FGM Model Research Articles

On the natural frequency analysis of the shear deformable aircraft wing using an FE-based multilayered FGM model

On the natural frequency analysis of the shear deformable aircraft wing using an FE-based multilayered FGM model

LES investigation of a swirl stabilized technically premixed hydrogen flame with FGM and TFM models

Climate change due to carbon emissions is one of the aspects that must be kept under control nowadays. In this fashion, the employment of hydrogen as fuel provides a fundamental solution for both power generation and transportation since lean premixed combustions allow to reset the carbon emissions and reduce the pollutant ones. Indeed, the higher reactivity of hydrogen permits to operate with a very low equivalence ratio which can drastically limit the NOx production with respect to the common fossil fuels. On the other hand, lean hydrogen mixtures are characterized by peculiar aspects that make their study through CFD simulations not straightforward. The present work aims to analyze through two different numerical approaches a technically premixed hydrogen flame experimentally investigated at the Technische Universität Berlin (TUB). In particular, the main differences between the Flamelet Generated Manifold and the Thickened Flame Model strategy are deeply analyzed as well as the effects of the thermal boundary conditions on the flame stabilization mechanism. The comparison with the experimental data shows the treatment employed drastically influences the accuracy of the obtained outcomes.

Projection of ecological water consumption under carbon emission in Chinese provinces

Under the background of “double carbon”, ecological water has become one of the significant resources to ensure the healthy and sustainable development of the regional ecological environment. And the ecological water consumption prediction is a prerequisite for optimizing water supply structures. Considering the impact of CO2 emissions on ecological water consumption, the FGM(1,1) model was firstly used to predict CO2 emissions considered as an impact factor in this paper. Then, an adjacent accumulative grey multivariate convolution model (AGMC(1,N)) was combined with the Average Weakening Buffer Operator (AWBO) to predict the annual ecological water consumption of 30 provinces (municipalities and autonomous regions) in China. The results show that the AGMC(1,N) model combined with the AWBO has better prediction effect. In addition, in the next decade, only six provinces in the northern region will have a decreasing trend in ecological water consumption. However, the other provinces are showing an upward trend. The ecological water consumption trends deviate from the CO2 emission trends in 12 provinces. The research results are beneficial for the formulation of the ecological water consumption policies and the achievement of the dual carbon goals.

Research on the Corporate Innovation Resilience of China Based on FGM(1,1) and Fuzzy-Set Qualitative Comparative Analysis Model

Over the past few years, the uncertain business environment has shaped the resilient development thinking of firms. Measuring and predicting innovation resilience plays a crucial role in fostering the sustainable development of enterprises. This paper used the entropy-weight TOPSIS model and FGM(1,1) model to measure the innovation resilience of companies based on an indicator system, covering aspects such as tolerance for factor scarcity, R&D safety, core technology self-sufficiency, and organizational change capacity. The results show that the MAPE of the FGM(1,1) model is 0.0136, which is lower than that of the GM(1,1) model, with the predicted annual growth rate of the resilience being −0.95% from 2020 to 2025. Consequently, the study investigated what policy configuration may improve innovation resilience using the fuzzy-set qualitative comparative analysis (fsQCA) model. It identified four policy configuration paths, of which the combination of a tax policy for an additional deduction of enterprise R&D expenses and an income tax reduction policy is an effective policy configuration. This research expands the application of the FGM(1,1) model and inspires managers to develop innovative policies to enhance corporate resilience.

Finite element analysis of natural frequencies of the FGM porous cooling plate with cutouts: A multilayered FGM approach

This study comprehensively investigates the natural frequency analysis of a shear-deformable functionally graded porous plate with cutouts, utilizing an FE-based multilayered FGM model. Analyzing natural frequencies is vital to prevent catastrophic failure in porous plates, particularly in cooling plates. Cutouts in cooling plates enhance heat dissipation, improve airflow or fluid contact, reduce weight, customize battery layouts, optimize structural integrity, simplify installation, and enable precise thermal management in critical areas. The present study employs an FE-based multilayered FGM model that considers three distinct porosity distributions (even, uneven, and sinusoidal) and incorporates a power law distribution based on a modified rule of mixture to derive the effective material properties of the FGM porous plate. Furthermore, this investigation comprehensively explores the influences of variables such as volume fraction index, thickness ratio, porosity distribution, and porosity index on the natural frequency analysis of shear-deformable FGM porous plates with cutouts, encompassing both conventional and unconventional boundary conditions. This extensive examination elucidates the collective impact of these variables on the vibrational behavior of FGM plates featuring cutouts. These parameters significantly impact the vibration behavior of the FGM plate with cutouts. The results affirm the efficacy of the presented model in analyzing intricate FGM structures.

Predicting of elderly population structure and density by a novel grey fractional-order model with theta residual optimization: a case study of Shanghai City, China

Background Accurately predicting the future development trend of population aging is conducive to accelerating the development of the elderly care industry. This study constructed a combined optimization grey prediction model to predict the structure and density of elderly population.MethodsIn this paper, a GT-FGM model is proposed, which combines Theta residual optimization with fractional-order accumulation operator. Fractional-order accumulation can effectively weaken the randomness of the original data sequence. Meanwhile, Theta residual optimization can adjust parameter by minimizing the mean absolute error. And the population statistics of Shanghai city from 2006 to 2020 were selected for prediction analysis. By comparing with the other traditional grey prediction methods, three representative error indexes (MAE, MAPE, RMSE) were conducting for error analysis.ResultsCompared with the FGM model, GM (1,1) model, Verhulst model, Logistic model, SES and other classical prediction methods, the GT-FGM model shows significant forecasting advantages, and its multi-step rolling prediction accuracy is superior to other prediction methods. The results show that the elderly population density in nine districts in Shanghai will exceed 0.5 by 2030, among which Huangpu District has the highest elderly population density, reaching 0.6825. There has been a steady increase in the elderly population over the age of 60.ConclusionsThe GT-FGM model can improve the prediction accuracy effectively. The elderly population in Shanghai shows a steady growth trend on the whole, and the differences between districts are obvious. The government should build a modern pension industry system according to the aging degree of the population in each region, and promote the balanced development of each region.

Prediction of the Share of Solar Power in China Based on FGM (1,1) Model

In recent years, fossil energy reserves have decreased year by year, and the development and use of renewable energy has attracted great attention of governments all over the world. China continues to promote the high-quality development of renewable energy such as solar power generation. Accurate prediction of the share of solar power in China is beneficial to implementing the goals of carbon peaking and carbon neutralization. According to the website of China’s National Bureau of statistics, the earliest annual data of China’s solar power generation is 2017, which leads to there being very few data on the share of China’s solar power generation. Therefore, the prediction accuracy of most prediction methods is low, and the advantages of the grey prediction model are shown. Based on the share of solar power in China from 2017 to 2020, this paper constructs an FGM (1,1) model, calculates r using the Particle Swarm Optimization (PSO) algorithm, and predicts the share of solar power in China in the next few years. r = 0.3858 and MAPE = 0.20% were obtained by calculation of the model. The prediction results show that the share of solar power generation in China will increase year by year, and it will reach about 4.2301% by 2030. In addition, it is found that the share of China’s solar power generation in 2021 is 2.1520%, and the predicted value is 2.1906%. It can be seen that the prediction error is small. Finally, the limitations and future research directions are elucidated. The prediction results presented in this paper will help to guide the development of solar power generation in China, and are of great significance in speeding up the pace of energy structural adjustment, accelerating the construction of a clean, low-carbon, safe and efficient energy system, and promoting sustainable development.

LES/FGM investigation of ignition and flame structure in a gasoline partially premixed combustion engine

This paper presents a joint numerical and experimental study of the ignition process and flame structures in a gasoline partially premixed combustion (PPC) engine. The numerical simulation is based on a five-dimension Flamelet-Generated Manifold (5D-FGM) tabulation approach and large eddy simulation (LES). The spray and combustion process in an optical PPC engine fueled with a primary reference fuel (70% iso-octane, 30% n-heptane by volume) are investigated using the combustion model along with laser diagnostic experiments. Different combustion modes, as well as the dominant chemical species and elementary reactions involved in the PPC engines, are identified and visualized using Chemical Explosive Mode Analysis (CEMA). The results from the LES-FGM model agree well with the experiments regarding the onset of ignition, peak heat release rate and in-cylinder pressure. The LES-FGM model performs even better than a finite-rate chemistry model that integrates the full-set of chemical kinetic mechanism in the simulation, given that the FGM model is computationally more efficient. The results show that the ignition mode plays a dominant role in the entire combustion process. The diffusion flame mode is identified in a thin layer between the ultra fuel-lean unburned mixture and the hot burned gas region that contains combustion intermediates such as CO. The diffusion flame mode contributes to a maximum of 27% of the total heat release in the later stage of combustion, and it becomes vital for the oxidation of relatively fuel-lean mixtures.

Prediction of the Total Output Value of China’s Construction Industry Based on FGM (1,1) Model

The total output value of the construction industry (TOVCI) reflects its own development level to a certain extent. An accurate prediction of the construction industry’s total output value is beneficial to the government’s dynamic regulation. The grey prediction model is widely used for its simple calculation process and high prediction accuracy. Based on the TOVCI of China from 2017 to 2020, this paper constructs an FGM (1,1) model, calculates r by a simulated annealing algorithm, and forecasts the TOVCI of China in next few years. At present, the Particle Swarm Optimization algorithm (PSO) is employed in the calculation of r in the literature. However, the advantage of the simulated annealing algorithm is its powerful global search performance. The prediction results indicate that the TOVCI of China will continue to grow, but the growth rate will slow down. Therefore, the construction industry of China should not simply pursue the high-speed growth of the total output value, but pay more attention to high-quality development, such as technological innovation, energy conservation and environmental protection. Finally, the limitations and future research directions are elucidated.

A novel seasonal grey model for forecasting the quarterly natural gas production in China

As a green and clean source of energy, natural gas plays an indispensable role in changing the energy structure and reducing greenhouse gas emissions. In this context, forecasting natural gas production becomes particularly important. In China, natural gas production has obvious seasonal and cyclical characteristics. To this end, a grey prediction model combined with particle swarm optimization (PSO) is proposed: the PSO-based data grouping grey model with a fractional order accumulation (PSO-FDGGM (1,1)). The traditional grey model has shortcomings such as low prediction accuracy and poor adaptability, and its application is limited. Compared with the traditional grey models, this model can be used to predict time series with seasonal characteristics, and the prediction accuracy is higher. Based on the data grouping-based grey modelling method (DGGM (1,1)), this model introduces the modeling method of the grey system model with the fractional order accumulation (FGM (1,1)), that is, combining data grouping with fractional accumulation, and using PSO to optimize fractional-order parameters, which improves the performance and adaptability of the model. In order to verify the effectiveness of the model, the model is compared with the traditional grey model (GM (1,1)), FGM (1,1) model, DGGM (1,1) model, autoregressive comprehensive moving average (ARIMA) model and the PSO-based grey forecasting model (PSOGM (1,1)). The mean absolute percent errors (MAPEs) of the comparison model in the test set are 7.46%, 9.28%, 4.38%, 8.60% and 5.97% respectively, while that of PSO-FDGGM (1,1) model is only 3.19%. The results show that PSO-FDGGM (1,1) has good adaptability and prediction accuracy for seasonally fluctuating sequences. In order to further verify the effectiveness and applicability of PSO-FDGGM (1,1), this paper adopts two ways: adjusting the parameters of PSO algorithm in the new model and applying the new model to the prediction of solar power generation, and the empirical results show that the new model is effective in forecasting seasonal data. Finally, the new model is used to predict the quarterly production of natural gas in China from the third quarter of 2021 to the second quarter of 2024. The forecast results can provide a basis for formulating natural gas production plans and environmental policies.

Prediction of Whole Social Electricity Consumption in Jiangsu Province Based on Metabolic FGM (1, 1) Model

The achievement of the carbon peaking and carbon neutrality targets requires the adjustment of the energy structure, in which the dual-carbon progress of the power industry will directly affect the realization process of the goal. In such terms, an accurate demand forecast is imperative for the government and enterprises’ decision makers to develop an optimal strategy for electric energy planning work in advance. According to the data of the whole social electricity consumption in Jiangsu Province of China from 2015 to 2019, this paper uses the improved particle swarm optimization algorithm to calculate the fractional-order r of the FGM (1, 1) model and establishes a metabolic FGM (1, 1) model to predict the whole social electricity consumption in Jiangsu Province of China from 2020 to 2023. The results show that in the next few years the whole social electricity consumption in Jiangsu Province will show a growth trend, but the growth rate will slow down generally. It can be seen that the prediction accuracy of the metabolic FGM (1, 1) model is higher than that of the GM (1, 1) and FGM (1, 1) models. In addition, the paper analyzes the reasons for the changes in the whole society electricity consumption in Jiangsu Province of China and provides support for government decision making.

Prediction of Water Consumption in 31 Provinces of China Based on FGM(1,1) Model

AbstractHuman production activities and social development cannot be separated from the indispensable water resources. In recent years, with the increasing speed of China's economic development, the consumption of water resources has gradually become the focus of attention of the Chinese government and the public. Based on the original data of water use of 31 provinces (municipalities and autonomous regions) in China from 2014 to 2018, a fractional order accumulative gray prediction model (FGM(1,1)) is established to predict the water use of 31 provinces (municipalities and autonomous regions) in China in the short term, and the applicability of the model is verified by the mean absolute percentage error (MAPE) value. According to the MAPE value, the data obtained by the FGM(1,1) model is relatively accurate. The prediction results show that in case of little change in total water consumption, agricultural water and industrial water use show a downward trend, while domestic water use shows an upward trend. The government's water management policy for urban residents needs to be adjusted, and the publicity work to improve the water‐saving awareness of urban residents needs to be improved.

Numerical Investigation on Flame Stabilization of Cavity-Based Scramjet Combustor Using Compressible Modified FGM Model

The technology of flame stabilization on cavity-based scramjet combustor has great significance in the field of future spacecraft. In this paper, a compressible modified FGM model was established based on the idea of the flamelet model, which was adopted to simulate the unsteady combustion process of the hydrogen transverse jet in the upper cavity of the scramjet. The results show that the compressible modified FGM model can accurately reflect the flow field and the propagation process of the flame in the supersonic cavity, and can capture the fine shock structure in the flow field. The coupling effect of shock waves and shear layer cause the shear layer to quickly destabilize, resulting in the turbulence effect, which promotes the mixing of air and fuel. The boundary layer separation at the upper wall of the combustion chamber will reduce the stability of the shear layer.

Application of a new grey multivariate forecasting model in the forecasting of energy consumption in 7 regions of China

Scientific prediction of regional energy is of practical significance for rational control of energy supply. In this paper, to further minimize the influence of subjective factors, the grey relational analysis and the FGM(1,1) model whose forecast results are affected by the fixed order are selected to analyze the samples. Then, a new grey multi-variable AGMC(1,N) model with better prediction performance is used to study 13 provinces (cities) in 7 different regions of China in detail. The results show that only the energy consumption in Central China will decrease in the short term. Energy consumption in the remaining 6 regions will continue to rise, and the energy consumption of East China, Northeast China, and Northwest China have a remarkable growth trend. It is important to provide reliable data to China's energy regulators and provide a reference for regional energy reform in the short term.

Analytical Capabilities of FGM and EDM Combustion Models in Partially Premixed Burners for HVAC Applications

Analytical Capabilities of FGM and EDM Combustion Models in Partially Premixed Burners for HVAC Applications

Grey Relational Entropy Calculation and Fractional Prediction of Water and Economy in the Beijing-Tianjin-Hebei Region

The implementation of the Beijing-Tianjin-Hebei coordinated development strategy promotes the rapid development of the regional economy, but the consequent water shortage has become a major concern. How to optimize the allocation of water resources, promote the cooperation of water resources among various water-using departments, and maximize the water efficiency of the limited water resources in the region has become the main issue of research. Thus, this paper mainly studies the entropy value and the entropy difference of the grey relational entropy between water resources and economic systems. First, use the grey correlation entropy method to calculate the existing data to explore the relationship between the two systems, then use the FGM(1, 1) model to predict the grey correlation entropy value of Beijing-Tianjin-Hebei in 2020–2024, and finally, calculate the entropy difference of the grey relation entropy for the region from 2015 to 2024. The results show the following: (i) The connection between the water resources system and the economic system in the Beijing-Tianjin-Hebei region is poor, the entropy value between the two will continue to decrease from 2015 to 2024, and the degree of coordination has shown a decreasing trend. (ii) The entropy change value between the water resources system and the economic system in the Beijing-Tianjin-Hebei region reflects a gradual and orderly change trend. The research results can provide reasonable suggestions for improving the correlation between water resources and economic systems for government departments, local residents, and industrial enterprises in the Beijing-Tianjin-Hebei region, ultimately realizing the sustainable development of water resources and economic systems.

Prediction of China’s Express Business Volume Based on FGM (1, 1) Model

With the continuous development of the economy, people’s lifestyle has changed greatly, online shopping has become a better choice for many people, and the express business volume is also increasing. Forecasting express business volume is of benefit to the healthy development of the logistics industry. Based on the data of China’s express business volume from 2015 to 2019, this paper uses the improved Particle Swarm Optimization algorithm to calculate the fractional-order r of the FGM (1, 1) model and forecasts China’s express business volume from 2020 to 2023. The results indicate that in the next few years, China’s express business volume will show a large growth trend, indicating that the express delivery industry still has a lot of room for development.

A Predictive Analysis of the Business Environment of Economies along the Belt and Road Using the Fractional-Order Grey Model

This paper determined the optimal order of FGM (1, 1) model through particle swarm optimization algorithm and combined with the World Bank business environment data to predict and analyze the business environment of economies along the Belt and Road. The empirical results show that the FGM (1, 1) model has a good predicting effect on the business environment. In terms of prediction accuracy, the FGM (1, 1) model based on particle swarm optimization algorithm to determine the optimal order is significantly better than the traditional GM (1, 1) model. The predict results show that the business environment level of economies along the Belt and Road will increase year by year from 2021 to 2022, but the overall level is still relatively low. The main innovation of this paper lies in the introduction of the fractional-order grey model into the predictive analysis of the business environment, which is of great significance to the extension and application of fractional-order models in management and economic systems.

A Fractional Grey Multivariable Model for Modeling Fresh Graduates’ Career Choice

Aiming at exploring the effect of four factors on fresh graduate’s three popular career choices of continuing studying, working in state-owned enterprises, and working in private enterprises, this paper collects the specific information of 3237 students and builds the GM (0, N) model. The four variables include student’s grade point average (GPA), socioeconomic status (SES), gender, and whether the student comes from an urban household. Furthermore, this paper also considers the effect of the fractional order and proposes a fractional grey model (FGM (0, N) model) to enhance the performance of the traditional model. Eventually, the study finds that there are still some students with financial problems, which makes some negative effects on their choices of continuing studying and working in state-owned enterprises. Additionally, all the other three factors show the positive influence on the three choices. Besides, GPA shows the most positive effect on the choices of continuing studying as well as working in a state-owned enterprise; gender and SES have the greatest impact on the choice of working in a private enterprise.

Forecast of Energy Consumption Based on FGM(1, 1) Model

The normal supply of energy is related to the stable development of the economy and society. Forecasting energy consumption helps prepare for the normal supply of energy. In the study of energy consumption forecasting, different scholars have used different forecasting models. This paper uses five-year energy consumption data in the Beijing-Tianjin-Hebei region and uses the grey fractional FGM(1, 1) model to analyze the next six years. Then, the energy consumption of three places is predicted. The advantage of the grey score FGM(1, 1) model is that it can get more accurate prediction results based on a small amount of information. In this study, relatively outdated information affects the accuracy of prediction results. However, other prediction models have great limitations on data. Choosing the grey number fractional model for prediction research can get a more reasonable prediction result. We use the FGM(1, 1) model to make predictions and get the prediction results. In Beijing, the growth rate of natural gas consumption has slowed down and will be basically stable by 2023. The average annual deceleration of coal consumption is 32%. The average annual deceleration of coke consumption is 10%. Crude oil consumption decreased by 6.3% annually. Gasoline consumption is slowly increasing. The consumption of kerosene increased about 8% annually. Diesel consumption is slowly decreasing. Fuel oil consumption is reduced by 17% annually. The average annual growth rate of power consumption exceeds 6%. In Tianjin, the annual growth rate of natural gas consumption is about 5%. Coal consumption is reduced by about 8% every year. The average annual deceleration of coke consumption is 7%. Crude oil consumption decreased by 2.4% annually. Gasoline consumption is slowly decreasing. The consumption of kerosene has increased by about 20% annually. Diesel consumption is slowly decreasing. Fuel oil consumption is reduced by 20% annually. Electricity consumption is slowly increasing. In Hebei Province, the annual growth rate of natural gas consumption is about 15%. Annual coal consumption is reduced by about 3%. Coke consumption remained stable. Crude oil consumption is reduced by 3% annually. Gasoline consumption is slowly increasing, and kerosene consumption has increased by about 31% annually. Diesel consumption is reduced by about 3% annually. Fuel oil consumption remained stable. Electricity consumption is slowly increasing.