This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The frac...This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.展开更多
In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractio...In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay,the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.展开更多
In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode (CCM) are established based on the fractional cal...In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode (CCM) are established based on the fractional calculus and the Adomian decomposition method. Some dynamical properties of the current-mode controlled fractional-order Buck- Boost converter are analysed. The simulation is accomplished by using SIMULINK. Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary. At the same time, the simulation results show that the converter goes through different routes to chaos.展开更多
The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the origin...The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the original data,the fractional-order accumulation calculus could be used to do preprocessing. In this paper, the residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM(1,1) and improve the accuracy of predictor. The state space model of optimally modified GM(1,1)predictor is given and genetic algorithm(GA) is used to find the smallest relative error during the modeling step. Furthermore,the fractional form of continuous GM(1,1) is given to enlarge the content of prediction model. The simulation results illustrated that the fractional-order calculus could be used to depict the GM precisely with more degrees of freedom. Meanwhile, the ranges of the parameters and model application could be enlarged with better performance. The method of modified GM predictor using optimal fractional-order accumulation calculus is expected to be widely used in data processing, model theory, prediction control and related fields.展开更多
A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the tra...A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode.展开更多
The purpose of this paper is to present a numerical approach based on the artificial neural networks(ANNs)for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the pr...The purpose of this paper is to present a numerical approach based on the artificial neural networks(ANNs)for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the presented system.The method is constructed with the combination of the ANNs along with the Levenberg-Marquardt backpropagation(LMB),named the ANNs-LMB.This technique is tested for solving the novel problem for three cases of the fractional-order values and the obtained results are compared with the reference solution.Fifteen numbers neurons have been used to solve the fractional-order chaotic financial model.The selection of the data to solve the fractional-order chaotic financial model are selected as 75%for training,10%for testing,and 15%for certification.The results indicate that the presented approximate solutions fit exactly with the reference solution and the method is effective and precise.The obtained results are testified to reduce the mean square error(MSE)for solving the fractional model and verified through the various measures including correlation,MSE,regression histogram of the errors,and state transition(ST).展开更多
In this paper,we formulate and analyze a new fractional-order Logistic model with feedback control,which is different from a recognized mathematical model proposed in our very recent work.Asymptotic stability of the p...In this paper,we formulate and analyze a new fractional-order Logistic model with feedback control,which is different from a recognized mathematical model proposed in our very recent work.Asymptotic stability of the proposed model and its numerical solutions are studied rigorously.By using the Lyapunov direct method for fractional dynamical systems and a suitable Lyapunov function,we show that a unique positive equilibrium point of the new model is asymptotically stable.As an important consequence of this,we obtain a new mathematical model in which the feedback control variables only change the position of the unique positive equilibrium point of the original model but retain its asymptotic stability.Furthermore,we construct unconditionally positive nonstandard finite difference(NSFD)schemes for the proposed model using the Mickens’methodology.It is worth noting that the constructed NSFD schemes not only preserve the positivity but also provide reliable numerical solutions that correctly reflect the dynamics of the new fractional-order model.Finally,we report some numerical examples to support and illustrate the theoretical results.The results indicate that there is a good agreement between the theoretical results and numerical ones.展开更多
This study considers a nonlinear grey Bernoulli forecasting model with conformable fractionalorder accumulation,abbreviated as CFNGBM(1,1,λ),to study the gross regional product in the ChengYu area.The new model conta...This study considers a nonlinear grey Bernoulli forecasting model with conformable fractionalorder accumulation,abbreviated as CFNGBM(1,1,λ),to study the gross regional product in the ChengYu area.The new model contains three nonlinear parameters,the power exponentγ,the conformable fractional-orderαand the background valueλ,which increase the adjustability and flexibility of the CFNGBM(1,1,λ)model.Nonlinear parameters are determined by the moth flame optimization algorithm,which minimizes the mean absolute prediction percentage error.The CFNGBM(1,1,λ)model is applied to the gross regional product of 16 cities in the Cheng-Yu area,which are Chongqing,Chengdu,Mianyang,Leshan,Zigong,Deyang,Meishan,Luzhou,Suining,Neijiang,Nanchong,Guang’an,Yibin,Ya’an,Dazhou and Ziyang.With data from 2013 to 2021,several grey models are established and results show that the new model has higher accuracy in most cases.展开更多
Simplified equations of fluid mud motion, which is described as Bingham-Plastic model under waves and currents, are presented by order analysis. The simplified equations are non-linear ordinary differential equations ...Simplified equations of fluid mud motion, which is described as Bingham-Plastic model under waves and currents, are presented by order analysis. The simplified equations are non-linear ordinary differential equations which are solved by hybrid numerical-analytical technique. As the computational cost is very low, the effects of wave current parameters and fluid mud properties on the transportation velocity of the fluid mud are studied systematically. It is found that the fluid mud can move toward one direction even if the shear stress acting on the fluid mud bed is much smaller than the fluid mud yield stress under the condition of wave and current coexistence. Experiments of the fluid mud motion under current with fluctuation water surface are carried out. The fluid mud transportation velocity predicted by the presented mathematical model can roughly match that measured in experiments.展开更多
The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collisi...The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.展开更多
This paper reviews research that studies the principle of self-support(PSS) in some control systems and proposes a fractional-order generalized PSS framework for the first time.The existing PSS approach focuses on pra...This paper reviews research that studies the principle of self-support(PSS) in some control systems and proposes a fractional-order generalized PSS framework for the first time.The existing PSS approach focuses on practical tracking problem of integer-order systems including robotic dynamics,high precision linear motor system,multi-axis high precision positioning system with unmeasurable variables,imprecise sensor information,uncertain parameters and external disturbances.More generally,by formulating the fractional PSS concept as a new generalized framework,we will focus on the possible fields of the fractional-order control problems such as practical tracking,λ-tracking,etc.of robot systems,multiple mobile agents,discrete dynamical systems,time delay systems and other uncertain nonlinear systems.Finally,the practical tracking of a first-order uncertain model of automobile is considered as a simple example to demonstrate the efficiency of the fractional-order generalized principle of self-support(FOGPSS) control strategy.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11790282,U1534204,and 11472179)the Natural Science Foundation of Hebei Province of China(No.A2016210099)
文摘This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.
基金supported by National Natural Science Foundation of China(61573194,61374180,61573096)China Postdoctoral Science Foundation Funded Project(2013M530229)+3 种基金China Postdoctoral Science Special Foundation Funded Project(2014T70463)Six Talent Peaks High Level Project of Jiangsu Province(ZNDW-004)Science Foundation of Nanjing University of Posts and Telecommunications(NY213095)Australian Research Council(DP120104986)
文摘In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay,the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 51177117)the Specialized Research Fund for the Doctoral Program of Higher Education,China (Grant No. 20100201110023)
文摘In this paper, the fractional-order mathematical model and the fractional-order state-space averaging model of the Buck-Boost converter in continuous conduction mode (CCM) are established based on the fractional calculus and the Adomian decomposition method. Some dynamical properties of the current-mode controlled fractional-order Buck- Boost converter are analysed. The simulation is accomplished by using SIMULINK. Numerical simulations are presented to verify the analytical results and we find that bifurcation points will be moved backward as α and β vary. At the same time, the simulation results show that the converter goes through different routes to chaos.
基金supported by the National Natural Science Foundation of China(61174145)
文摘The major advantage of grey system theory is that both incomplete information and unclear problems can be processed precisely. Considering that the modeling of grey model(GM) depends on the preprocessing of the original data,the fractional-order accumulation calculus could be used to do preprocessing. In this paper, the residual sequence represented by Fourier series is used to ameliorate performance of the fractionalorder accumulation GM(1,1) and improve the accuracy of predictor. The state space model of optimally modified GM(1,1)predictor is given and genetic algorithm(GA) is used to find the smallest relative error during the modeling step. Furthermore,the fractional form of continuous GM(1,1) is given to enlarge the content of prediction model. The simulation results illustrated that the fractional-order calculus could be used to depict the GM precisely with more degrees of freedom. Meanwhile, the ranges of the parameters and model application could be enlarged with better performance. The method of modified GM predictor using optimal fractional-order accumulation calculus is expected to be widely used in data processing, model theory, prediction control and related fields.
基金Project supported by the National Natural Science Foundation of China(No.10972117)
文摘A fractional-order Maxwell model is used to describe the viscoelastic seabed mud. The experimental data of the real mud well fit the results of the fractional-order Maxwell model that has fewer parameters than the traditional model. The model is then used to investigate the effect of the mud on the surface-wave damping. The damping rate of a linear monochromatic wave is obtained. The elastic resonance of the mud layer is observed, which leads to the peaks in the damping rate. The damping rate is a sum of the modal damping rates, which indicates the wave damping induced by the mud motion of particular modes. The analysis shows that near the resonance, the total damping rate is dominated by the damping rate of the corresponding mode.
基金This research received funding support from the NSRF via the Program Management Unit for Human Resources&Institutional Development,Research and Innovation(Grant Number B05F640088).
文摘The purpose of this paper is to present a numerical approach based on the artificial neural networks(ANNs)for solving a novel fractional chaotic financial model that represents the effect of memory and chaos in the presented system.The method is constructed with the combination of the ANNs along with the Levenberg-Marquardt backpropagation(LMB),named the ANNs-LMB.This technique is tested for solving the novel problem for three cases of the fractional-order values and the obtained results are compared with the reference solution.Fifteen numbers neurons have been used to solve the fractional-order chaotic financial model.The selection of the data to solve the fractional-order chaotic financial model are selected as 75%for training,10%for testing,and 15%for certification.The results indicate that the presented approximate solutions fit exactly with the reference solution and the method is effective and precise.The obtained results are testified to reduce the mean square error(MSE)for solving the fractional model and verified through the various measures including correlation,MSE,regression histogram of the errors,and state transition(ST).
文摘In this paper,we formulate and analyze a new fractional-order Logistic model with feedback control,which is different from a recognized mathematical model proposed in our very recent work.Asymptotic stability of the proposed model and its numerical solutions are studied rigorously.By using the Lyapunov direct method for fractional dynamical systems and a suitable Lyapunov function,we show that a unique positive equilibrium point of the new model is asymptotically stable.As an important consequence of this,we obtain a new mathematical model in which the feedback control variables only change the position of the unique positive equilibrium point of the original model but retain its asymptotic stability.Furthermore,we construct unconditionally positive nonstandard finite difference(NSFD)schemes for the proposed model using the Mickens’methodology.It is worth noting that the constructed NSFD schemes not only preserve the positivity but also provide reliable numerical solutions that correctly reflect the dynamics of the new fractional-order model.Finally,we report some numerical examples to support and illustrate the theoretical results.The results indicate that there is a good agreement between the theoretical results and numerical ones.
基金Supported by the National Natural Science Foundation of China(72001181,71901184)the Sichuan Federation of Social Science Associations(SC20B122)。
文摘This study considers a nonlinear grey Bernoulli forecasting model with conformable fractionalorder accumulation,abbreviated as CFNGBM(1,1,λ),to study the gross regional product in the ChengYu area.The new model contains three nonlinear parameters,the power exponentγ,the conformable fractional-orderαand the background valueλ,which increase the adjustability and flexibility of the CFNGBM(1,1,λ)model.Nonlinear parameters are determined by the moth flame optimization algorithm,which minimizes the mean absolute prediction percentage error.The CFNGBM(1,1,λ)model is applied to the gross regional product of 16 cities in the Cheng-Yu area,which are Chongqing,Chengdu,Mianyang,Leshan,Zigong,Deyang,Meishan,Luzhou,Suining,Neijiang,Nanchong,Guang’an,Yibin,Ya’an,Dazhou and Ziyang.With data from 2013 to 2021,several grey models are established and results show that the new model has higher accuracy in most cases.
基金financially supported by the 300000DWT Waterway of Lianyungang Harbor Construction Projectthe National Natural Science Foundation of China(Grant No.11272116)
文摘Simplified equations of fluid mud motion, which is described as Bingham-Plastic model under waves and currents, are presented by order analysis. The simplified equations are non-linear ordinary differential equations which are solved by hybrid numerical-analytical technique. As the computational cost is very low, the effects of wave current parameters and fluid mud properties on the transportation velocity of the fluid mud are studied systematically. It is found that the fluid mud can move toward one direction even if the shear stress acting on the fluid mud bed is much smaller than the fluid mud yield stress under the condition of wave and current coexistence. Experiments of the fluid mud motion under current with fluctuation water surface are carried out. The fluid mud transportation velocity predicted by the presented mathematical model can roughly match that measured in experiments.
基金Project supported by the National Key Basic Research and Development Program of China(No.G1999-0222-08)
文摘The USM-θ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-θ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-θ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-θ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.
基金supported by the National Natural Science Foundation of China(61304004,61503205)the Foundation of China Scholarship Council(201406715056)+1 种基金the Foundation of Changzhou Key Laboratory of Special Robot and Intelligent Technology(CZSR2014005)the Changzhou Science and Technology Program(CJ20160013)
文摘This paper reviews research that studies the principle of self-support(PSS) in some control systems and proposes a fractional-order generalized PSS framework for the first time.The existing PSS approach focuses on practical tracking problem of integer-order systems including robotic dynamics,high precision linear motor system,multi-axis high precision positioning system with unmeasurable variables,imprecise sensor information,uncertain parameters and external disturbances.More generally,by formulating the fractional PSS concept as a new generalized framework,we will focus on the possible fields of the fractional-order control problems such as practical tracking,λ-tracking,etc.of robot systems,multiple mobile agents,discrete dynamical systems,time delay systems and other uncertain nonlinear systems.Finally,the practical tracking of a first-order uncertain model of automobile is considered as a simple example to demonstrate the efficiency of the fractional-order generalized principle of self-support(FOGPSS) control strategy.