FGM Model Research Articles

Fitting IGM, FGM and NLS switching models to NaNO2-PVA composite transients for its microscopic parameter estimation

Domain switching process is a complex process and is not as simple in occurrence as appears from conceptual framework. Fortunately, the theories of nucleation and crystal growth successfully applied to switching domains help in understanding switching kinetics in ferroelectric samples. Direct methods of parameter estimation can provide only the local information of the target region while the ‘universal integrating methods’ provide domain kinetic parameters with their response proportional to the fraction of the phase grown at that time. Besides being statistical, the later is much simpler and popular in delivering more credible results. In this paper, an indirect estimation of significant microscopic parameters of optimized NaNO2-PVA ferroelectric composites is made by fitting their current transients with IGM, FGM and NLS switching models The fitting of these models into the experimental switching transient helps (i) in finding dimensionalityn, characteristic timeto, nucleation rate R and domain size L and (ii) to identify whether a thin film can be considered to be an ensemble of a number of independent elementary regions switching their states independently with exponential distribution of their relaxation times. IGM model suggests that polarization switching proceeds through a continuous nucleation process. The results of FGM fitting the transients supports the points that with increase in signal-amplitude, new regions are nucleated leading to reduction of adjacent relative distance between the domains The excellent NLS fit over whole range of switching times suggests that composite film can be considered an ensemble of elementary regions individually characterized by independent relaxation times.

Influencing factors and future trends of natural gas demand in the eastern, central and western areas of China based on the grey model

Due to the various ecological environment, economic development and resources, the main influencing factors of natural gas consumption are different in the eastern, central and western areas of China. To fully understand such discrepancy, we adopted the grey relation analysis (GRA) to select three main significant factors from 7 potential impacts including gross domestic product (GDP), industry structure, environmental protection mechanism, urbanization rate, population density, energy consumption intensity and energy consumption structure. Then, we analyzed the internal relevance between the selected three factors and the regional natural gas consumption. Furthermore, we established the GM(1,N) model with fractional order accumulation (FGM(1,N)) to predict the future demand of natural gas consumption in the eastern, central and western areas of China based on the selected three factors. The following results were achieved. (1) Energy consumption structure, GDP, and urbanization rate are three main influencing factors of natural gas demand in the eastern and central areas, while in the western area, the three main factors are urbanization rate, industry structure and population density. (2) In terms of planning natural gas consumption policies, adjustment of energy consumption structure should be strengthened in the eastern area, relationship between economic development and energy consumption should be focused on in the central area, urbanization should be speeded up in the western area. (3) The FGM(1,N) model based on three main factors, well fitting historic demand data, will have a good prediction performance. (4) Natural gas demand in the eastern, central and western areas will achieve a sustainable growth in 2020–2025. However, such growth rate may decrease due to energy reform and external economic environment. By 2025, natural gas demand in these three areas will be about 244 billion cubic meters (bcm), 64 bcm and 100 bcm respectively, with a total value of 408 bcm for the whole China.

Evaluation of Modeling Approaches for MILD Combustion Systems With Internal Recirculation

Numerical simulations employing two different modeling approaches are performed and validated against experimental results from a Moderate or Intense Low-Oxygen Dilution (MILD) system with internal recirculation. The FGM and PaSR closures are employed in a RANS framework to carry out the numerical simulations. The results show that FGM model strongly overpredicts temperature profiles in the reactive region, while yielding better results along the central thermocouple. The PaSR closure based on a prescribed mixing time constant, 𝐶!"#, of 0.01, 0.1 and 0.5 results are compared, showing that a 𝐶!"# value of 0.5 is the most appropriate choice for the cases under investigations. A PaSR formulation allowing to locally estimate the 𝐶!"# value is found to provide improved results for both the lateral and central thermocouples. A flame index analysis, used to assess the ability of FGM and PaSR to capture intense mixing of the cyclonic burner, indicates how the FGM model predicts a typical non-premixed region after the injection zone, contrary to the experimental observation.

A Predictive Analysis of China’s CO2 Emissions and OFDI with a Nonlinear Fractional-Order Grey Multivariable Model

Since the implementation of the Belt and Road Initiative, China’s total amount of outward foreign direct investment (OFDI) has increased each year and this has caused its relationship with carbon emissions (CO2e) to receive great attention recently. Forecasting China’s CO2e accurately by considering the impact of OFDI is important since the government can use it to formulate an appropriate emissions plan to fulfill its carbon reduction commitments. Because the relationship between OFDI and CO2e has nonlinear characteristics, a nonlinear grey multivariable model with fractional-order accumulation (NFGM(1,N)) was proposed in this study. To enhance the prediction accuracy, an optimization process was used to determine the parameters. The outcomes of the variable fractional order showed that fractional-order accumulation can better extract the grey information hidden in the original data, which confirmed the principle of new information priority. The result of the power coefficient indicated a nonlinear relationship between the CO2e and OFDI. Based on the prediction performance, the prediction accuracy of the NFGM(1,N) model was proven to be superior to those of the ARMA model, linear regression model, the GM(1,1), GM(1,N), and FGM(1,N) models. The empirical results also revealed that OFDI increased the CO2e in China. The relationship between the CO2e and OFDI exhibits a U-shaped development based on further predictions for the 2018–2030 period. Finally, some suggestions for long-term CO2e reduction plans were provided in this paper.

Numerical study of the laminar premixed flame stabilization on a slot burner: comparison between detailed and FGM models

It is still a challenging task to numerically solve flames using detailed chemical kinetics in multidimensional geometries of practical applications. To overcome this difficulty, many efforts have been done to develop chemical kinetics reducing techniques, such as ILDM, FPV, FPI, and FGM. Although these techniques are widely discussed in the literature, their implementation is not straightforward. In the present work, the FGM technique is implemented to solve a two-dimensional laminar premixed flame of \(\hbox {CH}_4/\hbox {air}\) stabilized by heat losses to the burner rim. This configuration is explored to test the FGM prediction capabilities for some stable conditions, one of them close to the blow-off limit. Temperature, mass fraction of selected species, and the burning velocity variation along the flame surface are presented, and limitations of the technique were identified by comparing FGM results against the direct integration of the full set of conservation equation. In general, the FGM technique has shown a good quantitative agreement when compared with the direct integration.

Prediction of Renewable Energy Production Using Grey Systems Theory

Due to the reduction of renewable energy resources such as fossil fuels, the energy crisis is one of the most critical issues in today’s world. The application of these resources brings about many environmentalpollutionsthatleadtoglobalwarming. Therefore,variouscountrieshaveattemptedto reducepotentialdamageanduserenewableenergiesbytheintroductionandpromotionofrenewable energies as an essential strategy to reduce CO2 emissions and to find alternatives to fossil energy in the transportation and electricity generation sectors. This study attempts to predict the production process of renewable energies in Iran by 2025 and study the characteristics of this energy and its usage in the world and Iran. Since there are very few data in this field, four grey prediction models are used including GM(1,1), DGM(2,1), Grey Verhulst and FGM(1,1) models. According to the threeindicesoftheerrorvaluesofMSE,RMSE,andMAPE,allthepredictionsdonebythemethods aboveareamongthebestpredictionmethods. Byexaminingtheresultsachieved,FGM(1,1)method was the best model concerning its less error than other models and has estimated 16740.45 MW for renewable energy production in 2025.

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

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

A Novel Method for Optimizing Fractional Grey Prediction Model

Aiming at the shortcoming that the classical FGM(1,1) model regards the gray action quantity as a fixed constant, the DGM(1,1) model is used to dynamically simulate and predict the gray action quantity, so that the gray action quantity can change dynamically with time. On this basis, a new FGM(1,1,b) model with dynamic gray quantity change with time is proposed, and the total primary energy consumption in the Middle East is taken as a numerical example for simulation prediction. The results show that the prediction accuracy of the dynamic FGM(1,1,b) model proposed in this paper is higher than that of the classical FGM(1,1) model, and the practicability and effectiveness of the FGM(1,1,b) model are verified. At the same time, it also provides relevant theoretical basis for the study of world energy development.

Forecasting of Wastewater Discharge and the Energy Consumption in China Based on Grey Model

Water pollution control is currently an important development strategy for China. Analysis and forecasting of wastewater discharge and the energy consumption are critical for this strategy. In this paper, we proposed the two time series models, namely, improved GM(0,n) model (IGM(0,n)) and optimized FGM(1,1) model (OFGM(1,1)). Two numerical experiments were used to test the validity of these models. It was indicated that the forecasting ability of two models had remarkably improved, compared to traditional FGM(1,1) and GM(0,n), respectively. We applied the two models to forecast wastewater discharge and energy consumption in China. The forecasting results have shown that the current growth rate in treated wastewater could meet the planning target of the 13th Five-Year Plan. The wastewater discharge and the energy consumption would reach 77.39 billion tons and 22.75 billion kWh, respectively, in 2020.

Using the seasonal FGM(1,1) model to predict the air quality indicators in Xingtai and Handan.

The air pollution problem in Xingtai and Handan is the focus of public attention. The seasonal gray model with fractional order accumulation is proposed to predict the quarterly concentrations of PM2.5, PM10, NO2, and CO in Xingtai and Handan. The new model has higher forecasting performance and can describe the characteristics of seasonal fluctuation very well. The forecasting results indicated that except for the PM10 in Xingtai that will increase slowly, the other indicators in the two places will decrease. The changes of the air quality indicator concentration in different quarters are obvious, and in the same quarter tend to be stable. Except for CO and NO2 in some seasons, other indicators are in the state of exceeding the standard. The effect of air pollution control is not good. The governance needs to be further strengthened.

Using FGM(1,1) model to predict the number of the lightly polluted day in Jing-Jin-Ji region of China

This paper focuses on the problem of poor air quality in Jing-Jin-Ji region of China. According to the data of the report on the state of the environment in Jing-Jin-Ji region in 2013–2016, the fractional order accumulation GM(1,1) model was adopted to predict the number of the lightly polluted day and the annual average concentration of PM2.5 in the Jing-Jin-Ji region in 2020. The forecasting results show that it will be difficult for the Jing-Jin-Ji region to achieve the goal of more than 80% lightly polluted day in 2020. The Jing-Jin-Ji region should adjust measures according to the local conditions, to achieve a significant improvement of air quality.

Random vibrations of functionally graded nanobeams based on unified nonlocal strain gradient theory

In present study the dynamic response of a functionally graded nanobeam supported by visco-elastic foundation to a stationary random excitation, based on non-local strain gradient theory has been investigated for the first time. The governing equations of motion are derived in framework of a unified beam theory (which includes different beam theories such as Euler–Bernoulli, Timoshenko and Reddy beam theories as special case), and Hamilton’s principle. The results of present study for some limit cases have been compared with results available in open literature and excellent agreement is observed. Effects of various parameters (i.e. non-local parameter, strain gradient length scale, power-low index of FGM model, different beam theories etc.) have been investigated comprehensively and illustrated graphically.

An extended finite element framework for vibration analysis of cracked FGM shells

Given the widespread use of FGM shell elements in numerous industrial fields and their extreme vulnerability to crack formation, the present work is directed towards investigating the vibrational behavior of cracked FGM shells. A general XFEM formulation, with tested accuracy and performance, is presented due to its intrinsic capability to handle problems with discontinuities, such as cracks. To demonstrate the performance of the adopted approach, multiple examples are introduced and analyzed and the effects of various parameters such as the length and angle of the crack and different distribution patterns of material stiffness and density across the thickness of the shell, are extensively studied. Five cracked FGM models, including a rectangular plate, a circular plate with four radial cracks, a cylindrical shell, a conical shell and a spherical dome are simulated by the proposed approach and the results are discussed.

An experimental and numerical study of MILD combustion in a Cyclonic burner

The implementation of MILD combustion systems is limited by a lack of fundamental insight into such combustion regime and therefore novel tools are indispensable compared to traditional combustion systems. In this context CFD simulations for the prediction of the burner behaviour and for design and optimization appears essential for a successful introduction of such concept in some industries. Detailed chemistry has to be included in fluid-dynamics simulations in order to account for the strong turbulence-chemistry interaction in the MILD regime. An effective strategy to overcome this aspect is represented by tabulated chemistry techniques. In particular the implementation of Flamelet Generated Manifold with IML tabulation seems to be a promising tools for MILD systems and therefore high fidelity and comprehensive experimental data are needed for the assessment of such model. The present study is framed in this context and it investigates the characteristics of MILD Combustion in a Cyclonic lab-scale burner that operates with high level of internal recirculation degrees induced by a cyclonic fluid-dynamic pattern obtained by the geometrical configuration of the reactor and of the feeding system. Experimental tests were realized varying the mixture composition. Detailed measurements of local mean temperatures and concentrations of gas species at the stack for several operating conditions were used to validate the FGM model under such unconventional operating conditions. Results suggest that FGM with IML is a promising tool for modeling the complex flame structures of cyclonic MILD burner, with many aspects that need to be further investigated.

Time Prediction Models for Echinococcosis Based on Gray System Theory and Epidemic Dynamics.

Echinococcosis, which can seriously harm human health and animal husbandry production, has become an endemic in the Xinjiang Uygur Autonomous Region of China. In order to explore an effective human Echinococcosis forecasting model in Xinjiang, three grey models, namely, the traditional grey GM(1,1) model, the Grey-Periodic Extensional Combinatorial Model (PECGM(1,1)), and the Modified Grey Model using Fourier Series (FGM(1,1)), in addition to a multiplicative seasonal ARIMA(1,0,1)(1,1,0)4 model, are applied in this study for short-term predictions. The accuracy of the different grey models is also investigated. The simulation results show that the FGM(1,1) model has a higher performance ability, not only for model fitting, but also for forecasting. Furthermore, considering the stability and the modeling precision in the long run, a dynamic epidemic prediction model based on the transmission mechanism of Echinococcosis is also established for long-term predictions. Results demonstrate that the dynamic epidemic prediction model is capable of identifying the future tendency. The number of human Echinococcosis cases will increase steadily over the next 25 years, reaching a peak of about 1250 cases, before eventually witnessing a slow decline, until it finally ends.

Vibration characteristics of fluid-conveying FGM cylindrical shells resting on Pasternak elastic foundation with an oblique edge

The flow-induced vibration characteristics (natural frequency and critical flow velocity) of FGM cylindrical shells partially resting on elastic foundation are investigated by an analytical method. These shells are completely filled with fluid or subjected to a flowing fluid. The cylindrical shells are partially surrounded by an elastic foundation with an oblique edge which is represented by the Pasternak model. The boundary edge of an elastic foundation lies in a plane that is oblique at an angle with the shell axis. The effective material properties of FGM models are predicted based on two homogenization methods such as Voigt and Mori-Tanaka models. Material properties vary continuously through the thickness according to a four-parameter power law distribution in terms of volume fraction of the constituents. The thermal effects are also included and the material properties of FGMs are assumed to be temperature-dependent. The fluid is described by the classical potential flow theory. The governing equation for eigenvalue problem is obtained using the Rayleigh-Ritz method. To validate the present method, numerical examples are presented and compared with the available existing results.

A stochastic inverse solution for functionally graded acoustic layered metamaterial validation

Functionally graded acoustic metamaterials (FGAMs) can be designed to have specific waveguide properties. In sonar applications, FGAMs can be tailored to resist incident wave reflection. As these materials do not exist naturally, they must be fabricated by gradually layering manufactured, resulting in a (usually smooth) variation of properties. Validating material properties of FGAMs is difficult with conventional tests, as the distribution of material properties over the layered structure results in a non-unique solution if typical data (e.g., compressive strain) is measured. This talk will demonstrate an approach to characterize the functionally graded material properties by parameterizing how the functionally graded material changes throughout the specimen. Experiments designed to minimize the uncertainty surrounding the FGM model parameters are formulated and evaluated numerically. The FGM model parameters are estimated by Markov chain Monte Carlo so that a probability distribution surrounding each parameter is recovered. Probability distributions enable uncertainty quantification (UQ) surround the validated material parameters. UQ is important as uncertainty surrounding the parameter results directly translates into uncertainty surround the FGM performance. The approach is verified by bootstrap analyses of known FGAM distributions.

A general study of counterflow diffusion flames at subcritical and supercritical conditions: Oxygen/hydrogen mixtures

A theoretical framework is established to study the effect of flow strain rate on counterflow diffusion flames for general fluids over the entire thermodynamic regime. The formulation accommodates fundamental thermodynamics and transport theories, along with detailed chemical mechanisms. Both steady and unsteady burning branches of a complete flame-response curve (the S-curve) are considered. An improved two-point flame-controlling continuation method is employed to solve the singularity problem at the turning points on the S-curve. As a specific example, oxygen/hydrogen flames are systematically investigated over a pressure range of 0.5–200atm. The strain rate is varied from 102 to 108s−1. Two different inlet temperatures for oxygen (120 and 300K) and hydrogen (20 and 300K) are treated to explore flame behaviors at the ideal-gas and cryogenic-liquid states. General flame similarities (in terms of flame temperature, flame thickness, species concentrations, reaction rates, and heat release rate) are developed in a normalized strain-rate space (a/aext) for the entire range of pressures under consideration. Quantitative mapping of flame properties from one pressure to another is obtained. In addition, an analytical model is developed to refine and elucidate a previously established relationship between the heat release rate and pressure and strain rate in the form of q̇∼p0.534a. The heat release rate, when normalized with respect to p0.534aext, correlates well with the normalized strain rate (a/aext). Both numerical and analytical results show that the extinction strain rate is approximately proportional to pressure; this allows for a priori mapping of flame solutions between different pressure conditions. This in turn will significantly improve the computational efficiency of combustion modeling using tabulated chemistry, including the flamelet, FGM, and FPI models. Cryogenic inlet temperature affects only the flame location, without discernibly modifying the flame structures, which suggests that the ideal-gas flame solutions can be used for flame tabulation.

On the fit and forecasting performance of grey prediction models for China’s labor formation

Motivated by the high probability of inconsistent and insufficient information from official statistics in China, this research paper conducted an out-of-sample forecasting competition between grey prediction and straightforward extrapolation for quantity and quality of laborers in China under the assumption that the performance of grey prediction is superior in dealing with uncertain and insufficient data inputs. In line with previous comparative studies on time-series forecasting techniques, the purpose of this study was to verify that the GM(1,1), GM(1,1) rolling and FGM(1,1) models derived from grey system theory would provide forecasts that are at least as accurate as the straightforward extrapolation approach for China’s labor variables. The findings revealed that the forecasting efficiency of GM(1,1) and GM(1,1) rolling models were superior to straightforward extrapolation and FGM(1,1). The results can offer valuable insights and provide a basis for further research in model building for short-term estimation under the circumstances of data incompleteness or information inconsistency.

Characterization of the variation of the material properties in a freestanding inhomogeneous thin film

This Letter presents a new technique for measuring the variation of the material properties along the thickness in a freestanding inhomogeneous thin film. The analytical results reveal a simple relation between the material properties and the set of cut-off frequencies of Lamb waves. The influence of the graded properties on the variation of cut-off frequencies in three different kinds of models, including artificial FGM model, sub-surface damage model, and nano-porous thin film model, is discussed. These results provide theoretical guidance for characterizing the material property variations of MEMS/NEMS.