Discrete Grey Model Research Articles

Assessment and prediction of environmental sustainability: novel grey models comparative analysis of China vs. the USA.

Emission forecasting is vital for policy-making and emission reduction goals globally. This research aimed to perform an accurate model for forecasting and assessing CO2 emissions and the production of renewable electricity for the top two countries contributing to these emissions, the USA and China. In this study, we employed three novel advanced mathematical grey models: optimized discrete grey model (ODGM), nonhomogeneous discrete grey model (NDGM), and variable speed and adaptive structure grey model (VSSGM) to estimate the future trends of CO2 emissions and renewable electricity production. These breakthrough models added value in this field of research by reducing uncertainty surrounding ambiguity and numerical ranges and improving accuracy in assessments by using small samples and imperfect information. The findings showed that, by 2026, China's electricity production based on renewable sources would be higher than that of the USA. We find CO2 emissions in a downward trend, with more significant reductions in the USA than in China by the year 2026. The contributions of this study are the application of novel VSSGM and the use of synthetic relative growth rate modeling for predicting the overall growth of CO2 emissions and the production of renewable electricity in analyzed countries. The originality of this study lies in proposing a novel synthetic doubling time model to compute how long it will take, for China and the USA, to reduce their CO2 emissions and doubling their increase in renewable electricity production.

Growing green? Sectoral-based prediction of GHG emission in Pakistan: a novel NDGM and doubling time model approach

Greenhouse gases (GHGs) are one of the leading causes of global warming. Therefore, accuracy estimates for greenhouse gases (GHGs) emissions are a key element in defining the best strategies for reducing GHG emissions from various source sectors of the economy. In the present study, an initial attempt has been made to estimate and forecast the GHG emissions in Pakistan from five major sectors, such as energy, industrial, agriculture, waste, and land-use change and forestry. The data were taken from the official website of the Pakistan climate database from 1990 to 2016. We employed advanced mathematical modeling, namely a non-homogenous discrete grey model (NDGM), to predict sector-wise GHGs emissions. Moreover, the present study is a milestone in the GHGs growth analysis by utilizing the synthetic relative growth rate (SRGR) and synthetic doubling time model (SDTM). The results reveal that the industry and land-use change and forestry contribute more in terms of increasing GHGs emissions till 2024, whereas agriculture and waste required comparatively less time to reduce GHGs emissions double in number among five sectors. All five sectors show an increasing trend in forecasting GHGs emissions between 1990 and 2016. However, the results indicate that land-use change and forestry and industrial sectors are more likely to be a reason for the increase in GHGs emissions in the future, followed by the agriculture, energy, and waste sectors. The land-use change and forestry was found prone to increase emission in the future, and the doubling time ( $${D}_{\mathrm{t}}$$ ) suggests less time expected to reduce GHGs. Finally, the study has suggested some policies for the policymakers, government, and decision-makers to reduce GHGs emissions and achieve sustainable development.

A novel adaptive discrete grey model with time-varying parameters for long-term photovoltaic power generation forecasting

The rapidly growing photovoltaic power generation (PPG) instigates stochastic volatility of electricity supply that may compromise the power grid’s stability and increase the grid imbalance cost. Therefore, accurate predictions of long-term PPG are of essential importance for the capacity deployment, plan improvement, consumption enhancement, and grid balance in systems with high penetration levels of PPG. Artificial neuron networks (ANNs) have been widely utilized to forecast the short-term PPG due to their strong nonlinear fitting competence that corresponds to the prerequisite for handling PPG samples characterized by volatility and nonlinearity. However, under the circumstances of the large time span, the insufficient data samples, and the periodicity existing in the long-term PPG datasets, the ANNs are easily stuck in overfitting and generate large forecasting deviations. Given this situation, a novel discrete grey model with time-varying parameters is initially designed to deal with various PPG time series featured with nonlinearity, periodicity, and volatility, which widely exist in the long-term PPG sequences. To be specific, improvements in this proposed model lie in the following aspects: first, the time-power item and periodic item are designated to compose the time-varying parameters to capture the nonlinear, periodic, and fluctuant developing trends of various time series. Second, owing to the complex nonlinear relationships between the above parameters and forecasting errors, the genetic algorithm applies shortcuts to seek optimum solutions and thereby enhances the prediction precision. Third, several practical properties of the proposed model are elaborated to further interpret the feasibility and adaptability of the proposed model. In experiments, a range of machine learning methods, autoregression models, and grey models are involved for comparisons to validate the feasibility and efficacy of the novel model, through the observations of the PPG in America and China. Finally, a superlative performance of the proposed model with the highest forecasting precision, small volatility of empirical results, and generalizability are confirmed by the aforementioned cases.

Predicting monthly natural gas production in China using a novel grey seasonal model with particle swarm optimization

Accurate prediction of short and medium-term monthly natural gas production in a country is the basis for understanding the supply capacity of natural gas in different months, and for the timely adjustment of natural gas production and import strategies. In China the monthly production of natural gas has obvious seasonal and cyclical variations, thus the use of a traditional grey prediction model is not very effective. As a result, a novel grey seasonal model is proposed in this paper. This is the Particle swarm optimized Fractional-order-accumulation non-homogenous discrete grey Seasonal Model (PFSM(1,1) model). This model enhances the adaptability to seasonal fluctuation data in two ways: the seasonal adjustment of the original data, and improvement of model self-adaptability. We use monthly natural gas production data of China for the period 2013–2018 as samples to predict those for the period 2019–2023. To demonstrate the PFSM(1,1) model does indeed exhibit better predictive capability, we also use the Holt–Winters model and a seasonal GM(1,1) model to predict monthly natural gas production, and compare the results with the model proposed here. The prediction results show that monthly natural gas production in China will continue to increase throughout the 2019–2023 period, that the peak-to-valley differences in monthly production values will also increase, and that the seasonal variations in production will become increasingly pronounced. Moreover, although Chinese production of natural gas is increasing, it will still be difficult to meet future demand, and hence the gap between supply and demand will increase year by year. We conclude that China needs to develop a more complete import plan for gas to meet expected natural gas consumption.

Forecasting cocoa production of six major producers through ARIMA and grey models

PurposeIn the current study, two grey prediction models, Even GM (1, 1) and Non-homogeneous discrete grey model (NDGM), and ARIMA models are deployed to forecast cocoa bean production of the six major cocoa-producing countries. Furthermore, relying on Relative Growth Rate (RGR) and Doubling Time (Dt), production growth is analyzed.Design/methodology/approachThe secondary data were extracted from the United Nations Food and Agricultural Organization (FAO) database. Grey forecasting models are applied using the data covering 2008 to 2017 as their performance on the small sample size is well-recognized. The models' performance was estimated through MAPE, MAE and RMSE.FindingsResults show the two grey models fell below 10% of MAPE confirming their high accuracy and forecasting performance against that of the ARIMA. Therefore, the suitability of grey models for the cocoa production forecast is established. Findings also revealed that cocoa production in Côte d'Ivoire, Cameroon, Ghana and Brazil is likely to experience a rise with a growth rate of 2.52, 2.49, 2.45 and 2.72% by 2030, respectively. However, Nigeria and Indonesia are likely to experience a decrease with a growth rate of 2.25 and 2.21%, respectively.Practical implicationsFor a sustainable cocoa industry, stakeholders should investigate the decline in production despite the implementation of advanced agricultural mechanization in cocoa farming, which goes further to put food security at risk.Originality/valueThe study presents a pioneering attempt of using grey forecasting models to predict cocoa production.

Forecasting the non-renewable energy consumption by an adjacent accumulation grey model

This paper proposes an adjacent accumulation discrete grey model to enhance the prediction accuracy of grey model and improve the utilization of new data. The stability of the proposed model is proved and the new model can obtain higher prediction accuracy through three cases. And it was applied to the prediction of the non-renewable energy consumption in Asia-Pacific Economic Cooperation. It proves that discrete grey model with adjacent accumulation is effective. According to the forecasting results, the oil consumptions in 15 countries have an increasing trend. The coal consumptions of five countries (South Korea, Indonesia, Vietnam, Malaysia and the Philippines) show a clear growth trend and The United States, Canada and Australia all show a downward trend. The consumptions of natural gas in the United States, Mexico, Singapore, China, Vietnam and Peru will all increase. For nuclear energy, China’s consumption will increase and South Korea’s consumption will decrease.

A novel discrete grey seasonal model and its applications

In order to accurately describe real systems with seasonal disturbances, which normally appear monthly or quarterly cycles, a novel discrete grey seasonal model, abbreviated as DGSM(1, 1), is put forward by incorporating the seasonal dummy variables into the conventional model. Moreover, the mechanism and properties of this proposed model are discussed in depth, revealing the inherent differences from the existing seasonal grey models. For validation and explanation purposes, the proposed model is implemented to describe three actual cases with monthly and quarterly seasonal fluctuations (quarterly wind power production, quarterly PM10, and monthly natural gas consumption), in comparison with five competing models involving grey prediction models, conventional econometric technology, and artificial intelligences. Experimental results from the cases consistently demonstrate that the proposed model significantly outperforms the other benchmark models in terms of several error criteria. Moreover, further discussions about the influences of different sequence lengths on the forecasting performance reveal that the proposed model still performs the best with strong robustness and high reliability in addressing seasonal sequences. In general, the new model is validated to be a powerful and promising methodology for handling sequences with seasonal fluctuations.

A novel discrete grey Riccati model and its application

PurposeTo develop the theory and application of the grey prediction model, this investigation constructs a novel discrete grey Riccati model termed DGRM(1,1).Design/methodology/approachBy examining a special kind of Riccati difference equation and the structure of the conventional discrete grey model (DGM), we advance a novel DGRM, and the model's prediction effect is evaluated by two numerical examples and an application case and compared with that of other conventional grey models.FindingsThe average relative simulation error of DGRM(1,1) does not change if the model is built after the original sequence has been transformed by a multiplier, and the new model is suitable to predict monotonically increasing, monotonically decreasing and unimodal sequences.Practical implicationsDGRM(1,1) is utilized to forecast the development cost of a small plane owned by the Aviation Industry Corporation of China (AVIC) with an original data sequence from 2006 to 2013. The outcomes indicate that DGRM(1,1) exhibits high precision and potential in development cost prediction.Originality/valueCombining the Riccati difference equation with the conventional DGM, the author advances a new grey model that is suitable to predict three kinds of data series with different changing trends.

Will China Achieve Its Ambitious Goal?—Forecasting the CO2 Emission Intensity of China towards 2030

China has set out an ambitious target of emission abatement; that is, a 60–65% reduction in CO2 emission intensity by 2030 compared with the 2005 baseline level and emission peak realisation. This paper aimed to forecast whether China can fulfil the reduction target of CO2 emission intensity and peak by 2030 based on the historical time series data from 1990 to 2018. Four different forecasting techniques were used to improve the accuracy of the forecasting results: the autoregressive integrated moving average (ARIMA) model and three grey system-based models, including the traditional grey model (1,1), the discrete grey model (DGM) and the rolling DGM. The behaviours of these techniques were compared and validated in the forecasting comparisons. The forecasting performance of the four forecasting models was good considering the minimum mean absolute percentage error (MAPE), demonstrating MAPE values lower than 2%. ARIMA showed the best forecasting performance over the historical period with a MAPE value of 0.60%. The forecasting results of ARIMA indicate that China would not achieve sufficient reductions despite its projected emission peak of 96.3 hundred million tons by 2021. That is, the CO2 emission intensity of China will be reduced by 57.65% in 2030 compared with the 2005 levels. This reduction is lower than the government goal of 60–65%. This paper presents pragmatic recommendations for effective emission intensity reduction to ensure the achievements of the claimed policy goals.

Future of quality management system (ISO 9001) certification: novel grey forecasting approach

Regarded as one of the most effective tools to guide quality systems management, ISO 9001 is a valuable certification. Yet, the growth observed throughout the world by this standard provides a strong polarisation of interest in this practice by the companies. Our research goals are to analyze and forecast trends involving ISO 9001 certification of six countries, China, Italy, Germany, Japan, the United Kingdom, and India. We gathered ISO 9001 countrywide certification data over nine years from 2018 to 2026. The methods used in this study include Even GM (1, 1), Discrete GM (1, 1) and Non-homogeneous discrete grey model (NDGM) with an accompanying synthetic growth rate and synthetic doubling time grey models to investigate the comparison among these countries. The result reveals that Germany will likely continue to lead ISO 9001 certifications at a country level through 2026. We also find that Japan and UK required more time for ISO 9001 certification to double than other countries. Our forecasting of the uptake of the ISO 9001 standard is significant for the certification bodies to understand market diffusion and trends. Implications include this study providing valuable policy guidelines for decision-makers, and new opportunities for further research for scholars.

Forecasting Pakistan's electricity based on improved discrete grey polynomial model

PurposeElectricity plays an important role in the economic condition of any country. Nowadays, Pakistan is badly affected by shortage of electricity, which directly affected the economic growth of state. The purpose of this study is to propose an improved grey model DGPM(1,1,N) to forecast Pakistan's production of electricity, installed capacity and consumption.Design/methodology/approachTo significantly simulate and predict accuracy, the discrete grey polynomial model DGPM(1,1,N) is improved with new information priority accumulation. The particle swarm optimization (PSO) algorithm is used for parameter optimization. The value of parameter is adjusted into improved grey model. By adjusting the parameter value in the model, the accuracy of prediction is enhanced.FindingsThe installed capacity of electricity needs more attention to improvement through implementation of effective polices, resolving major issues and funding scheme to fulfill the electricity demand of country. And improved DGPM(1,1,N) has better accuracy than original DGPM(1,1,N), DGM(1,1), nongrey models, linear regression and Holt–Winters methods.Practical implicationsThis paper provides a practical and efficient improved grey method to predict the electricity production, consumption and installed capacity in Pakistan. This research and suggestion will help Pakistani government to formulate better policies to decrease the consumption of electricity and increase the installed capacity of electricity.Originality/valueThis paper not only improves the grey model with accumulation generation operator but also forecasts Pakistan's electricity production, installed capacity and consumption. It is a new idea to predict the installed capacity of electricity and the findings provide suggestions for the government to make policies.

An Improved Nonhomogeneous Discrete Grey Model and Its Application

In recent years, the nonhomogeneous grey model has received much attention owing to its flexibility and applicability of forecasting small samples. To improve further the prediction accuracy of the nonhomogeneous grey model, this paper is to introduce a new whitening equation with variable coefficient into the original nonhomogeneous grey model, which is abbreviated as ONGM1,1,k,c. First of all, the detailed computational steps of the time response function of the novel model and the restored values of the raw data sequence are deduced through grey modelling techniques. Secondly, two empirical examples from the previous literature are conducted to prove the validity of the novel model. Finally, the novel model is applied to forecast natural gas demand of China, and the results show that the novel model has a better prediction performance compared with other commonly used grey models, including GM1,1, DGM1,1, NGM1,1,k,c, and NGBM1,1.

Application of a novel discrete grey model for forecasting natural gas consumption: A case study of Jiangsu Province in China

Natural gas increasingly has become an alternative low-carbon energy source for governments to modify the energy mix and fulfill the commitments that mitigate greenhouse gas emissions. Predicting natural gas consumption therefore is becoming crucial in such situations. In order to obtain accurate forecasts of natural gas consumption, this study has designed a novel discrete grey model considering nonlinearity and fluctuation, which can overcome the inherent drawbacks of the traditional discrete grey model and its optimized variants. Besides, to further enhance the forecasting performance of this proposed model, the Cultural Algorithm (CA) is employed to optimally determine the emerging parameters of this model. Subsequently, two empirical examples are provided for verifying the efficacy and reliability of the new model by comparing with other existing grey models and statistical models. Lastly, based on the original observations from 2005 to 2017, the novel model is built for predicting the total natural gas demand in Jiangsu province in China. The results indicate that the new model is much superior to other competitors, offering more accurate and reliable performances in the aspect of lower errors in both in-sample and out-of-sample forecasts. Then, based on the above projections, several main reasons for low gas consumption and reasonable suggestions are put forward for Jiangsu’s government, which has high potential to boost gas demand in the coming future.

Predict the particulate matter concentrations in 128 cities of China

To predict the concentrations of PM2.5 and PM10 in the 128 cities of China, the discrete gray prediction model with fractional order accumulation (DFGM(1,1)) was used to predict the annual average PM2.5 and PM10 concentrations from 2019 to 2023. The result is as following: the annual average PM2.5 concentrations of Xi’an, Xuzhou, Ordos, Jingmen, Meizhou, Huizhou, Panzhihua, Kunming, Jixi, and Yichun are increasing from 2019 to 2023. The annual average PM2.5 concentrations in the 118 other cities are decreasing from 2019 to 2023. While the annual average PM10 concentrations of Taiyuan, Ordos, Dongguan, Karamay, Foshan, Yichun, Qitaihe, Jinzhou, and Heihe are increasing from 2019 to 2023, the annual average PM10 concentrations in the 119 other cities are decreasing from 2019 to 2023.

Estimating Chinese energy-related CO2 emissions by employing a novel discrete grey prediction model

Under the background of green and low-carbon economy, comprehensively analyzing the influential factors and apply them to accurately estimate energy-related CO2 emissions make great sense for Chinese green-economy development. In this paper, the grey incidence analysis is employed to identify the influential factors that may generate strong and nonlinear effects on emissions. To consider these nonlinear effects, a new discrete grey power model is designed, through introducing grey power indexes into the model structure. Additionally, one-step ahead rolling mechanism is associated with the proposed technique so as to further improve its forecasting precision. To demonstrate its efficacy, the rolling discrete grey power model is utilized to forecast Chinese energy-related carbon emissions from 2011 to 2015, and then compared to projections provided by diversified competing techniques - the empirical applications show that the newly proposed rolling model clearly outperform other benchmark models in accordance with three measuring indices. Therefore, by using this optimum model, Chinese carbon emissions from 2016 to 2020 are quantified, which infers that it will rise to over 9936 million tons in 2020, and is consistent with those provided by other international agencies and scholars. Eventually, based on the forecasts, suggestions on reducing the CO2 emissions are provided for decision-makers.

Adaptive Edge Detection Algorithm Based on Improved Grey Prediction Model

Existing edge detection algorithms suffer from inefficient edge localization, noise sensitivity, and/or relatively poor automatic detection capability. Contemporary edge detection algorithms can be improved by targeting these problems to help bolster their performance. Grey system theory can be used to resolve the small data and poor information issues in the local information of uncertain systems. An automatic edge detection algorithm was developed in this study based on a grey prediction model to remedy these problems. Noise characteristics in grey images are used to deploy a noise-filtering algorithm based on local features. A mask with twenty-four edge direction information points (345°) was established based on edge line texture features. By compressing the amplitude of the sequence, the randomly oscillated grey prediction sequence can be converted into a smooth, new sequence. The discrete grey model (1,1) (DGM(1,1)) was established based on this new grey prediction sequence to obtain the grey prediction maximum value. A grey prediction image with enhanced edges was obtained by replacing the pixel value in the original image with the maximum grey prediction value. A grey prediction subtraction image with edges separated from non-edge points was also obtained by subtracting the original image from the grey prediction image. The optimal separation threshold in the grey prediction subtraction image can be determined via the global adaptive threshold selection method. The neighborhood search method was then deployed to remove stray points and burrs from the image after the target was separated from the background, creating the final edge image. Experiments were performed on a computer-simulated phantom to find that both the subjective visual effects and objective evaluation criteria are better under the proposed method than several other competitive methods. The proposed edge detection algorithm shows excellent edge detection ability and is highly robust to noise, though the grey prediction model needs further improvement to optimize the run time.

A Novel Discrete Grey Model and Its Application

This paper aims to further increase the prediction accuracy of the grey model based on the existing discrete grey model, DGM(1,1). Herein, we begin by studying the connection between forecasts and the first entry of the original series. The results comprehensively show that the forecasts are independent of the first entry in the original series. On this basis, an effective method of inserting an arbitrary number in front of the first item of the original series to extract messages is applied to produce a novel grey model, which is abbreviated as FDGM(1,1) for simplicity. Incidentally, the proposed model can even forecast future data using only three historical data. To demonstrate the effectiveness of the proposed model, two classical examples of the tensile strength and life of the product are employed in this paper. The numerical results indicate that FDGM(1,1) has a better prediction performance than most commonly used grey models.

Model comparison of GM(1,1) and DGM(1,1) based on Monte-Carlo simulation

Discrete grey model (DGM(1,1)) is considered to be superior to grey model (GM(1,1)) because it can completely simulate the pure exponential sequences. However, owing to practical data generation process is interfered by random factors, the superiority of DGM(1,1) model to GM(1,1) model cannot be widely and reliably validated in practical applications. Therefore, by utilizing the Monte-Carlo simulation method, groups of completely random sequences conforming to different distributions are randomly generated and the predictive capabilities of the two models are compared. In addition, the novel grey models of fractional order accumulation (FGM(1,1) and FDGM(1,1)) are introduced for further comparison. The results show that the predictive capabilities of the two models for random sequences conforming to normal distribution are nearly equivalent. However, the predictive capabilities of DGM(1,1) model for the other three kinds of random sequences are all superior to those of GM(1,1) model. The parameters change of completely random sequences influences the predictive capabilities of the two models. The parameters change of random sequences with exponential trend can influence the predictive capability of GM(1,1) model while has no significant influence on the predictive capability of DGM(1,1) model.

Forecasting Nitrous Oxide emissions based on grey system models.

Accurate forecasting is required to measure future national energy performance levels in order to establish clear policies for both monitoring and reducing Nitrous Oxide and other harmful emissions. Using the well-established and accepted measures, we predict the Nitrous Oxide emissions for the year 2030 based on actual data from the years 2000 to 2016 for six countries responsible for 61% of global emissions (China, Indonesia, India, Japan, Russia and the USA). Three advanced mathematical grey predictions models were employed, namely the Even Grey Model (1, 1), the Discrete Grey Model (1, 1) and the Non-homogeneous Discrete Grey Model, which is capable of working with poor or limited data. Results showed that the Non-homogeneous Discrete Grey Model was a better fit and proved more effective in forecasting Nitrous Oxide emissions because it produced the lowest mean absolute percentage error for all countries when compared to the Even Grey Model (1, 1) and the Discrete Grey Model (1, 1). The mean absolute percentage error of the Even Grey Model (1, 1) was 2.4%, that of the Discrete Grey Model (1, 1) was 2.16%, and that of the Non-homogeneous Discrete Grey Model was 1.9%. Furthermore, the results show that China has the highest Nitrous Oxide emissions during the years studied (China 20,578,144, Russia 1,705,110, India 7,806,137, Indonesia 3,405,389, USA 8,891,219 and Japan 780,118). This study also suggests some implications for both academicians and practitioners in respect of reducing Nitrous Oxide emission levels.

A novel GREY‒ASMAA model for reliability growth evaluation in the large civil aircraft test flight phase

PurposeThe purpose of this paper is to present a novel GREY‒ASMAA model for reliability growth evaluation in the large civil aircraft test flight phase.Design/methodology/approachAs limited data are collected during the large civil aircraft test flight phase, which are not enough to meet the requirements of the ASMAA model for reliability growth, four basic GM(1, 1) models, even grey model, original difference grey model, even difference grey model and discrete grey model, are presented. Then both forward and backward grey models GM(1,1) are built to forecast and obtain virtual test data on left and right sides. Then the ASMAA model for reliability growth evaluation can be built based on original and virtual test data.FindingsAiming at the background of poor information data during the large civil aircraft test flight phase, first, a novel GREY‒ASMAA model, which was combined by the grey model GM(1,1) with the ASMAA model, has been put forward in this paper.Practical implicationsThe GREY‒ASMAA model for reliability growth evaluation can be used to solve the problem of reliability growth evaluation with poor information data during the large civil aircraft test flight phase, and it has been used in reliability evaluation of C919 at the test flight stage.Originality/valueThis paper presents two new definitions of forward grey model GM(1,1) and backward grey model GM(1,1), as well as a novel GREY‒ASMAA model for reliability growth evaluation of large civil aircraft during test flight phase.