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This study considers an application of the first-order Grey Markov Model to foresee the values of Italian power generation in relation to the available energy sources. The model is used to fit data from the Italian energy system from 2000 to 2022. The integration of Markovian error introduces a random element to the model, which is able now to capture inherent uncertainties and misalignments between the Grey Model predictions and the real data. This application provides valuable insights for strategic planning in the energy sector and future developments. The results show good accuracy of the predictions, which could provide powerful information for the effective implementation of energy policies concerning the evolution of energy demand in the country. Results show an improvement in the performance of more than 50% in terms of Root Mean Squared Error (RMSE) when the Markov chain is integrated in the analysis. Despite advancements, Italy's 2032 energy mix will still significantly rely on fossil fuels, emphasizing the need for sustained efforts beyond 2032 to enhance sustainability. [ABSTRACT FROM AUTHOR]

The reliability of machine tool components, particularly the tool magazine manipulator, significantly affects the overall performance of the machine tool. To address the challenge of accurately evaluating the manipulator's health status using a single performance indicator, this study proposes a method that combines Fuzzy Comprehensive Evaluation (FCE) and a Combined Weighting Method (CWM). By considering both subjective and objective factors, this method provides a comprehensive evaluation of the manipulator's health status, enhancing the accuracy and reliability of the assessment. The method utilizes fuzzy distribution to construct membership matrices for different health levels and adopts the CWM that combines the Entropy Weight Method (EWM) and Analytic Hierarchy Process (AHP) to determine the combined weights of the health evaluation indices. This approach improves the accuracy and reliability by considering multiple indicators and objectively weighting them based on their importance. The current health status of the manipulator is evaluated using the fuzzy weighted average operator and the maximum membership principle. Moreover, a fault prediction method based on Particle Swarm Optimization (PSO) and GM(1,1) is proposed to overcome the information gap and small sample problems. The proposed model's prediction accuracy is verified by comparing it with other models, demonstrating its effectiveness and reliability. [ABSTRACT FROM AUTHOR]

International students play a crucial role in China's talent development strategy. Thus, predicting overseas talent mobility is essential for formulating scientifically reasonable talent introduction policies, optimizing talent cultivation systems, and fostering international talent cooperation. In this study, we proposed a novel fractional-order grey model based on the Multi-Layer Perceptron (MLP) and Grey Wolf Optimizer (GWO) algorithm to forecast the movement of overseas talent, namely MGDFGM(1,1). Compared to the traditional grey model FGM(1,1), which utilizes the same fractional order at all time points, the proposed MGDFGM(1,1) model dynamically adjusts the fractional-order values based on the time point. This dynamic adjustment enables our model to better capture the changing trends in the data, thereby enhancing the model's fitting capability. To validate the effectiveness of the MGDFGM(1,1) model, we primarily utilize Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) as the evaluation criteria for the prediction accuracy, as well as standard deviation (STD) as an indicator of the model stability. Furthermore, we perform experimental analysis to evaluate the predictive performance of the MGDFGM(1,1) model in comparison to NAÏVE, ARIMA, GM(1,1), FGM(1,1), LSSVR, MLP, and LSTM. The research findings demonstrate that the MGDFGM(1,1) model achieves a remarkably high level of prediction accuracy and stability for forecasting overseas talent mobility in China. The implications of this study offer valuable insights and assistance to government departments involved in overseas talent management. [ABSTRACT FROM AUTHOR]

Accurate forecasting of the enrollment scale of higher education and education expenditure is the key to scientific decision-making in education. Nevertheless, education data sets are usually small and affected by uncertainties including economy, education system policies, and so on, which result in difficulty in modeling. To address the tissues, we presented a novel time-delayed grey model based on a fractional-order accumulation time term, abbreviated as FHTDGM. The hyperparameters of the model are optimized using the particle swarm optimization. The experiment's results show that the FHTDGM model can fit and forecast enrollment scale and educational spending data with greater accuracy than a group of other grey models, and the forecast MAPEs are 2.396 and 1.244, respectively. The accurate prediction contributes to constructive suggestions for the decision-making of education. [ABSTRACT FROM AUTHOR]

Missing data presents a significant challenge when forecasting unknown data in lime series. To address this issue. this paper proposes an Altenuated Long and Short-Term Memory model based on a dec·aying filliction, which is abbreviated as A D-LSTM, for forecasting unknown data in time series. As strong correlations exist in adjacent data, the Grey model is level·aged to predict and impute missing values in small-sample datasets. To improve the accuracy offorecasting in time series with missing data, we introduce subspace decomposition, which can correct errors in the memory state cell caused by missing elements, and a time decay function, which utilizes the number of adjacent continuous missing data as a weight to modify the memory cell and enables the model to detect the existence of missing elements, into the LSTM unit. These enhancements reduce the impact of imptited data on model training in time series analysis. Finally, to verify the effectiveness of our proposed method, we conduct experimental validation and comparative analysis using the Beijing house price dataset. Our results indicate that the AD-LSTM model perfbrnis better in reducing the impact of missing data and achieving lower fbrecast ert·ors compared to the baseline models. [ABSTRACT FROM AUTHOR]

To improve the performance of the conventional grey model, emphasis should be based on the “new information prior using” principle. This paper presents detailed work on improving the precision of the conventional grey model by combining a data grouping technique with modification of initial condition to establish an optimized grey model. The data grouping technique and modification of initial condition methods have the advantage of adhering to the “new information prior using” principle. An empirical example of short-term traffic flow forecasting shows that the proposed optimized grey model, that is the modified initial condition grouped grey model, outperforms the existing models in both fitting and short-term forecasting. Moreover, the results demonstrate our claim that the distribution characteristic of the fitting error influences future short-term forecast accuracy. Now the proposed model can be of help in intelligent transportation systems for optimizing the use of existing infrastructure to enhance urban transportation systems in averting issues such as traffic congestion.

Energy is an important denominator for evaluating the development of any country. Energy consumption, energy production and steps towards obtaining green energy are important factors for sustainable development. With the advent of forecasting technologies, these factors can be accessed earlier, and the planning path for sustainable development can be chalked out. Forecasting technologies pertaining to grey systems are in the spotlight due to the fact that they do not require many data points. In this work, an optimized model with grey machine learning architecture of a polynomial realization was employed to predict power generation, power consumption and CO 2 emissions. A nonlinear kernel was taken and optimized with a recently published algorithm, the augmented crow search algorithm (ACSA), for prediction. It was found that as compared to conventional grey models, the proposed framework yields better results in terms of accuracy. [ABSTRACT FROM AUTHOR]

To improve the performance of the conventional grey model, emphasis should be based on the "new information prior using" principle. This paper presents detailed work on improving the precision of the conventional grey model by combining a data grouping technique with modification of initial condition to establish an optimized grey model. The data grouping technique and modification of initial condition methods have the advantage of adhering to the "new information prior using" principle. An empirical example of short-term traffic flow forecasting shows that the proposed optimized grey model, that is the modified initial condition grouped grey model, outperforms the existing models in both fitting and short-term forecasting. Moreover, the results demonstrate our claim that the distribution characteristic of the fitting error influences future short-term forecast accuracy. Now the proposed model can be of help in intelligent transportation systems for optimizing the use of existing infrastructure to enhance urban transportation systems in averting issues such as traffic congestion. [ABSTRACT FROM AUTHOR]

Based on particle swarm optimization (PSO), a new exponential time delay fraction order grey prediction model is proposed in this paper. Firstly, the original data is preprocessed by fractional-order accumulation; on the basis of fractional-order accumulation, it is proved that the initial value of the original sequence satisfies the fixed point theorem. On the basis of GM(1,1) model, a new model is established by adding exponential time delay term. The model is discretized by integral, the least square estimation of the linear parameters and the approximate time response equation are obtained. Finally, PSO is used to search the optimal parameters of the model and the experimental results are verified by Wilcoxon rank sum test. In order to test the good adaptability and strong prediction ability of the new model, two groups of data are verified for the production and consumption of oil and electricity in China. The results show that the new model has better prediction accuracy and adaptability than the other existing six grey models. [ABSTRACT FROM AUTHOR]

It is possible to determine a country's resilience or vulnerability to risks likely to affect the energy sector with the effect of internal or external dynamics by measuring accurately the concept of energy supply security, which is one of the important agendas of countries. Since the concept in question is affected by many factors, it should be handled in a versatile way in the analysis. Therefore, in this study, the energy supply security risk of Turkey was firstly calculated by taking into account the country diversity in imported energy supply. Afterwards, the index values calculated for the period 1990-2020 were modeled with grey models augmented with trigonometric functions. Four different grey models proposed according to two different approaches were used in the analyses. Using the best model determined, forecasts were made for the energy supply security risk of Turkey for the 2021-2023 period. The results show that the energy supply security risk will increase in 2021 compared to 2020, decrease in 2022 compared to the previous two years, and in 2023 it will be at the highest level compared to the last three years. [ABSTRACT FROM AUTHOR]

The accurate prediction of industrial power consumption is conducive to the effective allocation of power resources by power and energy institutions, and it is also of great significance for the construction and planning of the national grid. By analyzing the characteristics of the data of Suzhou's industrial power consumption between 2003 and 2005, this paper proposes a grey model with a seasonal index adjustment to predict industrial power consumption. The model results are compared with the traditional grey model, as well as the real value of Suzhou's industrial power consumption, which shows that our model is more suitable for the prediction of industrial power consumption. The lasted Suzhou's industrial power consumption data, from 2019–2021, are also investigated, and the results show that the prediction results are in very good agreement with the real data. The highlights of the paper are that all precision inspection indexes are excellent and the seasonal fluctuations in the data changes can be reflected in the present model. [ABSTRACT FROM AUTHOR]

Greenhouse gas emissions have brought a serious challenge to the global environment and climate. Efficient and accurate prediction of carbon emissions is essential for the decision-making sectors to control growth and formulate policies. Firstly, considering the economic, demographic, and energy factors, a novel nonlinear multivariate grey model (ENGM(1,4)) based on environmental Kuznets curve (EKC) is proposed with respect to the data characteristics of the incomplete information of carbon emission of transportation sector. The model integrates the IPAT ("Influence = Population, Affluence, Technology") equation and the extended atochastic impacts by regression on population, affluence, and technology model (STIRPAT). Secondly, the derivation method is used to solve the time response equation of the model and the quantum particle swarm optimization algorithm (QPSO) is designed to optimize the model parameters. Then, 18 years of carbon emission data from China, the USA, and Japan are selected as the validation set. Comparative analysis indicates that the prediction accuracy of the statistical models and the intelligent models depends on sufficient samples and complex variables, and has certain limitations in limited sample prediction. The calculation results show that the new model outperforms other models in various evaluation indicators, indicating that its prediction accuracy is higher. Finally, the projections show that in 2019–2025, the average increase in carbon emissions from the transport sector in China and the USA was 2.837% and 2.394%, respectively, while Japan shows a downward trend with an average decline rate of 1.2231%. The analyzed prediction results are consistent with current situation of the three countries and the transport sectors, demonstrating the high accuracy and reliability of the new model. [ABSTRACT FROM AUTHOR]

Energy is an important denominator for evaluating the development of any country. Energy consumption, energy production and steps towards obtaining green energy are important factors for sustainable development. With the advent of forecasting technologies, these factors can be accessed earlier, and the planning path for sustainable development can be chalked out. Forecasting technologies pertaining to grey systems are in the spotlight due to the fact that they do not require many data points. In this work, an optimized model with grey machine learning architecture of a polynomial realization was employed to predict power generation, power consumption and CO2 emissions. A nonlinear kernel was taken and optimized with a recently published algorithm, the augmented crow search algorithm (ACSA), for prediction. It was found that as compared to conventional grey models, the proposed framework yields better results in terms of accuracy.

Forecasting is one of the activities companies need to determine the policies that need to be taken for the continuity of operations. There are many methods for forecasting, one of which is the grey model GM(1,1). The GM(1,1) is one of the successful forecasting methods applied to economics, finance, engineering, and others. However, according to several previous studies, the GM(1,1) is not good enough to forecast data containing seasonal characteristics. Therefore, this study aims to develop a hybrid model so that the GM(1,1) can forecast seasonal time series. The hybrid model combines the decomposition method for seasonality adjustment and the grey model GM(1,1) for forecasting seasonal time series. The results are compared to the seasonal grey model SGM(1,1). Based on the evaluation using error criteria, it is found that the hybrid model is the best. [ABSTRACT FROM AUTHOR]

The reliability prediction of gearbox is a complex and challenging topic. The purpose of this research is to propose a hybrid difference iterative forecasting model to forecast reliability of the gearbox. On this score, a hybrid model based on the fractional Lévy stable motion (fLsm), the Grey Model (GM) and the metabolism method is proposed. To solve the problem of insensitivity to weak faults inside the gearbox, we use feature extraction method to reveal the gearbox degradation. Then, the least square theory is used to separate the degradation sequence in the gearbox into a deterministic term with monotonicity and a stochastic term with Long-Range Dependence (LRD). Next, the fLsm with LRD and non-Gaussian is used to forecast the stochastic term, the deterministic term is simulated by the GM, and the hybrid forecasting model is used to modify the prediction results. The metabolism method is used to update the degradation sequence and to forecast longer-term trend. Finally, a case demonstrated that superiority and generality of the hybrid forecasting model. • A new forecasting model is proposed based on long-range dependence and grey model. • The stochastic and deterministic of gearbox degradation are separately predicted. • The fractional Lévy stable motion have LRD, heavy tail and non-Gaussian. • The metabolic method is used to iterative forecasting the longer-term degradation. [ABSTRACT FROM AUTHOR]

With the manufacturing reshoring to the US, increasing attention are focus on its energy consumption and environmental effects and accurate prediction of carbon emissions is vital to controlling growth from the source. Considering the slowing growth in carbon emissions with the Gompertz's law, this paper establishes a Gompertz differential equation. According to the differential information principle and fractional accumulation operator, this differential equation is transformed into a fractional accumulation grey Gompertz model. Furthermore, the chaotic whale optimization algorithm is used to optimize the order of accumulation generation and the grey background value in the proposed model. Then the Gompertz's datasets and six validation cases about carbon emissions are used to show that the proposed model demonstrates better accuracy in all cases and efficiency in the carbon emissions forecasting with several existing models. Three case studies indicate that the proposed model can fit the trend of American industrial carbon emissions better. The model results also reveal the recent policy changes have promoted the uptrend of the industrial and the total carbon emissions in the U.S. The future forecasting suggests that U.S. carbon emission is estimated to be 17.01% (in total emissions) or 17.89% (in industrial emission) percent below 2005 levels by 2025 under current policies, falling short of its commitment submitted to the United Nations Framework Convention on Climate Change. [Display omitted] • This paper discussed the Gompertz's law in carbon emissions. • A FAGGM(1,1) model is created for predicting carbon emissions. • The case study reveals the rising of peak in the industrial carbon emission in U.S. • The reduction percentage of carbon emission on 2005 levels by 2025 will be 17.01% (in total), 17.89% (in industry) and 26.23% (in commerce) in U.S. [ABSTRACT FROM AUTHOR]

• Based on the derivation method, a new derived grey multi-parameter prediction model (DMGM (1, n)) is proposed. • The mathematical analysis is used to discuss the main reason why DMGM (1, n) is superior to GMC (1, n). • DMGM (1, n) outperforms the other grey multivariable models by comparing the results of these models in three cases. In this study, in order to reduce the morbidity and improve the structural stability of the existing grey multivariable convolution forecasting model, a new derived multivariable grey model based on the derivation method, abbreviated as DMGM (1, n), is presented. Firstly, the time response formula of DMGM (1, n) is deduced by derivation method, which can avoid solving the inverse matrix so as to reduce the morbidity of the model. Secondly, the parameter identification of the model is given based on the least-squares method. Then, it is proved theoretically that DMGM (1, n) is superior to GMC (1, n) because the solution of the former overcomes the shortcoming of the latter that the original model does not take full advantage of all the information from the raw data for modeling. Finally, three real cases with different variables were performed. The fitting and prediction results indicate that DMGM (1, n) is better than GMC (1, n) and the other multivariate grey prediction models in these cases, which also demonstrates that this novel model outperforms the other grey models in this paper. [ABSTRACT FROM AUTHOR]

Time series modelling is gaining spectacular popularity in the prediction process of decision making, with applications including real-world management and engineering. However, for short time series, prediction has to face unavoidable limitation for modelling extremely complex systems. It has to apply inadequate and incomplete data from short time to predict unknown observations. With such limited data source, existing techniques, such as statistical modelling or machine learning methods, fail to predict short time series effectively. To address this problem, this paper provides a global framework for short time series modelling predictions, integrating the rolling mechanism, grey model, and meta-heuristic optimization algorithms. In addition, dragonfly algorithm and whale optimization algorithm are investigated and deployed to optimize the framework by enhancing its predicting accuracy with less computational costs. To verify the performance of the proposed framework, three industrial cases are introduced as simulation experiments in this paper. Experimental results confirm that the framework solves corresponding short time series modelling predictions with greater accuracy and speed than the standard GM(1,1) models. The source codes of this framework are available at: https://github.com/zhesencui/HybridRollingGreyFramework.git. [ABSTRACT FROM AUTHOR]

For the purpose of exploring the long-term variation of regional sea surface temperature (SST), this paper studies the historical SST in regional sea areas and the emission pattern of greenhouse gases, proposing a Grey model of regional SST atmospheric reflection which can be used to predict SST variation in a long time span. By studying the Grey systematic relationship between historical SST data, the model obtains the development law of temperature variation, and further introduces different greenhouse gas emission scenarios in the future as the indexes coefficient to determine the corresponding changing results of seawater temperature in the next 50 years. Taking the North Atlantic Ocean as an example, the cosine similarity test method is used to verify the model proposed in this paper. The accuracy of the model is as high as 0.99984. The model predicts that the regional SST could reach a maximum of 15.3 ∘ C by 2070. This model is easy to calculate, with advantages of the high accuracy and good robustness. [ABSTRACT FROM AUTHOR]

The stock market is an important embodiment of a national economy and financial activities and has an important impact on a country, enterprises and individuals. Stock forecasting can allow investment institutions and investors to understand the trend of the stock market in advance, which is a challenging and meaningful study. First, through the impulse phenomenon of the stock market, this paper discusses the problem of stock price prediction with delay, and the impulse delay differential equation is established. Second, according to the difference between the differential and the difference, the nonlinear delay grey prediction model is established. Next, the model parameters are estimated and the solving steps are obtained. The nonlinear parameters and delay time are optimized by the particle swarm optimization algorithm. Finally, the new model is applied to the prediction of the Shanghai stock market and the Shenzhen stock market closing indexes; the results show that the new model can effectively predict stock prices, which is much better than the existing four grey models and a time series model. [ABSTRACT FROM AUTHOR]

Rainfall is the main source of water in India. Management of water and utilisation for various purposes is based upon its availability. Rainfall is the main component of any hydrological process and a key input factor for any rainfall-runoff model. Rainfall forecasting plays a major role to forecast the floods in advance with sufficient lead time. The accuracy of simulation of flow depends on the precision of rainfall data. Grey theory is widely used for forecasting in the field of hydrology. Grey model better handles the random and insufficient data. Adaptive grey model is an advancement of grey model where the trend of data set is considered. As rainfall is highly random, accurate and realistic forecasts are made with the knowledge of trends and patterns of the measured data. Hence, the adaptive grey model is used in this study to forecast the rainfall using previously measured rainfall. The model is applied to 15 storm events of Peechara watershed, Telangana, India. Both the individual and cumulative rainfall is considered in forecasting and the results showed the models' performance better by considering cumulative rainfall. The performance of the model is tested using Nash–Sutcliffe Efficiency (E), Root Mean Square Error (RMSE) and Correlation Coefficient (CC). It is observed that E >0.85, RMSE <0.2 and CC >0.9 for all the events in the watershed. The results obtained from this research work are quite significant and very much useful for flow forecasting in the watersheds. [ABSTRACT FROM AUTHOR]

The structure of energy production is constantly evolving, particularly in a low-carbon context, to align with the development of various industries. To pursue the global goal of carbon neutrality, it is essential to strike a balance between traditional energy and clean energy. Thus, it is of great practical significance to forecast different energy production effectively. Firstly, this paper proposes a novel local grey forecasting model to predict different energy production. Energy production has fluctuated in the past few years due to government policies. Secondly, the novel local grey forecasting model focuses on each year's production in the modeling process and uses a kernel function to measure the validity of the information. Meanwhile, different from other grey models, the dynamic model proposed makes it possible that there are no static parameters for the overall prediction. Then, the window width in the local model is determined using the particle swarm optimization algorithm. Furthermore, energy production prediction including traditional energy and clean energy production in total North America, Europe and Asia Pacific is conducted. Results show that the novel local grey model has satisfactory prediction accuracy compared with other models, whose MAPEs have controlled under 5% for different energy production. Finally, reasonable suggestions for energy production are proposed to meet various energy needs. [ABSTRACT FROM AUTHOR]

The coordinated development of the regional water-energy nexus is important for the rational utilization of resources. This study proposed an integrated assessment and prediction approach of the water-energy nexus at the provincial scale, focusing on Inner Mongolia, China as a case study. A comprehensive and objective water-energy nexus evaluation index system was constructed. The coupling coordination degree (CCD) model, which measures the coordination between water and energy, and the grey model (GM(1,1)), which is used to predict the trends of the water-energy nexus, were used to explore coordination now and in the future. The results showed that the coupling degree (CD) of the water-energy nexus in Inner Mongolia had remained high at above 0.9 from 2007 to 2019, which was a high-level coupling. The CCD of the water-energy nexus showed a steady increasing trend from 0.57 to 0.76 and will continue to increase in the coming years. This study recommends continuously increasing monitoring of water and energy and increased focus on the coordinated development of water and energy. The results of this study can act as a reference for the coordinated development of the provincial water-energy systems and can guide research approaches for studying the water-energy nexus. • An integrated assessment and prediction approach of water-energy nexus was proposed. • The coordination relationship between water and energy systems was discussed. • The coupling coordination degree ranged from barely to intermediate. • There was a linear increase in coupling coordination degree prediction. • Ecological water use and energy use in the tertiary should be increased. [ABSTRACT FROM AUTHOR]

To improve the prediction accuracy of Chinese grain yield, a hybrid metabolic grey forecasting model based on the weighted Markov method is proposed. Since the grain yield is affected by many uncertain factors, the grain yield is predicted by the error amended metabolism grey model. Later, considering that the grain yield is also affected by the outputs over the years, the state transition probability matrixes are calculated, and the yield influence weights of the past years are decided. Lastly, combining the predicted yield and the influence weights, the final yield is corrected by recent years' yields, and the metabolic grey model is constructed. By using above procedures, the yields of 2016 to 2020 are predicted based on the data of2005-2015, the results show that the forecasting error is less than 2% for al! predicted years, and the mean error for 5 years achieves to 1.04%, which can be used to predict the grain yield accurately in the medium and short term. [ABSTRACT FROM AUTHOR]

Energy saving and emission reduction are the most concerned issues in the world. Objective and accurate prediction of carbon emissions can provide reference and early warning for the implementation of the government's environmental strategy. Based on the traditional grey Verhulst model, this paper analyzes the main causes of its errors, introduces the extrapolation method to optimize the background value, and uses particle swarm optimization algorithm to optimize its parameters. In order to evaluate the performance of the models, six commonly statistical evaluation indicators are used to compare the new model with other optimization models and grey universal models, and the effect of the new model is basically better than other models. Finally, it is applied to the prediction of carbon dioxide emission of three kinds of coal in China. The results show that the increase of carbon dioxide related to raw coal slows down in 2016–2020, while the increase of carbon dioxide related to clean coal and other washed coal is 12.7097% and 19.2024%, respectively. Therefore, in order to prevent a strong rebound in carbon emissions, China should increase efforts to save energy and reduce emissions, and reduce energy consumption, especially coal consumption. [ABSTRACT FROM AUTHOR]

Precious metal recovery is the main economic power of electronic waste (e-waste) recovery. The prediction of e-waste and its precious metal content is of great significance to the realisation of China's circular economy. In this work, the generation mechanism of e-waste is firstly deduced to determine model characteristics suitable for its prediction. Fractional derivative grey models base on a weak singular power kernel function (PFGM(q ,1)) and a non-singular exponential kernel function (EFGM(q ,1)) are established. Compared with the PFGM(q ,1), the EFGM(q ,1) has the advantages of simpler solution, lower calculation complexity and wider scope of application. Next, some data are selected to verify the validity. The EFGM(q ,1) is used to predict mobile phone, laptop, desktop and television waste, and the weight of printed circuit boards (PCBs) in the waste and content of precious metals in these PCBs are calculated. Finally, the trend of e-waste and its precious metal contents are analysed and discussed based on the calculation results. • The kernel type of fractional derivative is considered when building model. • Two fractional derivative grey models are established. • The analytical solution of the novel models is obtained. • The EFGM(q,1) has the advantages of non-singularity, small computation. • The EFGM(q,1) can effectively predict the content of precious metals. [ABSTRACT FROM AUTHOR]

Water inflow from fault (WIF) and its secondary impacts are the main environmental challenges in the mining industry. Traditional prediction methods for WIF are exceedingly challenging and costly. In this article, two exponentially weighted moving average (EWMA) modified grey models (GMs, i.e., EGM and REGM) were established to predict the WIF. Particle swarm optimization (PSO) algorithm was employed to optimize parameters of the models. Based on actual WIF data from Buliangou coal mine, the optimized models (i.e., EGM-PSO, REGM-PSO) were used to obtain the prediction equations for WIF. To investigate the validity of the proposed models, the differences between actual values and predicted values were analyzed, and comparison results were obtained by the commonly used GM and GM-PSO. Results show that, for the sample with the larger initial particle swarm and smaller inertia weight, there is a faster convergence speed of the PSO algorithm. Particle search efficiency in the PSO-optimized EWMA-GM is higher than that in the GM-PSO. Through the predicted results of WIF, it is found that the REGM-PSO is the best choice for WIF prediction, and the more historical information, the higher the predicted accuracy. Besides, the parameter optimization by the PSO, the EWMA optimization method and optimization of residuals all can improve the predicted accuracy. Predicted results also show that WIF will have a substantial growth in the future. Therefore, reasonable measures (e.g., draining and grouting) need to be taken to mitigate the damage caused by fault water inflow. [ABSTRACT FROM AUTHOR]

The current study proposed the improved non-linear multi-variable Grey Bernoulli model and predicted the CO2 emissions in China. Firstly, the paper presents an improved multivariate grey Bernoulli model (INGBM(1, N)) that considers the nonlinearities of the system characteristic data and related factors in establishing the grey model. Secondly, the influence of the relevant factors on the grey model's forecast accuracy has been considered. The more the number of relevant factors, the higher the relative level with the system characteristic data, the higher the calculation accuracy. However, predictive accuracy began to decrease again after the number of relevant factors more than a specific value. Thirdly, we selected the number of relevant factors as 4 (coal energy consumption, urbanization rate, crude oil, population) and carried out compared analysis with other grey models and non-grey models. The results show that the proposed model has the best forecasting accuracy. The proposed model is a generalization of several other grey forecasting models. China's COz emissions for 2019-2021 is forecasted. It estimated that the value would continue to increase over the next three years and reach 9958.57Mt by 2021. Finally, several measures have briefly mentioned reducing COz emissions based on the influence of relevant factors. [ABSTRACT FROM AUTHOR]

This study presents a novel fractional order grey model FGM (α ,1) obtained by extending the grey model (GM (1,1)). For this, we generalize the whitenization first-order differential equation to fractional order by using the Caputo fractional derivative of order α. A real-world case study, scrutinize the economic growth influence on environmental degradation in Turkey, is performed to evaluate the significance of the projected model FGM (α ,1) in contrast to the current classical GM. We apply autoregressive distributed lags bounds testing co-integration approach to empirically examine the long-run and short-run relation among economic growth, agriculture, forestry and fishing (AFF), electricity utilization and CO2 emissions. Using the new fractional order model, all the variables are forecasted in the forthcoming years until 2030. Findings disclose that electricity utilization and economic growth (GDP) accelerate emission of CO2 though in the long run agriculture, forestry, and fishing reduce the environmental pollution in Turkey. [ABSTRACT FROM AUTHOR]

In this work, a novel diagnostic and prognostic framework is proposed to detect faults and predict remaining service life of large-scale rotating machinery in the presence of scarce failure data. In the proposed framework, a canonical variate residuals–based diagnostic method is developed to facilitate remaining service life prediction by continuously implementing detection of the prediction start time. A novel two-step prognostic feature exploring approach that involves fault identification, feature extraction, feature selection and multi-feature fusion is put forward. Most existing prognostic methods lack a fault-identification module to automatically identify the fault root-cause variables required in the subsequent prognostic analysis and decision-making process. The proposed prognostic feature exploring method overcomes this challenge by introducing a canonical variate residuals–based fault-identification method. With this method, the most representative degradation features are extracted from only the fault root-cause variables, thereby facilitating machinery prognostics by ensuring accurate estimates. Its effectiveness is demonstrated for slow involving faults in two case studies of an operational industrial centrifugal pump. Moreover, an enhanced grey model approach is developed for remaining useful life prediction. In particular, the empirical Bayesian algorithm is employed to improve the traditional grey forecasting model in terms of quantifying the uncertainty of remaining service life in a probabilistic form and improving its prediction accuracy. To demonstrate the superiority of empirical Bayesian–grey model, existing prognostic methods such as grey model, particle filter–grey model and empirical Bayesian–exponential regression are also utilized to realize machinery remaining service life prediction, and the results are compared with that of the proposed method. The achieved predictive accuracy shows that the proposed approach outperforms its counterparts and is highly applicable in fault prognostics of industrial rotating machinery. The use of in-service data in a practical scenario shows that the proposed prognostic approach is a promising tool for online health monitoring. [ABSTRACT FROM AUTHOR]

Summary: An accurate remaining useful life (RUL) prediction method is significant to optimize the lithium‐ion batteries' performances in an intelligent battery management system. Since the construction of battery models and the initialization of algorithms require a large amount of data, it is difficult for conventional methods to guarantee the RUL prediction accuracy when the available data are insufficient. To solve this problem, a synergy of sliding‐window grey model (SGM) and particle filter (PF) is exploited to build an innovative framework for battery RUL prediction. The SGM is adopted to explore the modelling of battery capacity degradation, and it characterizes the capacity changes during the battery's life‐time with a few data (eg, 8 data points). To promote the accuracy and traceability of prediction, the development coefficient of the SGM, which can dynamically reflect the capacity degradation, is extracted to update the state variables of state transition function in PF. Accordingly, the fusion of SGM and PF (SGM‐PF) can extrapolate the changes of the capacity and realize RUL prediction using fewer data. Furthermore, the performances of SGM‐PF are comprehensively validated using two types of batteries aged under different conditions. The RUL prediction results reveal that the SGM‐PF framework can achieve precise and reliable predictions in different prediction horizons with as few as 8 data points, and it has prominent performance in accuracy and stability over contrastive methods, especially in long‐term prognosis. [ABSTRACT FROM AUTHOR]

Aiming at the problem of inflection point sequence reconstruction and oscillation sequence prediction in stock price inflection point prediction research, this paper proposed a prediction method combining entanglement theory and similar gray model. First, based on the entanglement theory, it systematically gave the basic theory of sequence reconstruction. Aiming at the shortcomings of grey theory prediction in oscillation sequence, it proposed a similar grey prediction model combining longitudinal residual and lateral deviation correlation coefficient with grey theory . Second, it used the longitudinal deviation-transverse residual correlation coefficient to calculate the historical data, and obtained the gray model parameters with the smallest prediction error. Then, it realized stock price inflection point prediction with oscillation characteristics by weighted summation. The last two sets of stock price inflection point prediction experiments show that the summarized sequence reconstruction theory is effective . Compared with other common gray models, the similar gray model can effectively improve the prediction accuracy of the oscillation sequence. [ABSTRACT FROM AUTHOR]

The traditional grey models with two-parameters are always accompanied by the effect of extreme values in the raw sequence, which influences the accuracy of the simulation and prediction by grey models. This paper proposes a TPBVGM(1,1) model (three-parameters background values of the grey model with a single variable and a first order equation) by increasing the number of parameters in the background value. This novel model improves the smoothness of the background value and weakens the effects of extreme values in the raw sequence on the basis of proving that a two-parameter background value assignment is not reasonable. The objective of devising this model is to improve the accuracy of predictions. The TPBVGM(1,1) model is then applied to simulate and forecast the average water usage per person in the cities and towns along the Yangtze River basin; the simulation and prediction performance of the TPBVGM(1,1) model are then tested by comparison with the simulation and prediction results of traditional grey prediction models. The results show that the TPBVGM(1,1) model has a higher accuracy for simulation and prediction than the traditional grey prediction models. The results of the study provide a new research method for simulation and prediction with a grey system model. [ABSTRACT FROM AUTHOR]

Scientific and accurate prediction of energy production is important for exploring energy alternative paths, adjusting energy structure and industrial layout in a targeted manner, and promoting strategic energy transformation. In this paper, a time-lagged logistic grey forecasting model with harvesting term is established by combining the Logistic model, which has the ability of historical recurrence and short- and medium-term forecasting ability, and the grey forecasting model, which has the characteristics of strong adaptability and small computational effort. The least squares method is used to estimate the parameters of the new model, and the mathematical method is used to calculate the time response equation of the new model, and the modeling steps and flow chart of the new model are obtained. Finally, the oil production data of a province in China is used as the validity analysis of the model, and the new model is compared with two classical grey prediction models, three optimized grey prediction models, and one other prediction model. Through the comparison of seven indicators, the results show that the new model is significantly better than other models. Based on the validity analysis results, the new model is applied to the energy production forecast of three typical provinces in China. The horizontal and vertical comparison shows that the model can effectively predict the three kinds of energy production, and can provide technical support for the strategy and measures to adjust the energy security structure and promote the healthy and sustainable development of the energy industry. • A novel model (HDLGM(1,1,τ)) is established by considering the time-lagged Logistic. • Logistic harvest items are introduced into the novel model. • Modeling short- and medium-term forecasting ability was Enhanced. • The proposed model has been effectively applied to energy production. [ABSTRACT FROM AUTHOR]

PM2.5 has attracted widespread attention since the public has become aware of it, while attention to PM10 has started to wane. Considering the significance of PM10, this study takes PM10 as the research object and raises a significant question: when will the influence of PM10 on public health end? To answer the abovementioned question, two promising research areas, i.e., air pollution forecasting and health effects analysis, are employed, and a novel hybrid framework is developed in this study, which consists of one effective model and one evaluation model. More specifically, this study first introduces one advanced optimization algorithm and cycle prediction theory into the grey forecasting model to develop an effective model for multistep forecasting of PM10, which can achieve reasonable forecasting of PM10. Then, an evaluation model is designed to evaluate the health effects and economic losses caused by PM10. Considering the significance of providing the future impact of PM10 on public health, we extend our forecasting results to evaluate future changes in health effects and economic losses based on our proposed health economic losses evaluation model. Accordingly, policymakers can adjust current air pollution prevention plans and formulate new plans according to the results of forecasting, evaluation and early-warning. Empirical research shows that the developed framework is applicable in China and may become a promising technique to enrich the current research and meet the requirements of air quality management and haze governance.

There is a growing optimism that the farmers' organizations can act as a potential driving force for enhancing farmers' income. India has witnessed a positive growth of producer organizations in terms of types of organization, numbers and members. The Producer Company is a special case of producer organization that is registered under Section IXA of the Companies Act, 1956. A need was felt at that time to have an independent farmers’ organization which enables incorporation of producers into such an institution like the companies which will be controlled by them, having welfare and business outlook at a time while not compromising the sustainability issues. That creates the milieu for the genesis of Farmers’ Producer Company (FPC) in India. The FPCs are fundamentally farmer-owned and farmer-governed micro-enterprises which can be considered as hybrids between cooperative societies and private companies. The way of participation, membership and organization is similar to that of a cooperative, while the incorporation into corporate law allows greater flexibility and professionalism in their business actions. Till date 1048 FPCs are registered in India. In this article attempt has been made to review the issues of FPC, current status and future prospects. Forecasting the growth of FPC has been done up to the year 2020 utilizing Grey Model. Emphasis has been given to critically analyse the status, prospects and potentials with future outlook of 2020 concluding with strategies and policy needs.

Abstract This paper aims to better manage the reverse supply chain of the automotive industry in the context of green, circular, and sustainable development by predicting the number of end-of-life vehicles to be recycled through the establishment of a multi-factor model. The prediction of the number of end-of-life vehicles to be recycled in this paper will support the end-of-life vehicle recycling industry in terms of recycling management and investment decision-making and provide a reference for the formulation and implementation of policies relating to end-of-life vehicles. To solve the problems posed by nonlinear characteristics and uncertainty in the number of end-of-life vehicles recycled, and deal with the multiple factors influencing the recycling number, this paper presents a combined prediction model consisting of a grey model, exponential smoothing and an artificial neural network optimized by the particle swarm optimization (PSO) algorithm. Using Shanghai's end-of-life vehicle reverse logistics industry as an example, this study selects historical data about end-of-life vehicles recycled in Shanghai during the 2005–2016 period, identifies multiple influential factors, and validates the effectiveness and feasibility of the prediction model through empirical research. This paper proposes an effective prediction model for end-of-life vehicle industry managers, researchers, and regulators dealing with the industry's common challenges. Highlights • Hybrid prediction model based on grey model and artificial neural network predicts end-of-life vehicles recycling volume. • Hybrid prediction model improves prediction performance on data featuring randomness and small sample size. • Hybrid prediction model improves prediction performance of end-of-life vehicles recycling volume affected by multi-factors. • Artificial neural network prediction model using particle swarm optimization algorithm has better prediction performance. • Model proposed in this paper is tested by application to real-life data from the reverse logistics industry in Shanghai. [ABSTRACT FROM AUTHOR]

Abstract China is the world's largest net importer of oil and the second largest oil consumer; consequently, changes of China's foreign oil dependence significantly impact both the Chinese and the international oil market. To enhance the forecasting ability of China's foreign oil dependence, this study combines the nonlinear metabolic grey model (NMGM) with the linear autoregressive integrated moving average model (ARIMA), thus obtaining the combined NMGM-ARIMA model. The proposed technique uses the linear ARIMA to correct NMGM forecasting residuals, thus improving forecasting accuracy. The proposed technique achieves a mean absolute error of 2.1–2.3%, reflecting its high reliability. The proposed NMGM-ARIMA was used to forecast China's foreign oil dependence for the period of 2017–2030 from two dimensions. For the first dimension, the gap between China's oil demand and supply was forecast. To fill this gap, China has to import oil; therefore, this gap is responsible for China's foreign oil dependence. For the second dimension, the change of China's foreign oil dependence level was directly forecast. Both dimensions indicate a similar conclusion, namely that the Chinese foreign oil dependence level will increase from 65% in 2016 to over 80% in 2030. A high level of 80% dependence on foreign oil would bring major concern to China. The policy recommendations given at the end of the paper will help China's decision makers respond appropriately. Highlights • The proposed forecasting technique uses the linear ARIMA to correct NMGM residuals. • The mean absolute percent error of the proposed technique is 2.1–2.3%. • Forecasting China's oil gap between production and consumption for 2017–2030. • Forecasting China's foreign oil dependence for 2017–2030. • Two-dimensional forecasting results show China's foreign oil dependence will exceed 80% by 2030. [ABSTRACT FROM AUTHOR]

To maintain good continuous working performance in a vacuum plate seeder, it is important to monitor the distribution of seeds in real time and automatically adjust vibration parameters accordingly. Seed motion in a rectangular vibrating tray with vibration varying with time and interference by direction angle was simulated using the discrete element method (DEM). A plane model P was used to describe the variation of seed layer thickness. Four square areas on the bottom of the tray were divided symmetrically near the four corners to measure seed layer thickness, and a monitoring plane model P m was established. DEM simulation results showed that the models P m and P had the similar change rules, although there were some differences in fitting parameters. There was obvious time delay in the change of P m compared with P. Therefore, a grey system model (GM) was adopted to predict the change of P m , and two back-propagation (BP) neural networks which take GM prediction results as input parameters were developed respectively. Then, according to the BP neural networks outputs, a prediction plane model P p was proposed to predict the seed distribution. Experiments were carried out on a test-rig to validate these predictions. The seed distribution plane P was measured manually, the monitoring plane P m was established using seed layer thickness measurement results and the prediction plane P p was established using the GM and BP neural networks. The results indicated that the proposed method had good precision and stability and provides the basis for the design of an automatic control system for the vibrating tray to promote a uniform seed distribution. Highlights • Seed motion in a vibrating tray with varying interferences was DEM simulated. • Plane fitting model and monitoring method for seed distribution was developed. • Grey system model was adopted to predict the change of monitoring plane. • BP Neural networks were established to predict the seeds distribution variation. • Experiments were carried out to verify the prediction accuracy. [ABSTRACT FROM AUTHOR]

Accurate and reliable air passenger demand is very important for policy-making and planning by tourism management as well as by airline authorities. Therefore, this article proposed a novel hybrid method based on rough set theory (RST) to construct decision rules for long-term forecasting of air passengers. Level (mean) and trend components are first estimated from the air passengers time series data using DES model in the formulation of the proposed hybrid method. Then the rough set theory is employed to combine the output of DES model and generated decision rules is used to forecasting air passengers. We compare the proposed approach with other time series models using a corrected classified accuracy (CCA) criterion. For the empirical analysis, yearly air transport passenger from 1992 to 2004 is used. Empirical results show that the proposed method is highly accurate with the higher corrected classified accuracy. Also, forecasting accuracy of the proposed method is better than the other time series approaches. [ABSTRACT FROM AUTHOR]

Time Series models have the limitations of requiring more observations in order to construct the model. Sometimes, we usually are able to make only a few observations due to rapid innovation new technologies, in such circumstances grey model can be used as it requires as few as four observations to construct the model. In this study, we have utilized grey model for forecasting hybrid rice yield (1994-95 to 2009-10) of Bihar state of India as only few observations were available for model building. In addition, we used genetic algorithm technique to find the optimal parameters of the model. It is observed that implementation of genetic algorithm improved the precision of the model. [ABSTRACT FROM AUTHOR]

In grey system theory, the performance of an established grey forecasting model largely depends on how efficiently the grey information can be measured from data. Most existing grey forecasting models use grey accumulating generators to obtain grey information. However, not all grey information helps improve the performance of grey forecasting models. Consequently, simple accumulation leads to the accumulation of error from invalid grey information, which deteriorates the model performance. To address this issue, valid and invalid grey information were defined in this study according their contributions to the model performance. Further, it was proposed to use a Bernoulli distribution to simulate the distribution of valid/invalid grey information. Based on that probability, a probabilistic accumulation operator was designed to compute grey information, and this grey information was utilized to establish a probabilistic accumulation operator-based grey forecasting model (PGM(1,1)). PGM(1,1) is advanced in terms of forecasting because it is not negatively affected by invalid grey information. PGM(1,1) was tested on five public datasets and compared to other grey models as well as a wide range of other forecasting models, achieving state-of-the-art performance. In addition, a comprehensive analysis was conducted to demonstrate how the forecasting performance benefits from identifying valid/invalid grey information in PGM(1,1). [ABSTRACT FROM AUTHOR]

To perform better future trend prediction for an economy-energy-environment (3E) system and address the shortcomings of traditional multivariate grey models, this paper introduces a spatial correlation term into the multivariate discrete grey model, thus creating the SLDGM(1,n) model, and improves the final calculation of the model according to the priority of new information. The validity of the SLDGM(1,n) model is assessed using data from the 3E system in North China, and the SLDGM(1,n) model is applied to predict the future trends of the 3E system in North China. The following conclusions are obtained. First, the introduction of the spatial correlation term and the improvement of the final calculation method are reasonable; the prediction accuracy of the multivariate grey model is improved, and multiple systems are modeled simultaneously. Second, the SLDGM(1,n) model calculates the spatial spillover effect, and according to the simulation results for North China from 2010 to 2019, Hebei's energy consumption and carbon emissions are subject to the largest influence from other provinces, while its economic development level is subject to the smallest influence, and the carbon emissions of Shanxi and Inner Mongolia are subject to a negative spatial influence effect. Third, the prediction results indicate that under the effect of spatial correlation, the energy consumption of all five provinces in North China will continue to rise; the carbon emissions of Beijing will gradually decline while the carbon emissions of the other four provinces will all gradually rise, and the per capita GDP of the five provinces is expected to increase by more than 50% by 2025. [ABSTRACT FROM AUTHOR]