Background Value Optimization Research Articles

An improved GM (1.1) model with background value optimization and Fourier-series residual error correction and its application in cost forecasting of coal mine

An improved GM (1.1) model with background value optimization and Fourier-series residual error correction and its application in cost forecasting of coal mine

Multivariate Grey Prediction Model Application in Civil Aviation Carbon Emission Based on Fractional Order Accumulation and Background Value Optimization

The GM(1,N) model, as a classical multivariate grey prediction model, can make a holistic and dynamic analysis of multiple factors and reflect the dynamic change relationship between the variable series and the related factor series. However, numerous works in the literature show that the GM(1,N) model has mechanistic defects, parametric defects, and structural defects. Therefore, the thesis establishes the OGM(1,N) model based on the GM(1,N) model by adding the linear correction term and the amount of grey action. According to the principle of dynamic optimization, the PSO algorithm is used to determine the background value. On this basis, the fractional order idea is introduced to push the model order from the integer field to the real field, and the FOBGM(1,N) model is established to systematically reduce the model error. Second, the literature in the ScienceDirect database for the last ten years is reviewed, and the carbon emission impact factors of civil aviation are selected. The calculated carbon emission values are taken as sample data based on Method 2 of Civil Aviation in Volume 2 of the 2006 IPCC Guide to National Greenhouse Gas Inventories. The results show that the prediction accuracy of the model has an increasing trend after multi-layer and multi-angle optimization. Among them, the MAPE of the OGM model and FOBGM model decreased by 24.40% and 31.86% compared with the GM(1,N) model. The 5-year average prediction accuracy of the FOBGM model reaches 99.996%, which verifies the effectiveness and practicality of the model improvement and has certain practical significance and application prospects.

Predicting Spacecraft Telemetry Data by Using Grey–Markov Model with Sliding Window and Particle Swarm Optimization

Predicting telemetry data is vital for the proper operation of orbiting spacecraft. The Grey–Markov model with sliding window (GMSW) combines Grey model (GM (1, 1)) and Markov chain forecast model, which allows it to describe the fluctuation of telemetry data. However, the Grey–Markov model with sliding window does not provide better predictions of telemetry series with the pseudo-periodic phenomenon. To overcome this drawback, we improved the GMSW model by applying particle swarm optimization (PSO) algorithm a sliding window for better prediction of spacecraft telemetry data (denoted as PGMSW model). In order to produce more accurate predictions, background-value optimization is specially carried out using the particle swarm optimization technique in conventional GM (1, 1). For verifying PGMSW, it is utilized in the prediction of the cyclic fluctuation of telemetry series data and exponential variations therein. The simulation results indicate that the PGMSW model provides accurate solutions for prediction problems similar to the pseudo-periodic telemetry series.

Forecasting China's natural gas external dependence under the "Dual Carbon" goals by a new grey model.

As a low-carbon and cost-effective clean energy source, natural gas plays an important role in achieving China's "Dual Carbon" target. In this article, a new three-parameter discrete grey prediction model is used to simulate and forecast the production and consumption of natural gas in China from the perspective of background value optimization. Then the minimum mean absolute percentage error as the objective function from the perspective of fractional order cumulative generation in the real number field. Last, a fractional order in the real number field three parameter discrete grey prediction model TDGM(1,1,z,r(R)) is constructed under the condition of optimal background value. Then we use the model to simulate and predict China's Natural Gas External Dependence (NGED) under the "Dual Carbon" target. The results show that the performance of the new model is better than that of the traditional model GM(1,1) and DGM(1,1), thus proving the practicability and effectiveness of the new model. Put forward relevant policy suggestions according to the prediction results of China's NGED, and provide decision-making reference for the Chinese government to achieve the "Dual Carbon" goals.

Analysis and Prediction of the Coupling and Coordinated Development of Green Finance–Environmental Protection in China

Green finance is an important tool to help China accelerate the process of environmental protection, but the level of coupling and coordinated development between it and environmental protection has not yet been explored. This study measures the coupling and coordinated level of the green finance–environmental protection system (GE system) in 30 Chinese provinces from 2011 to 2020 and uses the improved GM (1,1) model based on background value optimization to predict the future development trend of the coupling and coordinated level of the green finance–environmental protection system. The results show that: (1) the national average coupling and coordinated level of the green finance–environmental protection system has been in mild disharmony from 2011 to 2020 all the time, and only Guangdong Province and Zhejiang Province among them have reached the coordination level. (2) The coupling and coordinated level of the green finance–environmental protection system based on regional differences has a large gap, ranking in order: Eastern region > Central region > Western region > Northeast region, where the first-ranked Eastern region leads the rise, while the last-ranked Northeast region even shows a decreasing trend year by year. (3) The national average coupling and coordinated level will reach the coordination level in 2077, which fails to get ahead of the “2060 carbon neutrality” goal. Additionally, from the regional division, the Eastern region will be the first to reach the coordination level (2040), the Central region will reach the coordination level in 2043, the Western region is difficult to reach the coordination level, and the Northeast region shows the deterioration of coupling and coordinated degree, and the regional differences are still obvious. This study aims to reduce regional disparities, improve the coupling and coordinated development level of the green finance–environmental protection system nationwide, and implement the process of green development in China.

Forecasting Chinese provincial carbon emissions using a novel grey prediction model considering spatial correlation

In response to the errors caused by the uniform background value coefficients in the traditional grey model and the lack of analysis ability of panel data, this study proposes a two-stage background value calculation method and introduces a spatial weight matrix to employ the spatial correlation of variables in the grey model, creating a spatial grey model SGM(1,1,m) and realizing the modeling of spatial data by a grey model. The validity of the SGM(1,1,m) model was tested using carbon emission data from 30 provinces in China, and the carbon emissions of these provinces are predicted from 2020 to 2025. Conclusions are drawn as follows. First, the two-stage background value optimization mode and the addition of spatial overflow term in the model are reasonable, and the SGM(1,1,m) model improves the modeling performance in a certain sense compared with the GM(1,1) model while realizing regional association modeling. Second, the SGM(1,1,m) model has some formal similarities with the grey multivariate model, but while both are similar in terms of modeling requirements, the modeling purposes or economic meanings represented are different and should not be confused. Third, the SGM(1,1,m) model can achieve modeling predictions while providing a simple analysis of the spatial correlation of carbon emissions. Fourth, the prediction results present that the rise of carbon emissions in eastern China will level off, but the rise of carbon emissions in the central and western China will accelerate, which is largely because of the faster rise of carbon emissions in key provinces such as Shaanxi, Gansu, Ningxia, and Inner Mongolia.

Forecasting the economic indices of the high-tech industries in China using the grey multivariable convolution model

Reliable output forecasts are critical for decision-making and planning in high-tech industries. Several endogenous and exogenous factors could influence the output dynamics, and thereby a univariate model that only incorporates historical data and single method improvement is typically insufficient to generate accurate projections. In this paper, a novel grey multivariable convolution model is designed from a collaborative optimization perspective. The core innovations of this study can be summarized as follows. Initially, a collaborative framework integrating background value optimization, data preprocessing, and model structure improvement is constructed, which overcomes the internal deficiencies of the conventional grey models. Secondly, the Particle Swarm Optimization algorithm is selected to determine the optimal values of the damping accumulation parameters to enhance the adaptability and flexibility of the proposed model. Further, for validation purposes, experiments on forecasting the output of high-tech industries considering R&D investments are conducted from the national and provincial levels, among which six competing models are involved. Moreover, Monte-Carlo Simulation, incorporated with probability density analysis and statistical analysis, is introduced to evaluate the robustness of the newly-designed model. It can be demonstrated from the empirical results that the novel model is a reliable and promising method for predicting the economic indices of the high-tech industries with enhanced forecasting capability.

Corrosion depth prediction of pipeline based on improved gray model

Establishing an accurate prediction model of pipeline corrosion depth is of great practical significance for effectively evaluating the service life of pipeline, which has the advantages of saving manpower and financial resources. Based on the basic theory of gray GM (1,1) model, the improved GM (1,1) models were established by using the method of background value optimization (improved model I), translation transformation (improved model II) and combination of background value optimization and translation transformation (improved model III), and the differences of prediction accuracy between the improved models and the traditional model were analyzed. The results show that the mean relative errors of improved models are lower than those of traditional model. When the coefficient C is 30, the mean relative errors of improved model II and improved model III are only 1.073% and 1.097%. The accuracy of each improved model is higher than that of the traditional model, and the accuracy of improved model III is generally high. With the increase of coefficient C, the prediction accuracy of improved model III and improved model II gradually increases, the reasonable selection of coefficient C is helpful to improve the accuracy of improved model II and improved model III.

Forecasting CO2 Emissions Using A Novel Grey Bernoulli Model: A Case of Shaanxi Province in China.

Accurate predictions of CO2 emissions have important practical significance for determining the best measures for reducing CO2 emissions and accomplishing the target of reaching a carbon peak. Although some existing models have good modeling accuracy, the improvement of model specifications can provide a more accurate grasp of a system’s future and thus help relevant departments develop more effective targeting measures. Therefore, considering the shortcomings of the existing grey Bernoulli model, in this paper, the traditional model is optimized from the perspectives of the accumulation mode and background value optimization, and the novel grey Bernoulli model NFOGBM(1,1,) is constructed. The effectiveness of the model is verified by using CO2 emissions data from seven major industries in Shaanxi Province, China, and future trends are predicted. The conclusions are as follows. First, the new fractional opposite-directional accumulation and optimization methods for background value determination are effective and reasonable, and the prediction performance can be enhanced. Second, the prediction accuracy of the NFOGBM(1,1,) is higher than that of the NGBM(1,1) and FANGBM(1,1). Third, the forecasting results show that under the current conditions, the CO2 emissions generated by the production and supply of electricity and heat are expected to increase by 23.8% by 2030, and the CO2 emissions of the other six examined industries will decline.

Exploiting fractional accumulation and background value optimization in multivariate interval grey prediction model and its application

In the context of small sample and poor information, the data often change rapidly and interact with multiple factors which make it a challenge to analyse and predict multivariate sequences efficiently. Due to the fact that real systems usually show fractional order characteristics, the aim of this paper is to consider the approach improving the forecast results of multivariate interval grey prediction model via exploiting fractional accumulation. Noting that fractional accumulation could disturb the exponential law, the connotation prediction method is introduced to balance the disturbance. Correspondingly, a fractional connotation prediction method is constructed. In addition, traditional background value coefficient is optimized by using the particle swarm optimization algorithm (PSO). Therefore, a multivariate interval grey fractional accumulative connotation prediction model with optimized background value coefficient is constructed, in which the interval grey number time series are transformed into kernel series and radius series. Finally, the developed model is applied to clean energy prediction in China to verify the feasibility and validity.

Application of non-equidistant gray model based on optimization of background value in settlement prediction

In order to solve the influence of different original data series on model adaptability and fitting accuracy in non-equidistant grey model. Because the background value in the gray model is a key factor affecting the accuracy and adaptability of the model. Faced with this situation, this article uses the Newton-Cotes quadrature formula to optimize the background value, which improves the adaptability and fitting accuracy of the non-equidistant gray model. By constructing the model, the Newton-Cotes quadrature formula is applied to the application of the non-equidistant GM (1,1) modeling method in the settlement and deformation of buildings. The analysis shows that the new model method prediction is more suitable for building settlement monitoring and analysis, and the degree of fit is improved by about 30%. The new model is better than the traditional model.

A new grey prediction model and its application to predicting landslide displacement

Landslide displacement prediction is an important part of reducing landslide hazard losses. The existing methods to predict landslide displacement are too complicated to be applied to engineering practice. The landslide displacement evolution and the grey model prediction mechanism show a good consistency. However, the existing grey prediction model also has some shortcomings including neglecting time term. A new grey prediction model called the background value optimization nonlinear grey prediction model (BNGM(1,1, t2)) is proposed to overcome the deficiencies. BNGM(1,1, t2) is a univariate prediction model that incorporates the influence of the time term. The integration method is used to determine the background value, and the minimum value method is employed to obtain a constant term of time response functions. Five accuracy test methods for BNGM(1,1, t2) are examined. BNGM(1,1, t2) can show better performances than other multivariate prediction models including the recursive discrete multivariate grey prediction model. BNGM(1,1, t2) is applied to four typical landslide case studies. The results indicate that the BNGM(1,1, t2) has the best prediction accuracy. The complexity of BNGM(1,1, t2) is lower than the nonlinear grey Bernoulli model, the Weibull–Bernoulli grey model, and the fractional accumulation nonlinear grey Bernoulli model. The comparison of comprehensive results demonstrates that the BNGM(1,1, t2)-based method has a wide application potential to predict landslide displacement.

Forecasting Oil Consumption with Novel Fractional Grey Prediction Model Based on Simpson Formula

With the development of human society, the evolving transition of energy will become a common challenge that mankind has to face together. In this context, it is crucial to make scientific and reasonable predictions about energy consumption. This paper presents a novel fractional grey prediction model FGM(1,1,k2) based on the classical fractional grey system theory. In order to improve the prediction accuracy of the FGM(1,1,k2) model, we further analyze the model error and propose improved grey model called as SFGM with optimization of background value. The numerical cases point out that SFGM(1,1,k2) significantly outperforms other existing fractional grey models. Finally, the proposed SFGM(1,1,k2) is applied to the forecasting of oil consumption, the predicted results would provide a reference for making energy policy in new situations.

Improved methods for parameter estimation of gray model GM(1,1) based on new background value optimization and model application

In the gray prediction, the GM(1,1) model has been applied widely, but the conventional GM(1,1) model prediction shows big errors sometimes. Many researchers improve prediction accuracy by changing the basic structure of model. The paper tries to make improvements in the models parameter estimation on the basis of new background value optimization without changing the models structure, and gives the following four methods: (1) estimating the parameter of gray model GM(1,1) with the optimized value of exponential curve as the background value; (2) estimating the parameter of gray model GM(1,1) with the optimized value of power function curve as the background value; (3) estimating the parameter of gray model GM(1,1) with the optimized value of polynomial curve as the background value; (4) estimating the parameter of gray model GM(1,1) with the optimized value of interpolation function as the background value. The last part of the paper builds the GM(1,1) model of China’s total clean energy consumption with the four improved methods. The simulation and prediction results show that these methods all improve the prediction accuracy of model significantly.

Forecasting slope deformation field using correlated grey model updated with time correction factor and background value optimization

Developing precise models to characterize the slope instability mechanism quantitatively and predict slope movement behavior accurately remains a challenge in engineering geology. This paper updates the traditional GM (1,1) grey model to the TGM (1,1,p,q) grey model by adding a nonlinear time correction factor and optimizing the weighting coefficients of the background values using Genetic Algorithm. Furthermore, the TGM (1,1,p,q) has been updated to the TGM (1,n,p,q) correlated grey model by using a multivariate model of multiple monitoring boreholes to characterize the integrated deformation field. Taking the Majiagou reservoir bank landslide as an example, the time-series data of five monitoring boreholes were compared with their predicted values. The results show that the prediction accuracy of the updated grey model TGM (1,1,p,q) is acceptable, and the accuracy of the correlated updated grey model TGM (1,n,p,q) is much better. TGM (1,n,p,q) holds the potential of attaining a satisfactory prediction accuracy for the landslide deformation field forecasting.

Wind Power Prediction Based on PSO-SVR and Grey Combination Model

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.

A VVWBO-BVO-based GM (1,1) and its parameter optimization by GRA-IGSA integration algorithm for annual power load forecasting.

Annual power load forecasting is not only the premise of formulating reasonable macro power planning, but also an important guarantee for the safety and economic operation of power system. In view of the characteristics of annual power load forecasting, the grey model of GM (1,1) are widely applied. Introducing buffer operator into GM (1,1) to pre-process the historical annual power load data is an approach to improve the forecasting accuracy. To solve the problem of nonadjustable action intensity of traditional weakening buffer operator, variable-weight weakening buffer operator (VWWBO) and background value optimization (BVO) are used to dynamically pre-process the historical annual power load data and a VWWBO-BVO-based GM (1,1) is proposed. To find the optimal value of variable-weight buffer coefficient and background value weight generating coefficient of the proposed model, grey relational analysis (GRA) and improved gravitational search algorithm (IGSA) are integrated and a GRA-IGSA integration algorithm is constructed aiming to maximize the grey relativity between simulating value sequence and actual value sequence. By the adjustable action intensity of buffer operator, the proposed model optimized by GRA-IGSA integration algorithm can obtain a better forecasting accuracy which is demonstrated by the case studies and can provide an optimized solution for annual power load forecasting.

Improved multi-variable grey forecasting model with a dynamic background-value coefficient and its application

Abstract In grey system theory, the value of the background-value coefficient has a significant impact on the performance of a multi-variable grey forecasting model (MGFM). However, for most existing MGFMs, the background-value coefficient is fixed at 0.5 to simplify the modelling process. For this, a new MGFM model is proposed, which is based on a dynamic background-value coefficient. Then, the time response function and the final restored expression of the new MGFM model are deduced, proved and simplified by a Gaussian function. After this, the dynamic background-value coefficient is optimized by the Particle Swarm Optimization algorithm. To evaluate the performance of the new model, the Mean Relative Simulation Percentage Errors (MRSPEs) of the new MGFM model are compared with those of models with other background-value coefficients for three typical cases. The results show that the new MGFM model outperforms the raw MGFM models with other background-value coefficients. In addition, the closer the background value coefficient is to the optimal coefficient, the smaller the MRSPE is and the better the model performs. Lastly, the new model is employed to simulate and forecast the number of users of wireless communications in China. The findings demonstrate that the new MFGM model achieves the best performance, which confirms the effectiveness of background-value optimization in a multi-variable grey forecasting model.

Grey-Markov prediction model based on background value optimization and central-point triangular whitenization weight function

Grey-Markov forecasting model is a combination of grey prediction model and Markov chain which show obvious optimization effects for data sequences with characteristics of non-stationary and volatility. However, the state division process in traditional Grey-Markov forecasting model is mostly based on subjective real numbers that immediately affects the accuracy of forecasting values. To seek the solution, this paper introduces the central-point triangular whitenization weight function in state division to calculate possibilities of research values in each state which reflect preference degrees in different states in an objective way. On the other hand, background value optimization is applied in the traditional grey model to generate better fitting data. By this means, the improved Grey-Markov forecasting model is built. Finally, taking the grain production in Henan Province as an example, it verifies this model's validity by comparing with GM(1,1) based on background value optimization and the traditional Grey-Markov forecasting model.

The improved grey model based on particle swarm optimization algorithm for time series prediction

Grey theory is one of the most common methods for solving uncertain problems using limited data and poor information, due to its high performance in time series prediction. However, the inappropriate background value and initial value are the main factors affecting prediction accuracy of the Grey Model GM(1,1). An improved grey model based on particle swarm optimization algorithm named PGM(1,1) is proposed for time series prediction in this paper. The development coefficient of the grey model is calculated by PGM(1,1) based on particle swarm optimization, targeting at minimizing the average relative errors between the restored value and real value of the model to avoid the problem caused by background value optimization. In addition, the initial value of the Grey Model GM(1,1) is optimized and a sliding window is introduced to improve both precision and adaptability. Finally, three data sets, featuring increasing trend, decreasing trend, and wide fluctuations, are used in the experiments, showing that the proposed method achieves better prediction accuracy.