Modeling and dynamics analysis of the fractional-order Buck-Boost converter in continuous conduction mode

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.

Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

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.

Modified Grey Model Predictor Design Using Optimal Fractional-order Accumulation Calculus

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.

Fractional-order Maxwell model of seabed mud and its effect on surface-wave damping

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.

Intelligent Networks for Chaotic Fractional-Order Nonlinear Financial Model

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).

On a new fractional-order Logistic model with feedback control

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.

Dynamics of Caputo fractional-order SIRV model:The effects of imperfect vaccination on disease transmission

Though vaccination protects individuals against many infectious diseases,such protection does not always last forever since a few vaccinated individuals could lose their lifelong immunity and eventually become infected.This study,therefore,determines the effects of imperfect vaccination and memory index on the spread of diseases through the Caputo fractional-order SIRV(Susceptible-Infected-Recovered-Vaccinated)epidemic model.Vital properties of the new model including the conditions for the existence of a unique solution determined through the fixed-point theory and the conditions for the existence of a positive solution of the model obtained via the Mittag-Leffler function along with the Laplace transformation-are thoroughly studied.Consequently,our simulation results report that an increase in the imperfect vaccination force increases the population of infected individuals.For the memory effect,the higher“memory”the epidemic system has of past states(which corresponds to decreasing values of fractionalorder parameter),the greater the peaks and magnitudes of infection shaping the epidemiological system dynamics.

Dynamical analysis and chaos control of a fractional-order Leslie-type predator-prey model with Caputo derivative

In this paper,the dynamical behaviors of a discrete-time fractional-order population model are considered.The stability analysis and the topological classification of the model at the fixed point have been investigated.It is shown that the model undergoes flip and Neimark-Sacker bifurcations around the co-existence fixed point by using the bifurcation and the normal form theory.These bifurcations lead to chaos when the parameter changes at critical point.In order to control chaotic behavior in the model result from Neimark-Sacker bifurcation,the OGY feedback method has been used.Furthermore,some numerical simulations,including bifurcation diagrams,phase portraits and maximum Lyapunov exponents of the presented model are plotted to support the correctness of the analytical results.The positive Lyapunov exponents demonstrate that chaotic behavior exists in the considered model.

Stability analysis of a fractional-order monkeypox epidemic model with quarantine and hospitalization

The monkeypox epidemic has become a global health issue due to its rapid transmission involving nonhuman-to-human transmission in nonendemic areas.Various actions,such as quarantine,vaccination,and hospitalization,have been implemented by worldwide governments.Given the relatively high cost and strict implementation of vaccination,our focus lies on quarantine and hospitalization.In this paper,we study the monkeypox epidemic involving quarantine and hospitalization through fractionalorder mathematical modeling.The proposed model considers six classes of human populations(susceptible,exposed,infected,quarantined,hospitalized,and recovered)and three classes of nonhuman populations(susceptible,exposed,and infected).The basic properties of the model have been investigated,and its equilibrium points have been obtained,namely monkeypox-free,nonhuman-free endemic,and endemic.We have derived the basic reproduction numbers for human-to-human and nonhuman-tononhuman transmissions,denoted as R0h and R0n respectively.The existence and stability(both locally and globally)of each equilibrium point depend on R0h and R0n relative to unity.We performed calibration and forecasting of the model on the weekly monkeypox case data of the human population in the United States of America from June 1 to September 23,2022.Research findings indicate that the fractional-order model shows better calibration and forecasting compared to the corresponding firstorder model based on the root mean square error.Furthermore,the best-fitting model calibration indicates R0=maxfR0h;R0ng>1,suggesting the potential for endemic conditions in humans.However,the best forecasting shows R0<1,possibly due to various policies such as vaccination.Given the relative cost and stringency of vaccination implementation for monkeypox control,we perform numerical simulations and sensitivity analyses on the basic reproduction number,particularly focusing on the impact of quarantine and hospitalization rates.Simulations and sensitivity analysis indicate that simultaneous increases in quarantine and hospitalization rates can reduce the basic reproduction number R0h below unity.Consequently,the monkeypox epidemic can be eradicated.Moreover,fractional-order derivative plays a crucial role in determining the spikes of monkeypox cases and the rapidity at which the disease undergoes either endemicity or extinction.Considerations of memory effects,quarantine,and hospitalization have a significant impact on monkeypox modeling studies,especially in capturing biological phenomena.

A Nonlinear Grey Bernoulli Model with Conformable Fractional-Order Accumulation and Its Application to the Gross Regional Product in the Cheng-Yu Area

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.

考虑参数随机性的压实黄土蠕变变形不确定性分析

现有蠕变模型的计算值为确定值,未能考虑岩土材料和参数评估过程中的随机性。为反映岩土材料的变形随机特性,基于多次重复的一维固结蠕变试验,本文研究了分级和分别加载条件下压实黄土的蠕变特性,建立了考虑参数随机性的改进Merchant模型,提出了一种蠕变变形的不确定性预测方法,并通过延安高填方工程进行了验证。结果表明,压实黄土具有明显的衰减蠕变特性,引入非线性元件的Merchant模型能更好描述土体的应变时间关系,考虑参数随机性的模型计算值近似服从正态分布;通过不确定性预测方法可以获得蠕变变形值的概率云图,且工程实测蠕变变形值落在预测范围的95%的置信区间内,说明了考虑参数随机性的蠕变变形不确定性预测方法的有效性。

考虑蠕变影响的堆载作用下被动排桩受力变形分析

为分析堆载作用下被动桩受力变形的时间效应,首先引入分数阶Merchant模型描述土体的蠕变特性,然后根据对应性原理和Laplace变换推导Boussinesq黏弹性解,计算堆载引发水平附加应力,并通过Terzaghi土拱模型将附加应力传递到桩上,得到堆载作用在桩上的被动荷载.其次,将桩简化为黏弹性Pasternak地基上的欧拉梁,建立桩身挠曲微分方程,并采用有限差分法及Laplace逆变换求解,随后通过与已有试验结果的对比分析,验证了本文方法的可行性.最后,对分数阶Merchant模型参数(虎克体的弹性模量Eh、Kelvin体的弹性模量Ek及黏滞系数η、分数阶阶次α)、堆载-桩身水平距离以及堆载荷载对桩身水平位移的影响进行了分析,分析结果表明:Eh越大,桩身初始水平位移越小;Ek越大,桩身水平位移随时间的增量越小;η越大,桩身到达最终变形量的时间越长;α越大,Kelvin体的黏滞性越大;堆载-桩身水平距离越小、堆载荷载越大,桩身水平位移越大;且随时间的增加,桩身水平位移对Eh的敏感度降低,对堆载-桩身水平距离和堆载荷载的敏感度会增大.

基于混合效应模型的相容性削度-材积方程研究

为构建一个能够准确估计树干从地面到任意部位高度的直径和材积的相容性削度-材积方程,以吉林省汪清林业局金沟岭林场的冷杉解析木数据为例,选择基于材积比方程和基于积分方法这2种方法来构建相容性削度-材积方程系统。在模拟时,采用3种参数估计方法来估计2个系统中的削度方程、全树干材积和商品材材积方程的参数,并考虑样木间的随机效应。选择均方根误差和平均绝对残差等指标,对精度进行比较。最后发展出一个能够准确预测树干任意高度的直径、全树干材积和商品材材积的相容性削度-材积方程系统。结果表明,在2个相容性削度-材积系统中,采用削度方程参数估计方法提供了商品材材积和全树干材积的最差预测,似乎不相关参数方法在材积比方程方法构建的相容性削度-材积方程系统中的精度最高,商品材材积参数方法在积分方法构建的相容性削度-材积方程系统中的精度最高。2个相容性削度-材积系统中无论采用商品材材积参数估计方法还是削度方程参数估计方法,在考虑单木的随机效应后,模型的模拟和验证效果都得到很大的提高。基于积分方法的相容性削度-材积方程系统的模拟和验证精度要高于基于材积比方程方法的相容性削度-材积方程系统的模拟和验证精度。总体来说,相容性削度-材积方程系统可以保证削度方程、商品材材积方程和全树干材积方程在形式和算法上相容。

碱渣土蠕变特性试验及数值模拟研究

碱渣土孔隙比大、含水量高、压缩性大,研究其蠕变特性对于准确预测碱渣土地基长期沉降、确保上部结构长期稳定性具有重要意义。以天津港碱渣土为研究对象,采用分级加载-卸载的方式对不同深度处碱渣土进行一维压缩固结试验(包括卸荷回弹与再压缩试验)。通过试样孔隙比随上部固结压力的变化曲线分析了碱渣土的压缩特性;利用“陈氏法”对分级加载过程的应变-时间试验数据进行处理,得到不同深度处碱渣土在不同固结压力下的应变-时间蠕变曲线。在此基础上,根据蠕变曲线衰减稳定规律以及应力-应变等时曲线所反映的非线性蠕变特征,提出采用Merchant元件模型对蠕变试验曲线进行拟合,并确定模型中3个参数的经验计算公式,建立碱渣土非线性蠕变模型。最后,通过编制有限元子程序实现数值开发,将数模计算值与蠕变试验数据、天津港碱渣土地基沉降实测值进行对比,验证所开发数值模型的合理性。

商船测深可信度评价体系研究

针对商船测深数据预处理阶段的测深数据可用性问题,引入“可信度”的概念,从三个方面进行可信度评价问题的研究:给出了8种可利用的可信度分级评价元数据,研究了基于固有属性的可信度评价模型;提出可利用重复的水深数据进行自一致性的可信度评价的研究;将商船测深数据与权威的水深测量数据进行比对后得出的外符合精度作为一项评价指标,进行基于权威数据的可信度评价。将这三种可信度评价指标进行加权平均,获得商船测深的最终水深数据值。

基于三维Merchant模型的公路改扩建工程路基变形特性研究

为进一步分析不均匀沉降对改扩建工程的影响,提出了适用于新疆地区的拼接路基填筑材料设计指标,采用有限元法分析了填筑材料特性对改扩建公路的影响。首先,介绍了三维DruckerPrager模型表达式。考虑到Drucker-Prager模型无法模拟路基工后沉降中存在的蠕变变形,采用了三维Merchant模型的Prony级数表达式模拟蠕变变形量。依据连霍高速(G30)新疆境内小草湖—乌鲁木齐段改扩建工程标准断面参数,建立了有限元模型并探讨了填筑材料物理参数对新旧路堤附加变形、沉降差异和路面变形的影响规律。结果表明:随着填筑材料弹性模量的增加,新旧路堤附加变形、沉降和沥青路面变形显著减少;拼接路基竖向位移和不均匀沉降随着黏聚力c的减小,先减小后增大。黏聚力c和内摩擦角j主要影响范围是新路基中心至右路肩处。

Identification Scheme for Fractional Hammerstein Models With the Delayed Haar Wavelet

The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix(HWOM). To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.

Comparative Analysis of Four Stem Taper Models for Quercus glauca in Mount Halla,Jeju Island,South Korea

This study was conducted to fit the diameter-height data of Quercusglaucain Jeju Island, South Korea to the four commonly used stem taper equations andto evaluate the performance of the four stem taper models using four statistical criteria： Fit index （FI）, root mean square error （RMSE）, bias （）,and absolute mean difference （AMD）. Results showed that the Kozak02stem taper equation provided the best FI（0.9847）, RMSE（1.5745）,（-0.0030 cm） and AMD （1.0990 cm） whileMax and Burkhart model had the poorest performance among the four stem taper models based on the four evaluation statistics （FI ： 0.9793,RMSE ： 1.8272, ： 0.3040 cm and AMD ： 1.3060 cm）. These stem taper equations can serve as a useful tool for forest managers in estimating the diameter outside bark at any given height, merchantable stem volumes and total stem volumesof the standing trees of Quercusglaucain theGotjawal forests located in Mount Halla, Jeju Island, South Korea.

A Fractional Drift Diffusion Model for Organic Semiconductor Devices

Because charge carriers of many organic semiconductors(OSCs)exhibit fractional drift diffusion(Fr-DD)transport properties,the need to develop a Fr-DD model solver becomes more apparent.However,the current research on solving the governing equations of the Fr-DD model is practically nonexistent.In this paper,an iterative solver with high precision is developed to solve both the transient and steady-state Fr-DD model for organic semiconductor devices.The Fr-DD model is composed of two fractionalorder carriers(i.e.,electrons and holes)continuity equations coupled with Poisson’s equation.By treating the current density as constants within each pair of consecutive grid nodes,a linear Caputo’s fractional-order ordinary differential equation(FrODE)can be produced,and its analytic solution gives an approximation to the carrier concentration.The convergence of the solver is guaranteed by implementing a successive over-relaxation(SOR)mechanism on each loop of Gummel’s iteration.Based on our derivations,it can be shown that the Scharfetter–Gummel discretization method is essentially a special case of our scheme.In addition,the consistency and convergence of the two core algorithms are proved,with three numerical examples designed to demonstrate the accuracy and computational performance of this solver.Finally,we validate the Fr-DD model for a steady-state organic field effect transistor(OFET)by fitting the simulated transconductance and output curves to the experimental data.

Merchant模型在漳诏高速路堤沉降预测中的应用

在沿海软土地区路堤沉降计算中,考虑主次固结的Merchant粘弹性模型是一个比较理想的模型,本文采用Biot固结有限元方法,对漳诏高速路堤的地基沉降进行了预测,通过计算验证了该模型预测沉降的思路和可行性,为高填方路堤工程设计和施工提供有益的借鉴。