-sample forecasting results suggest an upward trajectory in global shipping carbon emissions over the subsequent four years. Currently, the application of artificial intelligence in mitigating shipping-related carbon emissions has not achieved the desired inhibitory impact.Practical implicationsThis research not only deepens understanding of the mechanisms through which artificial intelligence influences shipping carbon emissions but also provides a scientific basis for developing effective emission reduction strategies in the shipping industry, thereby contributing significantly to green shipping and global carbon reduction efforts.Originality/valueThe multi-variable discrete grey prediction model developed in this paper effectively mitigates abnormal fluctuations in time series, serving as a valuable reference for promoting global green and low-carbon transitions and sustainable economic development. Furthermore, based on the findings of this paper, a grey prediction model with even higher predictive performance can be constructed by integrating it with other algorithms.

A novel intervention effect-based quadratic time-varying nonlinear discrete grey model for forecasting carbon emissions intensity

In the context of severe global warming, accurately exploring the trend of carbon emissions intensity (CEI) changes is of great significance for mitigating climate change issues. The implementation of China's Carbon Emissions Trading Scheme (ETS) in 2013 is a policy intervention aimed at influencing CEI. The impact of intervention events makes forecasting a complex problem, which poses significant challenges to the construction of forecasting models. We first develop a quadratic time-varying nonlinear discrete grey model (QDNDGM(1,1)) to assess the intervention effect of the ETS policy. Then, a novel intervention effect-based quadratic time-varying nonlinear discrete grey model (IE-QDNDGM(1,1)) is developed to conduct the prediction under intervention effect, including an intervention term. The Whale Optimization Algorithm (WOA) is used to calculate a nonlinear parameter. We assess the intervention effect of the ETS policy in China and find that it can indeed reduce CEI. We verify the IE-QDNDGM(1,1) model’s superiority by comparing its predictive performance with that of three grey models, one statistical technique, and one artificial intelligence model. The comparative study shows the proposed model’s excellent fitting and prediction performance. An ablation experiment is conducted to validate the design of the IE-QDNDGM(1,1) model. Policy implications of the ETS intervention effect are discussed.

Prediction of industrial electricity consumption based on grey cluster weighted Markov model

Accurate prediction of industrial electricity consumption is not only beneficial to maintaining the steady development of the economy but also to conserving energy. To improve the prediction accuracy of industrial electricity consumption, a grey cluster weighted Markov model is proposed. It is applied to predict the industrial electricity consumption in four different regions in China. The prediction results are compared with the traditional discrete grey prediction model, which shows that the present model is more effective in these aspects of prediction accuracy, stability and extensibility. The research can provide theoretical references for the “West-East electricity transmission project” in China.

Failure prediction of mechanical system based on meta‐action

AbstractHighly reliable mechanical systems can lead to significant losses in the event of failure, and the lack of comprehensive failure data presents challenges for developing techniques such as critical part identification and failure prediction. In light of this, this paper proposes a meta‐action‐based fault prediction method that effectively addresses the issue of limited fault data. Initially, the mechanical system is decomposed utilizing the “Function‐Motion‐Action” (FMA) methodology to derive individual meta‐action units (MAUs). Subsequently, the limited sample of fault data from the mechanical system is combined with processed expert knowledge to construct the corresponding fault propagation‐directed graph. Furthermore, the key MAUs are determined by applying the Decision–Making Trial and Evaluation Laboratory (DEMATEL) method. Last, the degradation data of the key MAUs is acquired by monitoring them, and a non‐homogeneous discrete grey model (DNGM) integrated with an improved BP neural network is proposed to facilitate the fault prediction of MAUs. Using an industrial robot as a case study, the prediction results demonstrate the superiority of the method proposed in this paper over a single gray model and neural network, thereby providing a reliable prediction approach for anticipating the future trends of data‐deficient mechanical systems.

Data-driven degradation trajectory prediction and online knee point identification of battery in electric vehicles

Nonlinear degradation prediction of lithium-ion batteries is of great value in battery management systems. Knee point in degradation is a significant signal for state of health. However, large data generated by diverse aging mechanisms and dynamic operating conditions cannot be used completely in prediction. Firstly, this paper proposes a novel data-driven discrete grey model for battery degradation with knee point based on small sample modeling. Secondly, combined with four non-numerical differential methods, knee point is identified according to the predicted degradation trajectory. Then, batteries in 24 different fast charging modes are selected as a set of experimental subjects. Results show that 40% data of total cycles is sufficient to effectively predict battery degradation trajectory and identify the knee point. Finally, performance of fast charging modes is analyzed based on the predicted knee point. This work demonstrates the strong applicability of the grey model in reasonably predicting battery degradation trajectory and accurately identifying the knee point, providing a reference for fast charging schemes in complex engineering systems.

Determining Safe Working Hours of Wearing Medical Disposable Protective Clothing From Physiological Thermal Limits: A Pilot Study

Despite the mandatory use of medical disposable protective clothing to protect against infectious hazards, how to determine optimal safe working hours induced by physical fatigue while wearing medical disposable protective clothing remains unknown. Driven by these questions, here we quantify the extent of physical fatigue experienced by medical staff wearing medical disposable protective clothings in isolation wards to identify a safe work duration. Eight healthy males were subjected to light (2.1 km/h) and moderate (4.3 km/h) treadmill exercises while wearing two different ensembles. Four physiological (tympanic temperature Tcore, mean skin temperature Tsk, heart rate, and sweat loss) and two subjective indicators (thermal sensation and humidity sensation) were measured. We then introduced a discrete gray model(1,1) to determine safe working hours. The study indicated that even at lower temperatures, prolonged wearing of medical disposable protective clothing could significantly affect physiological indicators such as Tcore and Tsk ( p < 0.001), with Tcore being the predominant factor limiting safe working hours. Regarding medical disposable protective clothing-1-light, medical disposable protective clothing-1-moderate, medical disposable protective clothing-2-light, and medical disposable protective clothing-2-moderate intensity activities, the safe working hours were 6.33, 2.83, 2.83, and 2.25 h. This article presented a new approach to determining safe working hours for wearing medical disposable protective clothing from physiological thermal limits with small sample data. However, this is a preliminary study, and further validation of the prediction model through additional experiments is necessary.

A novel structure adaptive discrete grey Bernoulli prediction model and its applications in energy consumption and production

It is well known that energy forecasts play an important role in guiding energy policy, economic development and technological progress. Therefore, based on the purpose of energy consumption and production forecasting, this paper proposes a novel structure adaptive discrete grey Bernoulli model, which is innovative in terms of both accumulated generating operator and model structure. In terms of accumulated generating operator, a new fractional order accumulated generating operator is proposed in this paper. The new accumulated generating operator has a different information priority by adjusting the values of the parameters. In terms of model structure, a novel discrete grey Bernoulli model is proposed in this paper. The novel model is well adapted to time series data containing nonlinear information, and can well mine and utilize the information contained in the original data. In addition, the Particle Swarm Optimization (PSO) algorithm was chosen to optimize the model parameters based on algorithm comparison experiments. This enables the model to flexibly adapt to a variety of complex data and has the ability of structure adaptive. Moreover, this paper conducts comparative experiments between the novel model and eight other forecasting algorithms for time series data. The numerical results show that the novel model has better forecasting performance for the data of China’s total energy consumption, China’s total electricity generation and China’s total domestic electricity consumption. In addition, for the model reliability problem caused by the optimization algorithm, the stability and accuracy of the model are verified by Monte Carlo simulation and probability density visualization analysis. Finally, the proposed model predicts the future development trend of energy consumption and production in China.

A novel grey multivariate convolution model based on the improved marine predators algorithm for predicting fossil CO2 emissions in China

The effective prediction of fossil carbon dioxide (CO2) emissions provides a foundation for environmental protection authorities to make relevant management and decisions. CO2 emissions are influenced by various factors and exhibit a nonlinear and complex trend. First, the weighted conformable fractional accumulation (WCFA) method is proposed. WCFA is a generalized form of the existing weighted accumulation and conformable fractional order accumulation. A nonlinear discrete grey Bernoulli multivariate convolution model is introduced to model the sequences processed by WCFA. Then, an improved marine predators algorithm (IMPA) is obtained by improving the marine predators algorithm by the tent map and cosine control parameter. The performance of IMPA is verified by algorithm comparison experiments and Friedman test. The feasibility and predictive effectiveness of the proposed model is validated through three case studies. In prediction of fossil CO2 emissions in China, the fitting and prediction errors of the proposed model reach 1.1773% and 0.5402%, respectively. Finally, the total fossil CO2 emissions in China from 2022 to 2026 are predicted and analyzed. The results indicate a gradual decrease in fossil CO2 emissions over the next five years. Some reasonable suggestions are made based on the prediction results and sources of fossil CO2 emissions.

Can China reach the CO2 peak by 2030? A forecast perspective.

With the continuous emission of greenhouse gases, climate issues such as global warming have attracted widespread attention. As the largest CO2 emitter, China proposes the target of reaching the CO2 emissions peak by 2030 at the 75th United Nations General Assembly. To determine whether China can realize the goal, we construct an assessment system consisting of a new discrete grey prediction model on the basis of a rolling mechanism and an improved IPCC method. First, the new grey prediction model is used to predict the CO2 emissions and GDP from 2021 to 2030, and then, the enhanced IPCC method is used to obtain the carbon intensity from 2021 to 2030. In line with the direct judgment based on CO2 emissions and the indirect judgment based on the comparison between the AADR of carbon intensity and the AAIR of GDP, we find that China faces great challenges and difficulties in achieving its carbon peaking target by 2030. Finally, based on the forecast data and China's current situation, some policy recommendations are put forward to accelerate China's CO2 peak goal.

Forecasting global plastic production and microplastic emission using advanced optimised discrete grey model.

Plastic pollution has become a prominent and pressing environmental concern within the realm of pollution. In recent times, microplastics have entered our ecosystem, especially in freshwater. In the contemporary global landscape, there exists a mounting apprehension surrounding the manifold environmental and public health issues that have emerged as a result of the substantial accumulation of microplastics. The objective of the current study is to employ an enhanced grey prediction model in order to forecast global plastic production and microplastic emissions. This study compared the accuracy level of the four grey prediction models, namely, EGM (1,1, α, θ), DGM (1,1), EGM (1,1), and DGM (1,1, α) models, to evaluate the accuracy levels. As per the estimation of the study, DGM (1,1, α) was found to be more suitable with higher accuracy levels to predict microplastic emission. The EGM (1,1, α, θ) model has slightly better accuracy than the DGM (1,1, α) model in predicting global plastic production. Various accuracy measurement tools (MAPE and RMSE) were used to determine the model's efficiency. There has been a gradual growth in both plastic production and microplastic emission. The current study using the DGM (1,1, α) model predicted that microplastic emission would be 1,084,018 by 2030. The present study aims to provide valuable insights for policymakers in formulating effective strategies to address the complex issues arising from the release of microplastics into the environment and the continuous production of plastic materials.

An optimal wavelet transform grey multivariate convolution model to forecast electricity demand: a novel approach

PurposeFor some years now, Cameroon has seen a significant increase in its electricity demand, and this need is bound to grow within the next few years owing to the current economic growth and the ambitious projects underway. Therefore, one of the state's priorities is the mastery of electricity demand. In order to get there, it would be helpful to have reliable forecasting tools. This study proposes a novel version of the discrete grey multivariate convolution model (ODGMC(1,N)).Design/methodology/approachSpecifically, a linear corrective term is added to its structure, parameterisation is done in a way that is consistent to the modelling procedure and the cumulated forecasting function of ODGMC(1,N) is obtained through an iterative technique.FindingsResults show that ODGMC(1,N) is more stable and can extract the relationships between the system's input variables. To demonstrate and validate the superiority of ODGMC(1,N), a practical example drawn from the projection of electricity demand in Cameroon till 2030 is used. The findings reveal that the proposed model has a higher prediction precision, with 1.74% mean absolute percentage error and 132.16 root mean square error.Originality/valueThese interesting results are due to (1) the stability of ODGMC(1,N) resulting from a good adequacy between parameters estimation and their implementation, (2) the addition of a term that takes into account the linear impact of time t on the model's performance and (3) the removal of irrelevant information from input data by wavelet transform filtration. Thus, the suggested ODGMC is a robust predictive and monitoring tool for tracking the evolution of electricity needs.