Search

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 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.

The incredible increase in carbon emissions is a major global concern. Thus, academicians and policymakers at COP26 are continuously urging to devise strategies to reduce carbon and other greenhouse gas emissions. The transportation sector is a major contributor to greenhouse gas emissions in developing countries. Therefore, this study projected an increase in fossil fuel demand for transportation and corresponding carbon dioxide emission in Pakistan from 2018 to 2030 by employing the Grey model and using annual data from 2010 to 2018. Furthermore, the determinant of fossil fuel demand is modeled using an environmental sustainability model such as stochastic regression IPAT that links environmental impact as a product of population, affluence, and technology on annual time series data spanning from 1990 to 2019. The projected values of oil demand and carbon emissions reveal an increasing trend, with average annual growth rates of 12.68% and 11.45%, respectively. The fully modified ordinary least squares (FM-OLS) findings confirmed the environmental Kuznets hypothesis. The increase in population growth emerged as the major driver for oil demand and carbon dioxide emissions, while technological advancement can reduce oil demand and corresponding carbon emissions. This study urges Pakistan to switch from oil to gas and other green energies by encouraging hybrid vehicles, as the number of vehicles on the road positively impacts the transport sector’s oil demand. Moreover, increasing economic growth and controlling the population growth rate by discouraging more children can be a valid policy for reducing oil demand and corresponding carbon emissions.

Oil monitoring for wind turbine gearboxes can reflect wear and lubrication conditions, and better identify pits on the tooth surface, fatigue wear, and other early faults. However, oil monitoring with one or several single predicting models brings inaccuracy due to the intrinsic merits and demerits of the models. In this work, oil monitoring and fault pre-warning of wind turbine gearboxes were studied based on oil inspection data of three wind turbines that have been working continuously for 3.5 years. The Grey Model (GM) and the Double Exponential Smoothing (DES) were combined by a modified inverse-variance weighting method proposed in this work, which used relative errors to calculate weight coefficients, reducing the errors and improving the accuracy as a whole. The predicted data were compared with the measured data to verify the predicting accuracy. Subsequently, a statistical method and linear regression method were adopted to jointly develop a pre-warning threshold for the oil inspection data. Comparing the predicted data with the threshold, the results showed that one of the wind turbines was in a warning state. The prediction was validated by an endoscope inspection of the gearbox, which found that some parts were slightly worn.

The electricity distribution in a planned way has been a difficult issue that the power supply bureau wishes to solve, and it is the lifeblood of economic development. Forecasting annual electricity consumption is very crucial for the planning of the power supply bureau and for booming economic development. We propose a novel unbiased fractional nonlinear grey Bernoulli model [i.e, UFNGBM (1,1)] to forecast China’s annual electricity consumption based on the nonlinear grey Bernoulli model [i.e, NGBM (1,1)]. First, UFNGBM (1,1) approach is designed to derive calculation formula of the novel model, and validity of the model is proved by the matrix perturbation theory. Second, a novel optimization algorithm is introduced based on the whale algorithm to find the optimal parameters (i.e., o r d e r and p o w e r ) of the proposed model. Third, the accuracy, stability, and effectiveness of our method are verified through three real-world cases in China. Finally, we collect the electricity consumption data of three provinces in China and successfully apply the proposed algorithm to predict the electricity consumption from 2019 to 2024. The experimental results demonstrate that our proposed model is significantly superior to nine alternative models on the electricity consumption data of Jilin and Jiangsu. The performance of our novel method is close to the state-of-the-art deep learning method on the electricity consumption data of Shandong. It is noticed that our method [as an extended version of NGBM(1,1)] is significantly better than NGBM(1,1) on these three real-world datasets, which further shows the effectiveness of the our proposed algorithm. Meanwhile, the electricity consumption of these three provinces in the next six years (2019–2024) is forecasted, which has a very good guiding significance and provides a more reliable reference for the economic and power bureau.

Grey models should give different weights to old and new information when dealing with different cases, whereas existing grey models always give greater weight to new information. With this in mind, a novel grey model is proposed in this paper. The model introduces an exponential parameter that regulates the weight of information by adjusting the size of the parameter. This model is used to study the carbon dioxide emissions of BRICS (Brazil, Russia, India, China and South Africa) countries. Firstly, the intelligent algorithm is used for multiple iterations to find the exponential order that minimizes the simulation error. Secondly, the raw data on CO2 emissions from BRICS countries are processed and grey differential equations are developed. Finally, the least squares method is used to solve the coefficients of the differential equation and to predict the CO2 emissions of these countries based on the corresponding time series. The results show that carbon dioxide emissions in Brazil and Russia are on a downward trend. China and South Africa show a slight upward trend in carbon dioxide emissions. India has a large trend of increasing carbon dioxide emissions. The results can provide reference value for the relevant authorities.

The bearing residual life prediction of coal mine machinery equipment is of great significance for equipment maintenance. The existing bearing residual life prediction methods are either difficult to establish an accurate mathematical model of bearing failure, or the prediction precision is constrained by the sample completeness and accuracy. And the degradation characteristic quantity usually adopts time domain and frequency domain indicators, which are greatly affected by the harsh working environment of coal mine machinery equipment, resulting in low prediction precision. In order to solve this problem, a bearing residual life prediction method of coal mine machinery equipment based on empirical mode decomposition(EMD) and grey model(GM) is proposed. EMD is used to filter the vibration acceleration signal of coal mine machinery equipment bearings. The root mean square of the filtered signal is extracted as the degraded characteristic quantity representing the bearing health state so as to form the degraded characteristic quantity sequence. The GM is trained with the degraded characteristic quantity sequence, then the GM bearing residual life prediction model is established to predict the change trend of the degraded characteristic quantity, and the time interval when the degraded characteristic quantity reaches the set threshold is used as the residual life prediction value. The test bench and engineering application results show that the method can effectively predict the bearing residual life of coal mine machinery equipment with high prediction precision, and the prediction results can guide field equipment maintenance.

Wind power generation has been developed rapidly due to rising global interest in renewable clean energy sources. Accurate prediction of the potential amount of such energy is of great significance to energy development. As wind changes greatly by season, time series analysis is considered as a natural approach to characterize the seasonal fluctuation and exponential growth. In this paper, a dual integrated hybrid model is presented by using random forest (RF) to incorporate the extreme gradient boosting (XGB) with empirical mode decomposition (EMD) and a fractional order accumulation seasonal grey model (FSGM). For seasonal fluctuation in vertical dimension processing, the time series is decomposed into high and low frequency components. Then, high and low frequency components are predicted by XGB and extreme learning machine (ELM), respectively. For the exponential growth in horizontal dimension processing, the FSGM is applied in the same month in different years. Consequently, the proposed model can not only be used to capture the exponential growth trend but also investigate the complex high-frequency variation. To validate the model, it is applied to analyze the characteristics of wind power time series for China from 2010 to 2020, and the analysis results from the model are compared with popularly known models; the results illustrate that the proposed model is superior to other models in examining the characteristics of the wind power time series.

Tailings dams in the seasonal frozen regions experience freeze–thaw cycles with the change in natural geography and climatic conditions, which may have a strong influence on the mechanical properties of the tailings. In this paper, the effects of freeze–thaw cycles on the mechanical properties and pore structure of tailings were investigated. Triaxial tests were carried out on tailings with different moisture contents (5%, 10%, 15%, 20%) under different confining pressures (50 kPa, 100 kPa, 200 kPa, 300 kPa) after different freeze–thaw cycles (10, 20, 30, 40, 50). The pore structures of tailings were quantitatively analyzed as well. Furthermore, grey system theory was applied to develop a shear strength prediction model for tailings in cold regions. The results showed that the optimal moisture content of tailings fell 10%–15%. The shear strength of the tailings increased under higher confining pressures, while it decreased after more freeze–thaw cycles. Irrecoverable large pore deformation between particles within the tailings was found after 40 freeze–thaw cycles. After 50 freeze–thaw cycles, the proportion of pores larger than 100 μm increased from 22.76% to 48.45%. Predictions based on the Grey Model were found to be consistent with the test results and the shear strength test law. The residual error and class ratio dispersion of the model were less than 0.2, indicating that the Grey Model has high prediction accuracy and thus can be used for the prediction of the shear strength of tailings.

Türkiye’nin turizm endüstrisinin gelişiminde ele alınması gereken temel konulardan biri turizm talep öngörüsüdür. Turizm talebinin doğru öngörülmesi, hem kamu hem de özel sektörün turizm planlaması açısından oldukça önemlidir. Bu çalışmanın amacı Türkiye’nin turizm talebinin gri modeller ile öngörülmesidir. Dolayısıyla, turizm talebi GM(1,1) gri modeliyle birlikte bu modelin kalıntılarının Fourier serileri ile düzeltildiği FGM(1,1) gri modeliyle ele alınmıştır. 2003-2021 dönemine ait yıllık toplam çıkış yapan ziyaretçi sayısı verisi kullanılarak, bu modellerin performanslarına ilişkin bir karşılaştırma yapılmıştır. Aynı zamanda söz konusu modeller kullanılarak kısa dönemli öngörülerde bulunulmuştur. Ulaşılan sonuçlar, Türkiye için turizm talebinin modellenmesi noktasında FGM(1,1) modelinin GM(1,1) modeline göre daha başarılı olduğunu göstermektedir. Modellerin güvenilirliğinin değerlendirilmesinde dikkate alınan, ortalama mutlak yüzde hata ölçütüne göre FGM(1,1) modelinin 2003-2020 dönemi kestirimleri ile bu model ile yapılan 2021 yılı turizm talep öngörüsü yüksek doğruluk düzeyindedir., Tourism demand forecasting is one of the key issues to be addressed in the development of Turkey’s tourism industry. Accurate forecasting of tourism demand is very important in terms of tourism planning of both public and private sectors. The aim of this study is to forecast the tourism demand of Turkey with grey models. Therefore, tourism demand is handled with GM(1,1) grey model and FGM(1,1) grey model, which is obtained by modifying the residuals of the GM(1,1) model with Fourier series. A comparison of the performances of these models was made by using the annual data related to the total number of departing visitors for the 2003-2021 period. At the same time, short-term forecasts were made by using these models.The results show that FGM(1,1) model outperforms GM(1,1) model in modeling the tourism demand for Turkey. According to the mean absolute percentage error criterion taken into account to analyze the reliability of the models, both the 2003-2020 period predictions and the 2021 year tourism demand forecast of the FGM(1,1) model are at a high accuracy.

Ülkelerin önemli gündemlerinden biri olan enerji arz güvenliği kavramının doğru ölçülmesi, bir ülkenin iç veya dış dinamiklerin etkisiyle enerji sektörünü etkilemesi muhtemel risklere karşı dayanıklılığının veya kırılganlığının belirlenmesine olanak sağlamaktadır. Söz konusu kavramın çok sayıda faktörden etkilenmesi nedeniyle yapılan analizlerde çok yönlü ele alınması gerekmektedir. Dolayısıyla, bu çalışmada ilk olarak ithal enerji tedarikinde ülke çeşitliliği dikkate alınarak Türkiye’nin enerji arz güvenliği riski hesaplanmıştır. Sonrasında, 1990-2020 dönemi için hesaplanan endeks değerleri trigonometrik fonksiyonlar ile güçlendirilmiş gri modeller ile modellenmiştir. Analizlerde iki farklı yaklaşım doğrultusunda önerilen dört farklı gri model kullanılmıştır. Belirlenen en iyi model kullanılarak 2021-2023 dönemi için Türkiye’nin enerji arz güvenliği riskine yönelik öngörüler yapılmıştır. Elde edilen sonuçlar enerji arz güvenliği riskinin 2020 yılı ile kıyaslandığında 2021 yılında artacağını, 2022 yılında önceki iki yıla göre azalacağını, 2023 yılında ise son üç yıla göre en yüksek seviyede olacağını göstermektedir., 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.

During spinning, the chemical component content of natural fibers has a great influence on the mechanical properties. How to rapidly and accurately measure these properties has become the focus of the industry. In this work, a grey model (GM) for rapid and accurate prediction of the mechanical properties of windmill palm fiber (WPF) was established to explore the effect of chemical component content on the Young’s modulus. The chemical component content of cellulose, hemicellulose, and lignin in WPF was studied using near-infrared (NIR) spectroscopy, and an NIR prediction model was established, with the measured chemical values as the control. The value of RC and RCV were more than 0.9, while the values of RMSEC and RMSEP were less than 1, which reflected the excellent accuracy of the NIR model. External validation and a two-tailed t-test were used to evaluate the accuracy of the NIR model prediction results. The GM(1,4) model of WPF chemical components and the Young’s modulus was established. The model indicated that the increase in cellulose and lignin content could promote the increase in the Young’s modulus, while the increase in hemicellulose content inhibited it. The establishment of the two models provides a theoretical basis for evaluating whether WPF can be used in spinning, which is convenient for the selection of spinning fibers in practical application.

With the rapid development of urbanization and the continuous improvement of living standards, China's domestic water consumption shows a growing trend. However, in some arid and water deficient areas, the shortage of water resources is a crucial factor affecting regional economic development and population growth. Therefore, it is essential to reliably predict the future water consumption data of a region. Aiming at the problems of poor prediction accuracy and overfitting of non-growth series in traditional grey prediction, this paper uses residual grey model combined with Markov chain correction to predict domestic water consumption. Based on the traditional grey theory prediction, the residual grey prediction model is established. Combined with the Markov state transition matrix, the grey prediction value is modified, and the model is applied to the prediction of domestic water consumption in Shaanxi Province from 2003 to 2019. The fitting results show that the accuracy grade of the improved residual grey prediction model is “good”. This shows that the dynamic unbiased grey Markov model can eliminate the inherent error of the traditional grey GM (1,1) model, improve the prediction accuracy, have better reliability, and can provide a new method for water consumption prediction. HIGHLIGHTS The prediction model of water resources is established.; The method of combining grey model with Markov model is put forward.; The modified method has a good prediction effect and application value.

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 .

The recent increase in the road transportation necessitates scheduling to reduce the adverse impacts of the road transportation and evaluate the effectiveness of previous actions taken in this context. However, it is impossible to undertake the scheduling and evaluation tasks unless previous information are available to predict the future. The grey model requires a limited volume of data for estimating the behavior of an unknown system. It provides high-accuracy predictions based on few data points. Various grey prediction models have been proposed so far, in which three different approaches are followed to increase the accuracy: (1) data preprocessing, (2) improved equation models, and (3) error improvement or error balancing. In this paper, firstly, a theorem is proposed and proved to recognize the parameters affecting two grey models, namely GM(1, 1) and FGM(1, 1). Then, the effective parameters are adjusted through particle swarm optimization (PSO) to formulate two adjusted models, namely IGM(1, 1) and IFGM(1, 1). According to the simulation results of the proposed models, accuracy of the modeling improved by a minimum of 14.24% and a maximum of 82.39%. Finally, the number of users of a public road transportation system was predicted using the proposed models. The results showed enhanced accuracy (by 7.7%) of the proposed models for predicting the number of users of the public road transportation system.

A primary challenge to the implementation of hybrid electric vehicles (HEVs) is the design of the energy management strategy for the vehicle. Most conventional strategies have been designed for passenger vehicles using rule-based or optimization-based control strategies that rely on navigation support; therefore, the optimal performance of heavy-duty HEVs that lack navigation support cannot be achieved using conventional strategies. In this study, we propose a nonlinear model predictive control (NMPC) for heavy-duty HEVs based on a random power prediction method. To obtain the models of multiple power sources, we analyzed the structure and powertrain of the vehicle using mathematical modeling methods. To account for the lack of navigation support, we used the data-driven prediction method by combining the grey model and Markov chain methods to obtain higher-accuracy ultra-short-term power prediction. Considering the predicted disturbance power, we established a multi-objective optimization function with explicit constraints to optimize fuel consumption, bus voltage, and battery state of charge. Under these constraints, a nonlinear programming problem based on the NMPC could be restricted to find an optimal numerical solution in real time. We validated the control strategy on a hardware-in-the-loop simulation platform and compared its results with those obtained using thermostat control, fuzzy, and dynamic programming approaches. The proposed control strategy achieved a considerably better all-round performance than rule-based control strategies; moreover, the results were considerably similar compared with those of offline global optimization strategies. Furthermore, the proposed method achieved excellent real-time operation capability, thereby providing a valuable reference for practical engineering applications.

Through analysis of the carbon emissions transfer network formed by the exchange of intermediate products among industries, we can promote the realization of national carbon emissions reduction goals. Therefore, it is of great significance to build a prediction model of the carbon emissions transfer network for more accurate predictions. According to the characteristics of the random oscillation sequence (ROS) of interindustry carbon emissions transfer, a hybrid prediction model denoted as the ROGM-AFSA-GVM is proposed based on the grey model (GM) for ROS and the general vector machine (GVM) optimized by the artificial fish swarm algorithm (AFSA). The proposed model uses the ROGM model to predict the general ROS trend and relies on the AFSA-GVM model to predict the nonlinear law of ROS. The predicted values of the two parts are combined to obtain predicted interindustry carbon emissions transfer values. The proposed model is used to simulate the interindustry carbon emissions transfer network of China. The simulation results show that the ROGM-AFSA-GVM model can effectively resolve the prediction problem of ROS. Comparing the predicted networks with the actually measured networks, it is verified that the proposed model is suitable for simulating the interindustry carbon emissions transfer network and has a good prediction performance.

The cloud computing environment provides easy-to-access service for private and confidential data. However, there are many threats to the leakage of private data. This paper focuses on investigating the vulnerabilities of cloud service providers (CSPs) from three risk aspects: management risks, law risks, and technology risks. Additionally, this paper presents a risk assessment model that is based on grey system theory (GST), defines indicators for assessment, and fully utilizes the analytic hierarchy process (AHP). Furthermore, we use the GST to predict the risk values by using the MATLAB platform. The GST determines the bottom evaluation sequence, while the AHP calculates the index weights. Based on the GST and the AHP, layer-based assessment values are determined for the bottom evaluation sequence and the index weights. The combination of AHP and GST aims to obtain systematic and structured well-defined procedures that are based on step-by-step processes. The AHP and GST methods are applied successfully to handle any risk assessment problem of the CSP. Furthermore, substantial challenges are encountered in determining the CSP's response time and identifying the most suitable solution out of a specified series of solutions. This issue has been handled using two additive features: the response time and the grey incidence. The final risk values are calculated and can be used for prediction by utilizing the enhanced grey model (EGM) (1,1), which reduces the prediction error by providing direct forecast to avoid the iterative prediction shortcoming of standard GM (1,1). Thus, EGM (1,1) helps maintain the reliability on a larger scale despite utilizing more prediction periods. Based on the experimental results, we evaluate the validity, accuracy, and response time of the proposed approach. The simulation experiments were conducted to validate the suitability of the proposed model. The simulation results demonstrate that our risk assessment model contributes to reducing deviation to support CSPs with the three adopted models.

As part of China’s compulsory nine-year education system, junior secondary education (JSSE) plays a vital role in supporting students’ physical and mental development. The accurate prediction of the development scale trend of JSSE is helpful for the government to estimate the scale of educational development within a chosen time frame so as to aid decision making.Nevertheless, China’s education system is complex, highly dimensional, and largely influenced by policy and other factors, which results in difficulty in modeling the education sample. Based on gray system theory, this paper proposes an improved fractional-order grey prediction model, OCFNGBM(1,1), to predict the development scale of JSSE. We describe the basic expressions of the model, the parameter estimation method, and the optimization method for hyperparameters and construct a scheme for optimizing the background value coefficients. Data collected from official websites from 2011 to 2021 are used to build the forecasting model, and data from 2011 to 2017 are used to evaluate the model’s accuracy. Our experimental results indicate that the OCFNGBM(1,1) model has higher accuracy than the classical nonlinear gray prediction model. The OCFNGBM(1,1) model was employed to forecast the development scale of JSSE in China from 2022 to 2024, which provided useful information. This research provides a resource to help the national education department to develop a comprehensive and long-term plan for the development goals, scale, speed, steps, and measures of relevant education.

The prediction of cyber security situation plays an important role in early warning against cyber security attacks. The first-order accumulative grey model has achieved remarkable results in many prediction scenarios. Since recent events have a greater impact on future decisions, new information should be given more weight. The disadvantage of first-order accumulative grey models is that with the first-order accumulative method, equal weight is given to the original data. In this paper, a fractional-order cumulative grey model (FAGM) is used to establish the prediction model, and an intelligent optimization algorithm known as particle swarm optimization (PSO) combined with a genetic algorithm (GA) is used to determine the optimal order. The model discussed in this paper is used for the prediction of Internet cyber security situations. The results of a comparison with the traditional grey model GM(1,1), the grey model GM(1,n), and the fractional discrete grey seasonal model FDGSM(1,1) show that our model is suitable for cases with insufficient data and irregular sample sizes, and the prediction accuracy and stability of the model are better than those of the other three models.

Landslides are frequent and catastrophic geological hazards, and forecasting their movement is an important aspect of risk assessment and engineering prevention. Based on the integrated deep displacement three-dimensional measuring sensor with sensing unit array structure, an improved multivariable grey model based on dynamic background value and multivariable feedback is proposed to build predictive models for the evolutionary condition of landslides. In the modeling process, the traditional grey model was replaced by extracting the trend information of each variable, instead of summing up each independent variable after assigning weights to it, besides, the Whale Optimization Algorithm (WOA) is used to modify the default value in the model’s background variables. By predicting more than 1000 sets of deep displacement monitoring data collected in the landslide simulation test conducted at the landslide simulation test device, the displacement prediction accuracy of our purposed model is 26%, 47%, and 87% respectively higher than the optimizing grey model (OGM) for three sensing units at different depths. Moreover, a new landslide risk assessment approach based on the orientation vector angle is proposed to make stability discriminations which is less susceptible to volatile data than the TOPSIS-Entropy weight theory and avoids the problem of lack of uniform standards due to the complexity of environmental factors.

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.

An inertial platform is the key component of a remote sensing system. During service, the performance of the inertial platform appears in degradation and accuracy reduction. For better maintenance, the inertial platform system is checked and maintained regularly. The performance change of an inertial platform can be evaluated by detection data. Due to limitations of detection conditions, inertial platform detection data belongs to small sample data. In this paper, in order to predict the performance of an inertial platform, a prediction model for an inertial platform is designed combining a sliding window, grey theory and neural network (SGMNN). The experiments results show that the SGMNN model performs best in predicting the inertial platform drift rate compared with other prediction models.

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters a, b and λ can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision.

The detection of edges in images is a pressing issue in the field of image processing. This technique has found widespread application in image pattern recognition, machine vision, and a variety of other areas. The feasibility and effectiveness of grey theory in image engineering applications have prompted researchers to continuously explore it. The grey model (GM (1,1)) with the first-order differentiation of one variable is the grey prediction model that is most frequently used. It is a typical trend analysis model and can be used for image edge detection. The traditional integer-order differential image edge detection operator has problems such as blurred and discontinuous edges, incomplete image details, and high influence by noise. We present a novel grey model for detecting image edges based on a fractional-order discrete operator in this paper. To improve the features of the original image, our model first preprocesses it before calculating the prediction of the original image using our fractional-order cumulative greyscale model. We obtain the edge information of the image by first subtracting a preprocessed image from the predicted image and then eliminating isolated noise points using the median filtering method. Based on the discrete wavelet transform, image edges are finally extracted. The comparison experiments with a traditional edge detection operator show that our algorithm can accurately locate the image edges, the image edges are clear and complete, and this model has better anti-noise performance.

Background: We aimed to compare the prediction efficiency of back propagation (BP) network and grey model (GM) (1.1) for mumps infectious diseases and compare the application effect of the two models. Methods: By calculating the average incidence rate of mumps in January 2014 -2016, we conducted the modeling of the BP time series, GM (1,1) grey model and the combination models of them, and predicted the incidence rate in June 2016 in comparison with the actual one. We compared the quarterly incidence rate to test the two prediction models, and compared the advantages and disadvantages of these models. Results: R value of BP model was 68.45%, for GM (1,1) was 58.49%, and for combined forecasting model was 86.95%. We used the principal component analysis clustering method to control the samples, and found that the samples were close to the population mean. We found that the GM (1.1) model was more suitable for the prediction of mumps infection mode. We carried out dimension reduction analysis on the model data, and the accuracy of the data after dimension reduction is within the range of Da. For the discrete degree of the data in the combined model, matlab pipeline was used to verify the reliability of the data and results. By calculation after manifold optimization small error probability was P=0.875 and semi mean relative error 2.43%. Conclusion: BP, GM (1,1) is a better method for modeling the epidemic trend of mumps in China, but the efficiency of prediction is not as high as the combination of them.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. 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.

Cloud computing is generally considered as a special energy-efficient form for the Internet of Things (IoT) resource usage. Dedicated server systems for cloud services, better capacity utilization and economies of scale because of the use of larger and more energy-efficient data centers are the reasons why cloud solutions typically use less energy than traditional on-premise systems. To scientifically and rationally configure the hardware and software resources of the cloud computing, the research on forecasting a cloud computing resource load becomes a research focus. However, the widely-used single forecasting model cannot contain all the characteristics of the cloud computing resource load sequence, resulting in inaccurate forecasting results. In this paper, a combined forecasting approach of cloud computing resource load based on wavelet decomposition is proposed, which combined the grey model and cubic exponential smoothing model. It can well preserve details and reduce noise. Firstly, the cloud computing resource load sequence is decomposed into several frequencies by the wavelet decomposition method. The decomposed load sequences with different characteristics are divided into different resolution scale subspaces in deferent frequencies. The noise of the load sequences is reduced by the wavelet threshold denoising method. And then, the load sequences are reconstructed according to the wavelet coefficients. The reconstructed load sequence not only contains less noise but also reserves detailed information. Consequently, it is closer to the real data and more regular. Experimental results show that our proposed combined forecasting model with wavelet decomposition can provide more accurate forecasting results than each single forecasting model or the combined forecasting model without using the wavelet decomposition method. Thus, our proposal is demonstrated to be efficient for forecasting the cloud computing resource load and helping to reduce energy consumption.

As a kind of green, clean and renewable energy, wind power generation has been widely utilized in various countries in the world. With the rapid development of wind energy, it is also facing prominent problems. Because wind power generation is intermittent, unstable and stochastic, it has caused serious difficulties for power grid dispatch. At present, the important method to solve this problem is to predict wind speed and wind power. Grey model is suitable for uncertain systems with poor information and needs less operation data, so it can be used for wind speed and wind power prediction. However, the traditional grey system model has the disadvantage of low prediction accuracy. Therefore, firstly the GM (1,1) for wind speed prediction is improved by background value optimization in this paper. In order to comprehensively reveal the inherent uncertainty of wind speed random series, the fractional order grey system models with different orders are constructed. Secondly, in order to overcome the shortcoming of single grey model, each grey model is effectively united, and a combination prediction model based on neural network is presented. The two NWP outputs, i.e. ECMWF and GRAPES-MESO, have been added to the prediction model for reducing the uncertainty. The structure parameters of the neural network are optimized by trial and error. Thirdly, the support vector regression model is established to fit the scatter operation data of wind speed-power, and the parameters of the model are optimized by the particle swarm algorithm. Then the power prediction value is obtained by the fitted wind speed-power relationship and the corresponding result of the grey combination model for wind speed prediction. Finally, wind speed and wind power are predicted based on the actual operation data. In addition, the prediction model based on ARIMA is also constructed as a benchmark model. The results show that the proposed grey combination model improves the prediction accuracy.

In order to solve the problem that the generalized likelihood test method cannot isolate the single fault of the four-gyro system and the double faults of the six-gyro system, a fault detection and isolation method combining the generalized likelihood test method with the residual error of the metabolism grey model is presented. The problem of isolating the single fault of the four-gyro system and the double faults of the six-gyro system using the generalized likelihood test method is analyzed. The method and process of fault detection and isolation are designed. The validity of the method presented in this paper is verified by simulation tests of the single fault of the four-gyro system and the double faults of the six-gyro system. By comparing the isolation performance with the generalized likelihood test method, it is proved that the isolation performance of the method proposed in this paper is better than that of the generalized likelihood test method. The method mentioned in this paper can effectively realize fault detection and isolation of the multi-gyro system and improve the inertial system’s reliability.

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 $$15.3\,^{\circ }{\mathrm {C}}$$ 15.3 ∘ C by 2070. This model is easy to calculate, with advantages of the high accuracy and good robustness.

Highlights • The Grey and Vector autoregressive models are coupled to improve their accuracy. • Five economic and demographic parameters are included in the new hybrid model. • This new model is a reliable forecasting tool for assessing energy demand., Forecasting energy demand in general, and electricity demand in particular, requires the developing reliable forecasting tools that can be used to monitor the evolution of consumers’ energy needs more accurately. The proposed new hybrid GM(1,1)-VAR(1) model is meant for that purpose. The latter is based on the Grey and Vector autoregressive approaches, and makes it possible to predict future demand, by taking into account economic and demographic determinants with an exponential growth trend. With an associated APE of 1.5, a MAPE of 1.628%, and an RMSE of 15.42, this new model thus presents better accuracy indicators than hybrid models of the same nature. Also, it proves to be as accurate as some recent hybrid artificial intelligence models. The model is thus a reliable forecasting tool that can be used to monitor the evolution of energy demand.•The Grey and Vector autoregressive models are coupled to improve their accuracy.•Five economic and demographic parameters are included in the new hybrid model.•This new model is a reliable forecasting tool for assessing energy demand., Graphical abstract Image, graphical abstract

In this study, the authors aim to solve the time series prediction problem through pre-predicting multiple influence factors of the target sequence. Focusing on two pre-prediction approaches of influence factors (i.e., factors driven approach and time driven approach), we propose a time series prediction method based on the least squares support vector machine and grey model (GM-LSSVM). This method could improve the prediction precision of the target time series by differentiating the data characteristics of influence factors. A case study is put forward to predict China's economy from the perspective of system innovation and technological innovation. We selected public statistics data from 2005 to 2014 from the national bureau. The numerical experiment results illustrate that the accuracy of the GM-LSSVM is able to reach 95%, which proves the effectiveness of our proposed method in practice.

As the progress of electronics and information processing technology continues, indoor localization has become a research hotspot in wireless sensor networks (WSN). The adverse non-line of sight (NLOS) propagation usually causes large measurement errors in complex indoor environments. It could decrease the localization accuracy seriously. A traditional grey model considers the motion characteristics but does not take the NLOS propagation into account. A robust interacting multiple model (R-IMM) could effectively mitigate NLOS errors but the clipping point is hard to choose. In order to easily cope with NLOS errors, we present a novel filter framework: mixture Gaussian fitting-based grey Kalman filter structure (MGF-GKFS). Firstly, grey Kalman filter (GKF) is proposed to pre-process the measured distance, which can mitigate the process noise and alleviate NLOS errors. Secondly, we calculate the residual which is the difference between the filtered distance of GKF and the measured distance. Thirdly, a soft decision method based on mixture Gaussian fitting (MGF) is proposed to identify the propagation condition through residual value and give the degree of membership. Fourthly, weak NLOS noise is further processed by unscented Kalman filter (UKF). The filtered results of GKF and UKF are weighted using the degree of membership. Finally, a maximum likelihood (ML) algorithm is applied to get the coordinate of the target. MGF-GKFS is not supported by any of the priori knowledge. Full-scale simulations and an experiment are conducted to compare the localization accuracy and robustness with the state-of-the-art algorithms, including robust interacting multiple model (R-IMM), unscented Kalman filter (UKF) and interacting multiple model (IMM). The results show that MGF-GKFS could achieve significant improvement compared to R-IMM, UKF and IMM algorithms.

International audience; This paper proposes an adaptive sensing algorithm for long-term IoT applications. The objective is to satisfy data and temporal accuracy requirements while prolonging the lifetime of battery-powered devices with energy-hungry transmission modules. The algorithm is based on the Send-on-Delta (SoD) technique combined with a GM(1,1) prediction and considers a moving temporal window and outliers removal. Numerical results show the superiority of our algorithm with respect to a linear approximation. The effectiveness of the proposal is demonstrated in terms of adaptability, accuracy, and reduction of data transfer. This is of particular relevance for applications requiring long sensing periods and high sampling rate.

International audience; 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.

Prediction of electricity energy consumption plays a crucial role in the electric power industry. Accurate forecasting is essential for electricity supply policies. A characteristic feature of electrical energy is the need to ensure a constant balance between consumption and electricity production, whereas electricity cannot be stored in significant quantities, nor is it easy to transport. Electricity consumption generally has a stochastic behavior that makes it hard to predict. The main goal of this study is to propose the forecasting models to predict the maximum hourly electricity consumption per day that is more accurate than the official load prediction of the Slovak Distribution Company. Different models are proposed and compared. The first model group is based on the transverse set of Grey models and Nonlinear Grey Bernoulli models and the second approach is based on a multi-layer feed-forward back-propagation network. Moreover, a new potential hybrid model combining these different approaches is used to forecast the maximum hourly electricity consumption per day. Various performance metrics are adopted to evaluate the performance and effectiveness of models. All the proposed models achieved more accurate predictions than the official load prediction, while the hybrid model offered the best results according to performance metrics and supported the legitimacy of this research.

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.

Effective forecasting of track irregularity development trend is critical to the railway maintenance and management. In China, track irregularity is commonly evaluated via an index called track quality index (TQI). According to the trend and random of the TQI development, a hybrid forecasting method composed of the improved grey model (GM(1,1)) and a particle swarm optimization support vector machine (PSO-SVM) is proposed in this paper. First, a non-equal interval sequence is transformed into an equal interval sequence, and an improved GM(1,1) based on the compound trapezoid quadrature formula is proposed to estimate the short-term rough trend of the TQI. Then, PSO-SVM is adopted to correct the rough results and obtain an accurate TQI trend. Numerical experiment results show that the proposed forecast method outperforms the track irregularity trend component and the grey nonlinear periodic correction method and the non-equal interval weighted grey model and neural networks in terms of relative error.

Accurate state-of-charge (SoC) estimation is crucial to guarantee the safety and reliability of lithium-ion batteries. This paper aimed to develop an advanced battery estimation method for electric vehicles based on the grey model without the need of a high-fidelity battery model demanding high computation power. The metabolic grey model (MGM) introduced metabolism mechanism to adjust the model parameters according to the evolving operating status and conditions and estimate the state of charge. To further validate the feasibility of the proposed method, the analog acquisition, communication system, and SoC estimation algorithms were programmed to embed within a LabVIEW platform. The performance of the proposed SoC estimation with MGM algorithm was finally investigated with a battery-in-loop platform under different dynamic loading profiles. The experimental results indicated that the MGM can estimate SoC that involved small samples and poor information in real time, with the maximum errors of no over 4% under various loading conditions.

The learning ability of neural networks (NNs) enables them to solve time series prediction problems. Off-line training can be applied to design the structure and weights of NNs when sufficient training data are available. However, this may be inadequate for applications that operate in real time, possess limited memory size, or require online adaptation. Furthermore, the structural design of NNs (i.e., the number of hidden neurons and connected topology) is crucial. This paper presents a novel algorithm, called the symbiotic structure learning algorithm (SSLA), to enhance a feedforward neural-network-aided grey model (FNAGM) for real-time prediction problems. Through symbiotic evolution, the SSLA evolves neurons that cooperate well with each other, and constructs NNs from the neurons with hyperbolic tangent and linear activation functions. During construction, the hidden neurons with the linear activation function can be simplified to a few direct connections from the inputs to the output neuron, leading to a compact network topology. The NNs share the fitness value with participating neurons, which are further evolved through neuron crossover and mutation. The proposed SSLA was evaluated through three real-time prediction problems. Experimental results showed that the SSLA-derived FNAGM possesses a partially connected NN with few hidden neurons and a compact topology. The evolved FNAGM outperforms other methods in prediction accuracy and continuously adapts the NN to the dynamic changes of the time series for real-time applications.

Breast Cancer forecasting is an important matter for governments, health sector investors, and other related companies. Although there are different forecasting models, choosing the suitable model is of great significance. This paper focuses on utilizing the performance of grey prediction model GM (1, 1) to the monthly total number of women referrals for Breast Cancer in Gaza Strip\Palestine from January 2002 to December 2016. The results show that the GM (1, 1) model exhibits good forecasting ability according to the MAPE criteria. Moreover, the forecasting results are compared with the results of exponential smoothing state space (ETS) and ARIMA models. The three techniques do similarly well in forecasting process. However, GM (1, 1) outperforms the ETS and ARIMA techniques according to forecasting error accuracy measure MAPE.

Energy consumption is an essential basis for formulating energy policy and programming, especially in the transition of energy consumption structure in a country. Correct prediction of energy consumption can provide effective reference data for decision-makers and planners to achieve sustainable energy development. Grey prediction method is one of the most effective approaches to handle the problem with a small amount of historical data. However, there is still room to improve the prediction performance and enlarge the application fields of the traditional grey model. Nonlinear grey action quantity can effectively improve the performance of the grey prediction model. Therefore, this paper proposes a novel incomplete gamma grey model (IGGM) with a nonlinear grey input over time. The grey input of the IGGM model is a revised incomplete gamma function of time in which the nonlinear coefficient determines the performance of the IGGM model. The WOA algorithm is employed to seek for the optimal incomplete coefficient of the IGGM model. Then, the validations of IGGM are performed on four real-world datasets, and the results exhibit that the IGGM model has more advantages than the other state-of-the-art grey models. Finally, the IGGM model is applied to forecast Japan&rsquo, s solar energy consumption in the next three years.

Despite the many benefits that energy consumption brings to the economy, consuming energy also leads nations to expend more resources on environmental pollution. Therefore, energy efficiency has been proposed as a solution to improve national economic competitiveness and sustainability. However, the growth in energy demand is accelerating while policy efforts to boost energy efficiency are slowing. To solve this problem, the efficiency gains in countries where energy consumption efficiency is of the greatest concern such as China, India, the United States, and Europe, especially, emerging economies, is central. Additionally, governments must take greater policy actions. Therefore, this paper studied 25 countries from Asia, the Americas, and Europe to develop a method combining the grey method (GM) and data envelopment analysis (DEA) slack-based measure model (SMB) to measure and forecast the energy efficiency, so that detailed energy efficiency evaluation can be made from the past to the future; moreover, this method can be extended to more countries around the world. The results of this study reveal that European countries have a higher energy efficiency than countries in Americas (except the United States) and Asian countries. Our findings also show that an excess of total energy consumption is the main reason causing the energy inefficiency in most countries. This study contributes to policymaking and strategy makers by sharing the understanding of the status of energy efficiency and providing insights for the future.

Maternal mortality rate (MMR) in China has reduced during a decade but still higher than many countries around the world. Rural China is the key region which affects over all maternal death. This study aims to develop a suitable model in forecasting rural MMR and offer some suggestions for rural MMR intervention. Data in this study were collected through the Health Statistical Yearbook (2017) which included the overall MMR in China and urban and rural mortality rate. A basic grey model (GM(1,1)), 3 metabolic grey models (MGM), and a hybrid GM(1,1)–Markov model were presented to estimate rural MMR tendency. Average relative error (ARE), the post-test ratio (C), and small error probability (P) were adopted to evaluate models’ fitting performance while forecasting effectiveness was compared by relative error. The MMR in rural China reduced obviously from 63.0 per 100,000 live births in 2005 to 21.1 per 100,000 live births in 2017. One basic GM(1,1) model was built to fit the rural MMR and the expression was X^((1)) (k + 1) = 553.80e^0.0947k – 550.00 (C = 0.0456, P > .99). Three MGM models expressions were X^((1)) (k + 1) = 548.67e^0.0923k – 503.17 (C = 0.0540, P > .99), X^((1)) (k + 1) = 449.39e^0.0887k – 408.09 (C = 0.0560, P > .99), X^((1)) (k + 1) = 461.33e^0.0893k – 425.23(C = 0.0660, P > .99). Hybrid GM(1,1)–Markov model showed the best fitting performance (C = 0.0804, P > .99). The relative errors of basic GM(1,1) model and hybrid model in fitting part were 2.42% and 2.03%, respectively, while 5.35% and 2.08%, respectively, in forecasting part. The average relative errors of MGM were 2.07% in fitting part and 17.37% in forecasting part. Data update was crucial in maintain model's effectiveness. The hybrid GM(1,1)–Markov model was better than basic GM(1,1) model in rural MMR prediction. It could be considered as a decision-making tool in rural MMR intervention.

The main distresses of asphalt pavements in seasonally frozen regions are due to the effects of water action, freeze-thaw cycles, and so on. Basalt fiber, as an eco-friendly mineral fiber with high mechanical performance, has been adopted to reinforce asphalt mixture in order to improve its mechanical properties. This study investigated the freeze-thaw damage characteristics of asphalt mixtures reinforced with eco-friendly basalt fiber by volume and mechanical properties&mdash, air voids, splitting tensile strength, and indirect tensile stiffness modulus tests. Test results indicated that asphalt mixtures reinforced with eco-friendly basalt fiber had better mechanical properties (i.e., splitting tensile strength and indirect tensile stiffness modulus) before and after freeze-thaw cycles. Furthermore, this study developed logistic damage models of asphalt mixtures in terms of the damage characteristics, and found that adding basalt fiber could significantly reduce the damage degree by about 25%, and slow down the damage grow rate by about 45% compared with control group without basalt fiber. Moreover, multi-variable grey models (GM) (1,N) were established for modelling the damage characteristics of asphalt mixtures under the effect of freeze-thaw cycles. GM (1,3) was proven as an effective prediction model to perform better in prediction accuracy compared to GM (1,2).

The factors influencing the effective utilization coefficient of irrigation water are not understood well. It is usually considered that this coefficient is lower in areas with large-scale irrigation. With this background, we analyzed the effective utilization coefficient of irrigation water using the analytic hierarchy process using data from 2014 to 2019 in Shihezi City, Xinjiang. The weights of the influencing factors on the effective utilization coefficient of irrigation water in different irrigation areas were analyzed. Predictions of the coefficient&rsquo, s values for different years were made by understanding the trends based on the grey model. The results show that the scale of the irrigation area is not the only factor determining the effective utilization coefficient of irrigation water. Irrigation technology, organizational integrity, crop types, water price management, local economic level, and channel seepage prevention are the most critical factors affecting the effective use of irrigation water. The grey model prediction results show that the effective utilization coefficient of farmland irrigation water will continuously increase and reach 0.7204 in 2029. This research can serve as a reference for government authorities to make scientific decisions on water-saving projects in irrigation districts in terms of management, operation, and investment.

In recent years, there have been international movements advocating more sustainable societies, and as a result of such movements, a remarkably important sub-branch has been shaped in systems studies called sustainability. It would be vital to propose methods that could deal with inherent complexities and uncertainties in such systems. Grey systems theory (GST) represents a nascent method that could help to solve complexities in the face of multifaceted problems, uncertainty, and complexity in systems, and the theory could considerably contribute to sustainability studies. The present study sought to fill a gap and provide an updated review of the literature on the roles and impacts of GST-based methods in sustainability studies as one of the most significant areas of exploring economic, social and environmental systems. Primarily, the theoretical foundations of sustainability and GST were briefly reviewed. Next, by categorizing the studies conducted in the literature on sustainability studies, GST-based methods used in such studies were identified. Finally, the advantages, effects and functions of GST-based theories and their applications in sustainability studies were explicated. The papers found in this systematic review were searched on such databases as Scopus, Web of Science, and ScienceDirect, as published from 2010 up to the first three months of 2020, based on these keywords: grey relation or grey relational, grey model, grey system or grey systems, grey prediction, grey control, grey incidence, grey cluster, grey decision, grey input-output. The total number of publications found on all of the databases was 446, although (following a more meticulous investigation of the publications) 145 ones were used for the comprehensive analysis. The 10 different areas in which GST was used to explore sustainability in the publications were: sustainability assessment, industrial sustainability, urban sustainability, energy sustainability, sustainability development, businesses sustainability, agricultural sustainability, sustainable products, tourism sustainability, social sustainability. The results revealed that complexity, uncertainty, and inaccessibility of a large set of data and initial statistical distributions led researchers to rely on GST in sustainability studies, and that the applied areas of GST in terms of sustainability issues had some features in common, including linguistic variables, long-term projects, technological demands, conflicting goals, and uncertainty. Moreover, compared to other methods used to deal with uncertainty, GST did not require the formation of an extensive databank of classified rules and was more practical and efficient in sustainability calculations (as complex systems) with fewer numerical calculations. Ignoring systematic approaches, causal relations, cause-effect loops, and dynamic feedback was the missing link in the application of GST in sustainability studies as complex economic, social and environmental systems.

Forecasting China&rsquo, s clean energy consumption has great significance for China in making sustainably economic development strategies. Because the main factors affecting China&rsquo, s clean energy consumption are economic scale and population size, and there are three variables in total, this paper tries to simulate and forecast China&rsquo, s clean energy consumption using the grey model GM (1, 3). However, the conventional grey GM (1, N) model has great simulation and forecasting errors, the main reason for which is the structural inconsistency between the grey differential equation for parameter estimation and the whitening equation for forecasting. In this case, this paper improves the conventional model and provides an improved model GM (1, N). The modeling results show that the improved grey model GM (1, N) built with the method proposed improves simulation and forecasting precision greatly compared with conventional models. To compare the model with other forecasting models, this paper builds a grey GM (1, 1) model, a regression model and a difference equation model. The comparison results show that the improved grey model GM (1, N) built with the method proposed shows simulation and forecasting precision superior to that of other models as a whole. In the final section, the paper forecasts China&rsquo, s clean energy consumption from 2019 to 2025 using the improved grey model GM (1, N). The forecasting results show that, by 2025, China&rsquo, s clean energy consumption shall reach the equivalent of 1.504976082 billion tons of standard coal. From 2019 to 2025, clean energy consumption shall increase by 11.32% annually on average, far above the economic growth rate, indicating China&rsquo, s economic growth shall have a great demand for clean energy in the future. Studies have shown that China&rsquo, s clean energy consumption shall increase rapidly with economic growth and population increase in the next few years.

The conflict between economic development and environmental protection has become increasingly prominent in the urbanization process of the Yangtze River urban agglomeration, the most economically developed region in Jiangsu Province in China. In order to investigate the sustainable development status, and thus provide decision support for the sustainable development of this region, the ecological footprint model was utilized to evaluate and analyze the ecological footprint per capita, the ecological carrying capacity per capita, and the ecological deficit per capita for the period from 2013 to 2017. Furthermore, the Grey model is employed to predict the development trend of the ecological footprint for 2018 to 2022. The evaluation results show that the ecological footprint per capita has been increasing year by year since 2013, reaching a peak of 2.3897 hm2 in 2015 before declining again. In the same period, the available ecological carrying capacity per capita and the ecological footprint per capita basically developed in the same direction, resulting in an ecological deficit per capita and gradually increasing from 2013 to a peak of 2.0303 hm2 in 2015 before declining. It is also found that the change of ecological carrying capacity is not substantial, and the change of the ecological deficit is mainly caused by a huge change of the ecological footprint. The forecast results show that the ecological deficit per capita will reach 1.1713 hm2 in 2018, which will be another deficit peak after 2015. However, in the later period until 2022, the ecological deficit per capita will begin to decline year by year. These results can provide effective inspirations for reducing the ecological deficit of the Yangtze River urban agglomeration, thus promoting the coordinated development of the economy and environment in this area.