Multivariable Grey Model Research Articles

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.

A novel data-driven seasonal multivariable grey model for seasonal time series forecasting

Rapid growth in solar power generation, accompanied by random fluctuations, has important implications for the security, stability, and productivity of the grid. Therefore, accurate predictions of solar power generation provide an essential benchmark for relevant institutions to conduct grid planning and power dispatch. Thereby, a novel data-driven seasonal multivariable grey model is proposed for simulating seasonal fluctuations and non-linear trends in solar power generation. To be specific, the novel model contains the following refinements: first, the seasonal factors and time-power item are introduced to modify the insensitivity of traditional multivariable grey models to seasonal fluctuations and non-linear trends. Second, to enhance the generalizability and adaptability of the model, the parameter associated with the time-power item is determined by using the genetic algorithm. Third, on the premise of proving the model’s requirements for period length and sample size, the derivation of the time response function is expounded. For illustration and verification purposes, comprehensive experimental studies are conducted with quarterly and monthly time series samples. In addition, forecasts of the novel model are compared with five prevailing models, including grey prediction models, traditional econometric technology, and artificial intelligence. Case studies indicate that this novel model exhibits improved generalizability, stability, and reliability in the face of quarterly or monthly time series data, confirming it as an auspicious and powerful tool for future solar power generation forecasting.

Estimation of the respiratory mortality attributable to comprehensive effects of air pollutants in China using an enhanced seasonal and self-adaptive multivariate grey convolution model

Exposure to air pollutants has become a major global health threat and is a dominant contributor to increasing respiratory mortality. Accurate projections of respiratory mortality are crucial to mitigating the adverse influences of air pollution on public health and guiding long-term policy implementation. However, the forecasting models' accuracy is difficult to guarantee because seasonal factors perturb the raw series of air pollutants and respiratory mortality. This paper proposes an enhanced seasonal and self-adaptive multivariate grey convolution model to solve this dilemma. The innovations of the proposed model reside in the following areas: firstly, a seasonal operator vector of multidimensional data is initially built to digitize the seasonality of air pollutants and related mortality. Secondly, a multivariate grey convolution model with an adaptive time-lag cumulative optimization item is put forward. The weight coefficients of each driving variable at different periods are intended to adapt dynamically. Thirdly, the self-adaptive time-delay coefficient is determined by the Particle Swarm Algorithm, enhancing the accuracy of predictions. Theoretically, the generalizability and adaptability of the newly presented model are well-validated. Moreover, its practical applicability and higher forecasting performance are further verified in estimating the respiratory mortality attributable to the comprehensive effects of air pollutants in China.

A novel conformable fractional nonlinear grey multivariable prediction model with marine predator algorithm for time series prediction

To promote the development of multivariate prediction modelling in small sample environments, this paper constructs a new multivariate prediction model named CFDNGBM(r,N) by integrating the marine predator algorithm (MPA), the modified conformable fractional-order accumulation operation (MCFAO) and the grey prediction model. In CFDNGBM(r,N), the MCFAO and time-delay polynomial are used to enhance the model prediction performance, the backward difference operation is used to activate the unbiasedness, and the unbiased regularization algorithm is used to estimate the model parameters. In addition, the MPA is used to optimize the hyperparameters in the model. The experimental results show that the CFDNGBM(r,N) outperforms the 12 benchmark algorithms and all the optimization measures are effective, both of which confirm the effectiveness of the proposed methods.

A spatial lagged multivariate discrete grey model for forecasting an economy-energy-environment system

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

Prediction of carbon dioxide emissions in China using a novel grey model with multi-parameter combination optimization

With the rapid development of industrialization and urbanization in China, the carbon dioxide emissions keep increasing for a long time. It is of great significance to reasonably predict the carbon dioxide emissions to realize “carbon peaking and carbon neutrality” goals in China. To this end, based on the new structure grey model, the variable orders are defined and optimized differentially, and the smoothing generation operator is introduced to variously design and optimize the driving term. Thus, a new multivariable grey prediction model with the combination optimization of multi-parameter is constructed. The new model is applied to predict the carbon dioxide emissions in China, and its comprehensive error is only 0.085%, which is far superior to the traditional similar grey prediction models (3.274%, 7.713%). This study provides a new modeling method for carbon dioxide emissions prediction, and has positive significance for enriching and improving the structural and methodological systems of grey prediction models.

A novel multivariable grey differential dynamic prediction model with new structures and its application to carbon emissions

The accurate prediction of carbon emissions is of great significance for countries to implement scientific and effective policies and measures. In this paper, a novel multivariable grey differential dynamic prediction model is established to analyse and forecast China’s carbon emissions. The differential term of the correlation variables is introduced to consider the influence of the rate of change of the related factors on the system. The linear correction term and grey action are introduced to increase the stability and adaptability of the model. The whitening differential equation of the model is solved by the Sadik transform, and the time response of the model is obtained. In the case study, the model used China’s carbon emissions and related data from 2004 to 2019 to calculate four cases. Its minimum simulation and prediction errors are 1.4435% and 3.1739%, respectively. Compared with the other four models, this model has better simulation and prediction accuracy, which proves the model’s effectiveness. Finally, the model forecasts China’s carbon emissions from 2020 to 2024, and some suggestions are put forwards based on the predicted results.

Two novel nonlinear multivariate grey models with kernel learning for small-sample time series prediction.

The online version contains supplementary material available at 10.1007/s11071-023-08296-y.

Application of the novel-structured multivariable grey model with various orders to forecast the bending strength of concrete

Bending strength of concrete is one of the significant indexes to measure the mechanical properties of concrete. A reliable prediction about the bending strength of concrete is of great importance to maintain the health state and service life of concrete. However, it is difficult to obtain reliable data of large samples due to the high cost, serious destructiveness and complex influencing factors of concrete bending strength test data collection. In view of this, based on the multivariable grey prediction model whose modeling object is small data, we construct a new novel-structured multivariable grey prediction model with various orders for predicting the bending strength of concrete. It defines and optimizes the accumulative orders differentially and introduces a nonlinear correction term to expand the model structure. Then, the bending strength of concrete is modeled using the new model, and its comprehensive error is only 0.035 %, which is much smaller than the conventional NSGM(1,N) and FMGM(1,N) models (5.232 % and 2.624 %, respectively). The findings provide a new modeling method for the prediction of concrete bending strength in areas with large temperature difference, and have significance for enriching and improving the methodologies of grey prediction models.

A new hybrid multivariate grey model based on genetic algorithms optimization and its application in forecasting oil products demand

PurposeConventional statistical forecasting methods typically need a large sample size or the use of overly confident hypotheses, like the Gaussian distribution of the input data. Unfortunately, these input data are frequently scarce or do no not follow a normal distribution law. A grey forecasting model can be developed and used to predict energy consumption for at least four data points or ambiguous data based on grey theory. The standard grey model, however, may occasionally result in significant forecasting errors.Design/methodology/approachIn order to reduce these errors, this paper proposes a hybrid multivariate grey model (namely Grey Modeling (1,N)) optimized by Genetic Algorithms with sequential selection forecasting mechanism, abbreviated as Sequential-GMGA(1,N). A real case of Cameroon's oil products consumption is considered to demonstrate the effectiveness of the proposed forecasting model.FindingsThe results show the superiority of Sequential-GMGA(1,4) when compared with the results of competing grey models reported in the literature, with a mean absolute percentage error as low as 0.02%.Originality/valueWithout changing the model's basic structure, the suggested framework completely extracts the evolution law of multivariate time series. Regardless of data patterns, Sequential-GMGA(1,4) actively enhances all model parameters over the course of each predicted timeframe. Consequently, Sequential-GMGA(1,4) improves forecast accuracy by resolving the discrepancy between the model's least sum of squares of prediction errors and the parameterization approach based on grey derivative.

Fractional multivariate grey Bernoulli model combined with improved grey wolf algorithm: Application in short-term power load forecasting

The accurate prediction of power load is helpful to make reasonable power generation plans and scientific dispatching schemes and achieve the goal of energy saving and emission reduction.There are many factors influencing the power load, and there may be a nonlinear relationship between the power load and these influencing factors. A new fractional multivariate grey Bernoulli model, referred to as MFGBM (q, r, N), is developed in this article for the short-term prediction of power load. The fractional differential equation and fractional accumulation generation are integrated into MFGBM (q, r, N). Second, this paper improves the grey wolf algorithm to better optimize many parameters in the model. The algorithm is improved by using a chaotic Tent map to optimize the initial population composition, adding inertia weights to change the position vector of the grey wolf, and introducing a nonlinear function and Lévy flight to enhance local exploitation and global exploration ability. Finally, this paper selects the daytime and nighttime power loads in Australia and takes the electricity price, humidity, and temperature as the influencing factors to validate the prediction capability of MFGBM (q, r, N). Our findings indicate that MFGBM (q, r, N) is highly applicable to short-term power system prediction.

Analysis of Air Quality Evolution Trends in the Chinese Air Pollution Transmission Channel Cities under Socioeconomic Development Scenarios

In this paper, based on the traditional grey multivariate convolutional model, the concept of a buffer operator is introduced to construct a single-indicator buffered grey multivariate convolutional model applicable to air quality prediction research. The construction steps of the model are described in detail in this paper, and the stability of the model is analyzed based on perturbation theory. Furthermore, the model was applied to predict the air quality composite index of the “2 + 26” Chinese air pollution transmission corridor cities based on different socioeconomic development scenarios in a multidimensional manner. The results show that the single-indicator buffered grey multivariate convolutional model constructed in this paper has better stability in predicting with a small amount of sample data. From 2020 to 2025, the air quality of the target cities selected in this paper follows an improving trend. The population density, secondary industry, and urbanization will not have a significant negative impact on the improvement of air quality if they are kept stable. In the case of steady development of secondary industry, air quality maintained a stable improvement in 96.4% of the “2 + 26” cities. The growth rate of population density will have an inverted U-shaped relationship with the decline in the city air quality composite index. In addition, with the steady development of urbanization, air quality would keep improving steadily in 71.4% of the “2 + 26” cities.

The Prediction of Steel Bar Corrosion Based on BP Neural Networks or Multivariable Gray Models.

The corrosion of steel bars in concrete has a significant impact on the durability of constructed structures. Based on the gray relational analysis (GRA) of the accelerated corrosion data and practical engineering data using MATLAB, a back propagation neural network (BPNN) model, a multivariable gray prediction model (GM (1, N)), and an optimization multivariable gray prediction model (OGM (1, N)) of steel corrosion were established by using a sequence of the key affecting factors. By comparing the prediction results of the three models, it is found that the GM (1, N) model has larger fitting and prediction errors for steel corrosion, while the OGM (1, N) model has smaller prediction errors in the accelerated corrosion data; the BPNN model offers more accurate predictions of the practical engineering data. The results show that the BPNN and OGM (1, N) models are all suitable for the prediction of steel bar corrosion in concrete structures.

A technique for improving petroleum products forecasts using grey convolution models and genetic algorithms

Forecasting energy consumption is a major concern for policymakers, oil industry companies, and many other associated businesses. Though there exist many forecasting tool, selecting the most appropriate one is critical. GM(1,1) has proven to be one of the most successful forecasting tool. GM(1,1) does not require any specific information and can be adapted to predict energy consumption using a minimum of four observations. Unfortunately, GM(1,1) on its own will generate too large forecast errors because it performs well only when data follow an exponential trend and should be implemented in a political-socio-economic free environment. To reduce these short-comings, this paper proposes a new GM(1,n) convolution model optimized by genetic algorithms integrating a sequential selection mechanism and arc consistency, abbreviated Sequential-GMC(1,n)-GA. The new model, like some recent hybrid versions, is robust and reliable, with MAPE of 1.44%, and RMSE of 0.833.•Modification, extension and optimization of grey multivariate model is done.•The model is very generic can be applied to a wide variety of energy sectors.•The new hybrid model is a valid forecasting tool that can be used to track the growth of households’ energy demand.

The Impact of Economic Growth, Renewable Energy, Non-renewable Energy and Trade Openness on the Ecological Footprint and Forecasting in Turkiye: an Case of the ARDL and NMGM Forecasting Model

In this study, the effects of economic growth, renewable and non-renewable energy production and trade openness on ecological footprint for Turkey were investigated. By using the annual data for the period 1980-2016, the short- and long-term relationship with the Autoregressive Distributed Lag Model (ARDL) was examined. In addition, a prediction model is presented with the Multivariate Gray Prediction Model (NMGM) method. According to the findings obtained from the ARDL model, economic growth, renewable and non-renewable energy production have a positive effect of 0.166, 0.1431 and 0.1118, respectively, on the ecological footprint in the long run. In the short run, economic growth, renewable energy production and non-renewable energy production has the same effect of 0.1941, 0.1673 and 0.1308 on the ecological footprint. In addition, no effect of trade openness on the ecological footprint has been detected, both in the long and short run. The originality of this study is to investigate the short- and long-term effects of economic growth and trade openness on the ecological footprint, in addition to the amount of renewable energy production and non-renewable energy production in Turkey, using the ARDL model. In addition, another originality of this study is a dynamic evaluation of the ecological footprint for Turkey and the determination of the impact values of the variables that affect the ecological footprint. ARIMA models, in which the dependent variable is estimated with its own past values, are generally used as estimation models. Likewise, univariate gray estimation models also make estimations with the dependent variable's own past values. Another unique aspect of this study is the use of a gray estimation model, in which the variables that have been shown to have a significant short- and long-term relationship with ARDL are also included in the model.

Research on the Landslide Prediction Based on the Dual Mutual-Inductance Deep Displacement 3D Measuring Sensor

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.

Grey Multivariable Prediction Model of Energy Consumption with Different Fractional Orders

The scientific prediction of energy consumption plays an essential role in grasping trends in energy consumption and optimizing energy structures. Energy consumption will be affected by many factors. In this paper, in order to improve the accuracy of the prediction model, the grey correlation analysis method is used to analyze the relevant factors. First, the factor with the largest correlation degree is selected, and then a new grey multivariable convolution prediction model with dual orders is established. Different fractional orders are used to accumulate the target data sequence and the influencing-factor data sequence, and the model is optimized by particle swarm optimization algorithm. The model is used to fit and test the energy consumption of Shanghai, Guizhou and Shandong provinces in China from 2011 to 2020 compared with other multivariable grey prediction models. Experimental results with the MAPE and RMSPE measurements show that our improved model is reasonable and effective in energy consumption prediction. At the same time, the model is applied to forecast the energy consumption of the three regions from 2021 to 2025, providing reliable information for future energy distribution.

A damping grey multivariable model and its application in online public opinion prediction

Online public opinion plays pivotal role in social stability, and predicting hotness of online opinion accurately can provide theoretical and practical guidance for government and enterprises. A damping accumulated multivariable grey model is proposed to forecast the online public opinion trends in this paper. Firstly, the dynamic damping trend factor is introduced into the accumulation process, so that the model can adjust the accumulating order of different sequences more flexibly. Secondly, considering that the accumulated sequences have grey exponential rate property, the damping grey multivariable model is established by optimizing the structure of the background values. Finally, due to the assumption that the relevant factor variables are grey constants, the systematic error occurs in the traditional grey multivariate model, the time response equation is given to reduce error by using the composite quadrature method. Two real cases are used for empirical analysis to verify the effectiveness of the new model. And the forecasting accuracy and robustness of the new model is better than those of other prediction models. Therefore, the model is an effective method dealing with nonlinear problems, which further improves the grey modeling theory and can be applied to the prediction of online opinion.

A nonlinear interactive grey multivariable model based on dynamic compensation for forecasting the economy-energy-environment system

Achieving the goals of emissions intensity reduction and energy structure transformation while ensuring stable economic development is essential for sustainable development in China. Establishing a concise and accurate model for predicting the 3E (economy-energy-environment) system is beneficial for decision-makers in developing optimal long-term energy and environmental planning. Although previous studies have concentrated on the interaction of variables in the 3E system, frameworks for prediction have thus far been limited. In this paper, we develop a novel nonlinear interactive grey multivariable model based on dynamic compensation, denoted as DCNIGM1,N, to perform the prediction of the 3E system. More specifically, the proposed model innovatively takes into account nonlinear driving effects to elucidate nonlinear interactive relationships between the system variables. A dynamic compensation mechanism is introduced into the systematic grey modeling for the first time to adapt to a dynamic system. In addition, the Whale Optimization Algorithm (WOA) is employed to determine the optimal nonlinear parameters to improve the forecast accuracy. To evaluate the performance of the DCNIGM1,N model in forecasting the 3E system, two existing grey forecasting models, three statistical approaches, and three machine learning models are selected as the benchmark models. Moreover, two more cases with different variables of the 3E system are applied to verify the feasibility and effectiveness of the proposed model. Experimental results indicate that the DCNIGM1,N model possesses the most excellent performance in all cases, showing the effectiveness and generalizability of the proposed method. The prediction from 2019 to 2020 shows that carbon emissions, total energy consumption, and gross domestic product will grow steadily.

Research and application of multi-variable grey optimization model with interactive effects in marine emerging industries prediction

Marine emerging industries have become an important growth point of the marine economy and a new driving force for the transformation and upgrading of the nation. Therefore, it is crucial to predict the future trend of output values of marine emerging industries for the development of the marine economy. To measure simultaneously the output value of China's three marine emerging industries (marine power industry, marine biopharmaceutical industry, and marine chemical industry) and considering the actual situation and internal connection of mutual influence and restriction among the three industries, the interaction term is introduced on the basis of the existing MGM(1,m) model, and a MGM(1,m) model with interactive effects (IMGM(1,m) model) is established. Also, the Particle Swarm Optimization (PSO) algorithm is used to optimize the predicted value in the model. The empirical results show that the MAPE of the training set is 2.04 %, 0.22 %, and 1.33 %, while those of the test set is 5.54 %, 3.68 %, and 4.80 %, respectively. The results of the proposed model are significantly better than other comparison models. Ultimately, the new model will be adopted to predict the output value of China's marine power, marine biopharmaceutical, and marine chemical industries from 2020 to 2023. It is estimated that by 2023, the output value of the three marine industries will reach 60.050, 59.790, and 84.497 billion yuan respectively, which will continue to maintain a growing trend. The forecast results will provide strong support for national policies and development plans for marine emerging industries.