Multivariable Grey Model Research Articles

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.

Estimating energy-related CO2 emissions using a novel multivariable fuzzy grey model with time-delay and interaction effect characteristics

An objective and accurate forecast of carbon emissions can provide the government with an important baseline for the implementation of the Green Economic Development Strategy. This paper considers the time-lag effect and the interaction effect of the influencing factors on carbon emissions simultaneously and establishes a new grey multivariate coupled model (CTGM(1,N)) for carbon emission projection by introducing the Choquet fuzzy integral and grey multivariate delay model. To further promote the prediction performance, the time-lag number of each influencing factor is determined by time-delay grey correlation analysis, and the whale optimization algorithm is designed to acquire the optimal parameters and accuracy of the model. The new model is designed to fitting carbon emissions data in three countries and compare it to six reference models. The performance test shows that the CTGM(1,N) model has high stability. The results of the forecasts show that China's carbon emissions are expected to rise by 1.17% by 2025 from 2020 levels. Meanwhile, emissions will decrease by 5.08% (US) and 0.88% (Japan). The prediction results were consistent with the development status of the three countries. According to the results, we can grasp the development trend of carbon emissions and formulate targeted strategies to achieve sustainable development.

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 novel multivariate grey model of energy consumption under carbon trading background and its application

Climate warming and the energy crisis have been high-profile issues today, and carbon trading is considered one of the essential means to solve the problem. Carbon trading cannot ignore the impact on energy consumption and carbon emissions. Therefore, it is beneficial to develop a low-carbon economy to scientifically predict the trend of energy consumption and make timely investment decisions and policies in carbon trading. Based on the modelling mechanism of energy economy and the grey forecasting model, this paper studies the dynamic relationship among energy consumption, carbon emissions, economic growth, and carbon trading price and then constructs a grey prediction model of energy consumption driven by carbon trading. The least-square method and recursive mathematical method were used to obtain the model’s parameter estimation and corresponding time formula, respectively. In the end, we apply the model to the energy consumption in China, and three experimental results reveal that the prediction performance of the novel model is significantly better than the existing four grey models. And it is predicted that the energy consumption of coal in China will increase by 15.3118% in 2025, which can provide an essential reference for the energy structure adjustment and environmental policymaking in China.

Optimized multivariate grey forecasting model for predicting electricity consumption: A China study

The power industry has significantly contributed to the prosperity of the national economy, and accurate prediction can reflect the development trend of the power system and power market. The short-term electricity consumption of a country exhibits both annual growth certainty and random change uncertainty, which can be suitably considered with the grey forecasting model. Regarding the short-term trends of electricity consumption in China, this study established an optimized multivariate grey forecasting model with variable background values (OGM(1, N) model) to forecast the electricity consumption level in China. The established model could be converted into the GM(1, N) model and different variant models by adjusting the model parameters. With Beijing, Tianjin and Shanghai as examples, the OGM(1, N) model is compared to the GM(1, N) model and its variant model. The excellent prediction results confirm the feasibility of the proposed model. Then, the proposed model is applied to study China’s electricity consumption. The research results indicated that the OGM(1, N) model attains an extraordinarily high precision in the prediction of electricity consumption and can provide a practical reference for accurate electricity consumption prediction.

A novel multivariate grey model for forecasting periodic oscillation time series

To solve the problem that the grey multivariate prediction model cannot well simulate systems with periodic oscillations, a novel multivariate grey model called the GM(1,N|sin) power model is proposed. The power exponential term and dynamic sinusoidal function are developed to represent the nonlinear relationship and periodic oscillations of the independent and dependent variables in the proposed model, respectively. First, the discrete time response formula for generating the simulated values at each time point is given. Second, the nonlinear programming model based on the particle swarm optimization algorithm is established to solve the power exponential and periodic coefficients. In addition, to enhance the generalization ability of the parameters, an improved nonlinear programming model considering the accuracy of the validation set is constructed. Finally, in the case studies, the quarterly electricity consumption of Jiangsu Province and PM2.5 concentrations in Nanjing are adopted to test the effectiveness of this model, and the results are obtained respectively through the GM(1,N|sin) power model and alternative models. The results indicate that the accuracy of GM(1,N|sin) power model in the time series with periodic oscillations outperforms the other six models in this paper.

A novel self-adaptive fractional multivariable grey model and its application in forecasting energy production and conversion of China

Energy production and conversion have a significant impact on the economic development of all countries in the world. China’s energy production and conversion are large. Therefore, accurate mid-to-long term China’s energy production and conversion forecasting is becoming more and more important for integrating energy systems and energy strategic planning. For this purpose, a novel fractional grey sequence is proposed based on Grunwald–Letnikov fractional calculus. Furthermore, a novel self-adaptive fractional multivariable grey model is proposed based on the novel sequence. In this article, we compare several classical optimization algorithms and finally choose Particle Swarm Optimization (PSO) to compute the parameters. In addition, Monte-Carlo simulation and probability density analysis (PDA) are presented in this article to verify the model’s performance. Monte-Carlo simulation reduces the randomness of the results of the model runs to a certain extent. Probability density analysis visualizes this randomness through kernel density estimation (KDE). This paper compares the new model with the existing seven grey models and predicts the total energy consumption per capita, energy conversion efficiency and total renewable energy in China, respectively. The experimental results show that the new model is superior to the other seven models in terms of stability and prediction accuracy.

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.

The impact of Google Trends index and encompassing tests on forecast combinations in tourism

El impacto de Google Trends en la previsión de viajes combinados y su evidencia relacionadaPropósitoDado que el uso de los datos de Google Trends es útil para mejorar la precisión de las predicciones, este estudio examina si el uso del índice de búsqueda web de Google Trends combinado con la agregación de relevancia puede mejorar la precisión del predictor.Diseño/metodología/enfoqueEl modelo predictivo gris genera predicciones bajo un único modelo, mientras que el modelomultivariado utiliza el indicador Google Trends como variable explicativa. Se generaron tresensamblajes generales, incluido el Modelo armónico único (CUGM), los ensamblajes de todos loscomponentes (CAGM) y la prueba de presencia de componentes con predicción (CSET). Laspredicciones individuales encada grupo luego se combinan utilizando métodos de correlación deuso común.RecomendacionesUtilizando el número de turistas en las cuatro ciudades más investigadas de Taiwán, los tresgrupos combinados se clasificaron según su precisión. Las pruebas incluidas muestran que losmodelos multivariados en escala de grises son importantes para la predicción. Además, losresultados de las pruebas muestran que el índice de Google Trends y las pruebas que incluyenmétodos de suma lineal son útiles porque los métodos combinados con CSET funcionan majorque los métodos combinados con CSET. CAGM y VCUG.Implicaciones practicesLa industria de viajes puede usar el índice de búsqueda web de Google Trends para desarrollarestrategias comerciales para atracciones basadas en un conjunto lineal de componentes.Autenticidad/valorCon el objetivo de mejorar la precisión de los pronósticos agregados, este estudio investiga larelación entre el índice de tendencias de Google y las expectativas generales de viaje junto con laevidencia global.Palabras claveDemanda de viajes, Experiencia global, Tendencias de Google, Predicción grisTipo de papelTrabajo de investigación

An interactive grey multivariable model based on the dynamic accumulative driving effect and its application

A novel systematic multivariable grey model called the interactive grey multivariable forecasting model based on the dynamic accumulative driving effect (IDCGM(1, N)) is developed to predict the trends of an interactive system. More specifically, a utility function to describe the dynamic relationships between system variables is designed and calculated using the impulse response function of the vector autoregressive regression model (VAR). Accounting for the accumulative impacts of historical variables, the accumulative utility term is used to describe the accumulative driving effects between variables. Considering the complex nonlinear relationships between system variables and time, a time power term is also introduced into the model framework. To improve the model's prediction performance, the particle swarm optimization algorithm (PSO) is used to optimize the nonlinear parameters. To demonstrate the effectiveness of the IDCGM(1, N) model in practice, we assess its performance by fitting seven benchmark models with data from 2000 to 2015 and using these models to produce forecasts for 2016–2019. Results show that the IDCGM(1, N) model achieves an optimal fit and prediction performance compared to other benchmark models, which also describes the inherent interactive relationship of the system composed of the technological innovation investment, energy intensity and carbon emission intensity.

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.

Impact of myocardial revascularization on long-term outcomes in a nationwide cohort of first acute myocardial infarction survivors.

The long-term clinical benefits of myocardial revascularization in a contemporary, nationwide cohort of acute myocardial infarction (AMI) survivors are unclear. We aimed to compare the mortality rates and clinical outcomes at 8 years of patients admitted in Italy for a first AMI managed with or without myocardial revascularization during the index event. This is a national retrospective cohort study that enrolled patients admitted for a first AMI in 2012 in all Italian hospitals who survived at 30 days. The outcomes of interest were all-cause mortality, major cardio-cerebrovascular events (MACCE), and re-hospitalization for heart failure (HF) at 8 years. Time to events was analysed using a Cox and Fine and Gray multivariate regression model. A total of 127 431 patients with AMI were admitted to Italian hospitals in 2012. The study cohort consisted of 62 336 AMI events, of whom 63.8% underwent percutaneous or surgical revascularization ≤30 days of the index hospital admission. At 8 years, the cumulative incidence of all-cause death was 36.5% (24.6% in revascularized and 57.6% in not revascularized patients). After multiple corrections, the hazard ratio (HR) for all-cause mortality in revascularized vs. not revascularized patients was 0.61 (P < 0.0001). The rate of MACCE was 45.7% and 65.8% (adjusted HR 0.83; P < 0.0001), while re-hospitalizations for HF occurred in 17.6% and 29.8% (adjusted HR 0.97; P = 0.16) in AMI survivors revascularized and not revascularized, respectively. In our contemporary nationwide cohort of patients at their first AMI episode, those who underwent myocardial revascularization within 1 month from the index event compared to those not revascularized presented an adjusted 39% risk reduction in all-cause mortality and 17% in MACCE at 8-year follow-up.

Unequal-order grey model with the difference information and its application

According to the principle of minimum information, new information priority, and difference information, most existing grey forecast models and their improvement are inconsistent with the grey theory. Therefore, a novel discrete multivariable grey model with unequal fractional-order accumulation is proposed. To improve the accuracy and stability of the model, an optimization algorithm for unequal fractional-order is proposed. The proposed model and algorithm are evaluated with four actual cases. The results show that the novel model has better performance and the proposed unequal fractional-order accumulation operator is better than other existing accumulation operators. Considering the energy consumption, the carbon dioxide emissions in the USA have been forecasted to decrease but remain at a high level by using the novel discrete multivariable grey model. Reducing energy consumption is conducive to reducing carbon dioxide emissions.

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.

A novel method for carbon emission forecasting based on EKC hypothesis and nonlinear multivariate grey model: evidence from transportation sector.

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

Forecasting carbon emissions from energy consumption in Guangdong Province, China with a novel grey multivariate model.

Carbon dioxide has a significant impact on global climate change due to its natural greenhouse effect. The objective and credible forecast of carbon emissions is very important for the government to formulate and implement the corresponding emission reduction targets. For controlling the growth of carbon emissions, Chinese government has put forward the low-carbon pilot policy and carbon trading policy. However, the existing grey models cannot measure the impact of policies and their interactions. In order to remedy the defect, a novel grey multivariable model based on dummy variables and their interactions is established. Two kinds of grey multivariable models and back propagation neural network model are chosen as comparison models to highlight that the introduction of dummy variables and their interactions plays an important part in improving the model performance. To verify the effectiveness, these four models are selected to simulate and predict the carbon emissions generated from primary energy consumption in Guangdong Province of China. The empirical results indicate that the mean absolute percentage errors of the novel model are 2.87% and 0.86%, respectively, which is significantly better than these three competing models. Finally, based on the outstanding performance of the novel model, it is chosen to forecast the fluctuating tendency of carbon emissions in the next 5years.

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 Novel Method for the Estimation of Higher Heating Value of Municipal Solid Wastes

The measurement of the higher heating value (HHV) of municipal solid wastes (MSWs) plays a key role in the disposal process, especially via thermochemical approaches. An optimized multi-variate grey model (OBGM (1, N)) is introduced to forecast the MSWs’ HHV to high accuracy with sparse data. A total of 15 cities and MSW from the respective city were considered to develop and verify the multi-variant models. Results show that the most accurate model was POBGM (1, 5) of which the least error measured 5.41% MAPE (mean absolute percentage error). Ash, being a major component in MSW, is the most important factor affecting HHV, followed by volatiles, fixed carbon and water contents. Most data can be included by using the prediction interval (PI) method with 95% confidence intervals. In addition, the estimations indicated that the MAPE from estimating the HHV for various MSW samples, collected from various cities, were in the range of 3.06–34.50%, depending on the MSW sample.