Multivariable Grey Prediction Research Articles

Prediction of water consumption in Beijing based on the multi-variable grey model with adjacent accumulation

Abstract With the rapid development of the social economy, the importance of water resources is becoming increasingly prominent. Urban water demand in Beijing has been growing rapidly. Accurate water consumption forecasting is of utmost importance for reasonable allocation and optimization of water supply systems. In this study, an innovative multi-variable grey prediction model with adjacent accumulation (AOGM(1,N)) is proposed to predict Beijing's annual water consumption for four different water usage scenarios (domestic water, agricultural water, industrial water, and environmental water) by incorporating the adjacent accumulation into the optimized grey model. Grey relational analysis is used to select the key influence factors. The adjustable parameter of the prediction model is chosen by using the particle swarm optimization algorithm. By comparing with other models in the existing literature, the proposed AOGM(1,N) model has evidently superior prediction performance based on the error indicators, which supports the novel method's merits and validity. This study could help us better understand water usage and be applied to the planning and management problems of urban water supply systems.

A novel dynamic grey multivariate prediction model for multiple cumulative time-delay shock effects and its application in energy emission forecasting

Energy emission systems are often influenced by external information and policy shock. However, conventional grey models ignore the existence of the impact of multiple shock events and cumulative time-delay effects, which are crucial for achieving accurate forecasts. From a dynamic perspective, we aim to establish a multivariable grey prediction model considering the impact of multiple shock events, namely MSGTDM(1,N) model. Specifically, to accurately describe the impact of different types of external shocks on the system, three kinds of nonlinear dynamic shock functions are designed, including growth dynamic shock function, decline dynamic shock function, and slope dynamic shock function. Based on this, multi-dimensional instantaneous shock utility terms and cumulative time-delay utility terms are constructed to accurately measure shock effects. And Whale Optimization Algorithm is employed to determine the optimal parameters of the shock functions through comprehensive comparative analysis. The findings affirm the MSGTDM(1,N) model's higher predictive accuracy and validity. Consequently, the forecast results of China's carbon emissions from coal and natural gas consumption in 2022–2025 provide a reliable basis for adjusting the energy structure and implementing the “dual-carbon” policy effectively.

A novel fractional order variable structure multivariable grey prediction model with optimal differential background-value coefficients and its performance comparison analysis

PurposeTraditional multivariable grey prediction models define the background-value coefficients of the dependent and independent variables uniformly, ignoring the differences between their physical properties, which in turn affects the stability and reliability of the model performance.Design/methodology/approachA novel multivariable grey prediction model is constructed with different background-value coefficients of the dependent and independent variables, and a one-to-one correspondence between the variables and the background-value coefficients to improve the smoothing effect of the background-value coefficients on the sequences. Furthermore, the fractional order accumulating operator is introduced to the new model weaken the randomness of the raw sequence. The particle swarm optimization (PSO) algorithm is used to optimize the background-value coefficients and the order of the model to improve model performance.FindingsThe new model structure has good variability and compatibility, which can achieve compatibility with current mainstream grey prediction models. The performance of the new model is compared and analyzed with three typical cases, and the results show that the new model outperforms the other two similar grey prediction models.Originality/valueThis study has positive implications for enriching the method system of multivariable grey prediction model.

Lithium-ion battery state of health monitoring based on an adaptive variable fractional order multivariate grey model

Accurate assessment of the state of health of lithium-ion batteries using relevant factors is crucial for the maintenance of lithium-ion batteries in electric vehicles. Firstly, data features are extracted from University of Maryland public dataset and dataset is pre-processed. Secondly, the extracted features were analysed using a grey relational analysis model to identify the most significant factors affecting the state of health. Thirdly, this paper proposed an adaptive variable fractional order multivariate grey prediction model to accurately estimate the state of health of lithium-ion batteries. The comparative results demonstrate the overall superiority of the proposed model.

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.

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.

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.

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.

Prediction of Gas Well Annulus Pressure Based on Neural Network

Abnormal pressure in the annulus is one of the main risks that threaten the safe production of gas wells and affect their production efficiency. To further improve the gas well annulus pressure management level based on the gray system theory and new information priority ideology, this study introduced a new perspective. First, we considered the influence of various factors related to the change of the gas well annulus pressure and performed a grey correlation analysis. Next, we established a multivariable grey prediction model of gas well annular pressure with the associated metabolic function. The measured data of high-pressure and high-yield gas wells in Northwestern Sichuan for 12 consecutive hours in a day, was used as a case study. The effectiveness of this proposed model was verified by comparing the predicted results with the measured data. The research results verify the feasibility of the gray system theory for the dynamic prediction of gas well annulus pressure and provide theoretical support for the early diagnosis and active prevention of continuous annulus pressure.

A novel discrete multivariable grey model with spatial proximity effects for economic output forecast

The temporal and spatial characteristics of the collected data typically play an essential role in time series forecasting. However, traditional grey models pay more attention to temporal information, meanwhile disregarding the presence of spatial features critical to producing accurate forecasts. Moreover, the grey theory has few attempts to overcome this problem. Given this situation, this paper proposes a novel multivariable grey prediction model considering the spatial proximity effect for time series forecasting. More specifically, the complete spatial distance index is defined initially based on the geographical and economic distance to quantify the intensity of the spatial proximity impact. On this basis, the spatial proximity effect term is constructed and incorporated into the conventional discrete multivariable grey model, establishing the novel model. Subsequently, the particle swarm optimization algorithm determines the optimal weight coefficient in the developed index. For illustration and verification purposes, the proposed model performs experiments predicting Jiangsu's economic outputs compared to five prevalent benchmarks. Furthermore, three statistical metrics, the Diebold-Mariano test, the Monte Carlo experiments, and the probability density analysis are employed to validate the model's efficacy and robustness. Empirical results demonstrate that the proposed method outperforms all five competitors with strong robustness and broad generalization. Therefore, this new model is used for forecasting Jiangsu's future economic outputs from 2021 to 2025.

A simulation approach of indoor temperature in existing buildings driven by short-term field measured data

ABSTRACT Simulation of indoor temperature provides important references for thermal environment not only for buildings at design stage but also for existing buildings. The current thermal environment simulation software tools suit for buildings at design stage, however not for an existing building. A model is proposed to simulate indoor temperature combining Optimization multivariable grey prediction model (OGM(1,N)) and Elman neural network. The proposed model is trained by short-term field measured data. A unit is assembled to measure and record thermal parameters in a case natural ventilated building at half-hourly intervals during 7:00 May 29 and 6:30 June 2010. Programming in Matlab implements the proposed model and referenced models. The maximum mean deviation is 0.46°C, the maximum standard mean square deviation is 0.65°C. Three referenced indoor temperature simulation models, OGM(1,N), Elman neural network, and Designer’s Simulation Toolkit are executed, respectively, in case building to provide comparison. Compared with referenced models, the proposed model has higher accuracy and stronger robustness. It is expected that this study provides important references for thermal environment assessment in existing buildings using short-term field measured data.

A novel multivariable grey prediction model with different accumulation orders and performance comparison

The uniformity of the accumulation orders of the dependant and independent variables in traditional multivariable grey prediction models ignores the differences in physical properties amongst the variables, which results in unstable or even abnormal model performance. To this end, a new multivariable grey prediction model with dual orders is proposed by differentially defining and optimizing the accumulation orders of the dependant and independent variables. The new model expands the functional structure of the traditional multivariable grey prediction model, improves the preprocessing effect of the accumulation orders based on the original sequences, and enhances the modelling performance of the multivariable grey prediction model. A comparative analysis of three cases verifies that the new model outperforms the other two mainstream multivariable grey prediction models, which confirms that the dual orders of the novel model are reasonable and effective.

Application of a novel time-delay grey model based on mixed-frequency data to forecast the energy consumption in China

It is of great constructive significance to predict total energy consumption accurately. At present, there are many prediction tools for processing and analyzing energy consumption, but most of them have the disadvantages of complex modeling or low accuracy, and less involve the modeling in the case of mixed-frequency data. For the sake of reflecting the timeliness of prediction, this paper analyzes the annual energy consumption influenced by high-frequency data. Based on mixed-frequency data, a novel grey model which comprehensively considers the time-delay cumulative effect of system behavior variable is designed. When there are high-frequency correlation factor sequences and low-frequency system behavior sequences, the model can automatically assign weights according to the characteristics of the high-frequency sequence. In addition, the inertia of the system behavior variable is considered more systematically, and the time-delay cumulative effect of the system behavior variable is incorporated into the original grey model. From the angle of verifying the feasibility of this new constructed model, an original multivariable grey prediction model and two non-grey methods are selected as the comparative models. Empirical findings indicate that the mean absolute percentage errors of the proposed model are 0.0387% and 0.0287% in the simulated stage and predicted stage, which is the lowest among the four models, and highlights the excellent performance. Eventually, the proposed model is applied to make a short-term forecast about total energy consumption in China from 2020 to 2023, and the predictions provide guidance for the formulation of energy consumption objectives.

A new multivariate grey prediction model for forecasting China's regional energy consumption.

Predicting energy consumption is an essential part of energy planning and management. The reliable prediction of regional energy consumption is crucial for the authority in China to formulate policies by with respect to the dual control of its energy consumption and energy intensity. Given that energy consumption is affected by a number of factors, this study proposes a non-homogeneous, discrete, multivariate grey prediction model based on adjacent accumulation to predict the regional energy consumption in China. Interestingly regional GDP was selected by grey relational analysis as the independent variable in the proposed model. The results show that it can outperform the other multivariate grey models considered in terms of predicting regional energy consumption in China. Moreover, we found that economic development and energy consumption of each region in China remain closely related. In the post-COVID-19 period, regional economic development will continue to grow and increase energy consumption.

A new multivariable grey model and its application to energy consumption in China

Based on the nonlinearity of energy consumption systems and the influence of multiple factors, this paper presents a nonlinear multivariable grey prediction model with parameter optimization and estimates the parameters and the approximate time response function of the model. Next, a genetic algorithm is applied to optimize the nonlinear terms of the novel model to seek the optimal parameters, and the modelling steps are outlined. Then, to assess the effectiveness of the novel model, this paper adopts Chinese oil, gas, coal and clean energy as research objects, and three classical grey forecasting models and one time series method are chosen for comparison. The results indicate that the new model attains a high simulation and prediction accuracy, basically higher than that of the three grey prediction models and the time series method.

Significance analysis of influencing factors of highway freight transportation in China and multi-variable grey prediction for its development

With the prosperity of national economy and the development of highway construction, highway freight transportation plays an increasingly important role in the market economy. Due to its great flexible characteristic, highway freight transportation has been the main mode of transportation in China. On the macro level, there are many factors affecting the development of highway freight transportation especially under the background of the new era. Based on the historical data of the development of highway freight transportation, grey entropy analysis method is applied to analyze the significance of influencing factors for the development of highway freight transportation whose key indicator is highway freight turnover. Then GM (1, N) model is established to predict the development trend of highway freight turnover and its significant influencing factors. Finally, main problems existing in highway freight transportation and development prospect were discussed and analyzed. The research results show that the three most significant factors affecting the development of road freight turnover in China are the total state revenue, GDP and average distance of highway freight. The established GM (1, N) model can conduct high precision prediction for the development of highway freight transportation. Opportunities and challenges of highway freight transportation industry coexist and its development prospect is promising. It is expected to provide beneficial references for the development strategy and decision-making of highway freight transportation in China.

Multi-parameter grey prediction model based on the derivation method

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

A multivariate grey prediction model based on energy logistic equation and its application in energy prediction in China

The energy consumption problem is an important issue in the development process of various countries, and scientific methods for predicting energy consumption can assist governments in making decisions. The energy consumption trend usually shows a saturated S-shaped curve, and the mathematical model of the Logistic function can be used to fit this trend. Based on the Energy Logistic equation, a novel multivariable grey prediction model of energy consumption is proposed in this paper. The least square method is used to estimate the parameters of the model, and the approximate time response formula of the model is obtained. The degree of correlation between several energy consumptions is calculated by the grey correlation analysis. Then, from the angle of the three main energy sources to establish the energy consumption prediction model respectively, and the validity of the model is verified by selecting the data of three typical coal, crude oil and natural gas consumption provinces in China (Shandong Province, Heilongjiang Province and Guangdong Province). Compared with the other six multivariate grey models, the results show that the new model is superior to the other models according to five test indexes. Finally, based on the modelling of three provinces in China, the model predicts the consumption of three kinds of energy in the next five years, and a correlation analysis is performed according to the prediction results.

A novel multivariable grey prediction model and its application in forecasting coal consumption

Coal is an important energy source worldwide. Objectively and accurately predicting coal consumption is conducive to healthy coal industry development, because such predictions can provide references and warnings that are useful in formulating energy strategies and implementing environmental policies. Population size and area economic development are the main factors that affect coal consumption. Considering the above influences, this paper first establishes a differential equation and proposes a novel multivariable Verhulst grey model (MVGM(1,N)) based on grey information differences. MVGM(1,N) extends classical model from single-variable to multivariate and diminishes the characteristics of Verhulst’s reliance on saturated S-shaped and single-peak data, making classical model more applicable to real situations. To prove the effectiveness of MVGM(1,N) simulation experiments are carried out in areas with high coal consumption. The result of this proposed model is more precise than that of NLARX, ARIMA and five classical grey models Finally, this novel multivariable model predicates coal consumption of Inner Mongolia and Gansu Provinces in China, the results show that MVGM(1,N) is preferable to other models, indicating that this model can effectively predict coal consumption.