This paper presents a novel active disturbance rejection control(ADRC)scheme based on a cascade connection of generalized proportional integral observers(GPIOs)with internal models designed to estimate both polynomial...This paper presents a novel active disturbance rejection control(ADRC)scheme based on a cascade connection of generalized proportional integral observers(GPIOs)with internal models designed to estimate both polynomial and resonant disturbances.In this estimator structure,referred to as Cascade GPIO(CGPIO),the total disturbance sensitivity is the product of the sensitivities at each cascade level.This approach improves system performance against both periodic and non-periodic disturbances and enhances robustness under frequency variations in harmonic components.Additionally,the decoupled nature of the estimator reduces the order of the GPIOs,thereby simplifying tuning and limiting observer gains.The proposed control scheme is supported by a frequency-domain analysis and is experimentally validated in the current control of a grid-connected converter subject to control gain uncertainties,harmonic distortion,frequency deviations,and measurement noise.Experimental results demonstrate that the CGPIO-based ADRC outperforms benchmark solutions,including proportional-integral(PI)and proportional-resonant(PR)controllers.展开更多
Fast and accurate monitoring of the phase,amplitude,and frequency of the grid voltage is essential for single-phase grid-connected converters.The presence of DC offset in the grid voltage is detrimental to not only gr...Fast and accurate monitoring of the phase,amplitude,and frequency of the grid voltage is essential for single-phase grid-connected converters.The presence of DC offset in the grid voltage is detrimental to not only grid synchronization but also the closed-loop stability of the grid-connected converters.In this paper,a new synchronization method to mitigate the effect of DC offset is presented using arbitrarily delayed signal cancelation(ADSC)in a second-order generalized integrator(SOGI)phase-locked loop(PLL).A frequency-fixed SOGI-based PLL(FFSOGI-PLL)is adopted to ensure better stability and to reduce the complexity compared with other SOGI-based PLLs.A small-signal model of the proposed PLL is derived for the systematic design of proportional-integral(PI)controller gains.The effects of frequency variation and ADSC on the proposed PLL are considered,and correction methods are adopted to accurately estimate grid information.The simulation results are presented,along with comparisons to other single-phase PLLs in terms of settling time,peak frequency,and phase error to validate the proposed PLL.The dynamic performance of the proposed PLL is also experimentally validated.Overall,the proposed PLL has the fastest transient response and better dynamic performance than the other PLLs for almost all performance indices,offering an improved solution for precise grid synchronization in single-phase applications.展开更多
In response to the complex working conditions of the power grid caused by the high proportion of new energy access,which leads to insufficient output accuracy of the second-order generalized integrator(SOGI)phaselocke...In response to the complex working conditions of the power grid caused by the high proportion of new energy access,which leads to insufficient output accuracy of the second-order generalized integrator(SOGI)phaselocked loop,this article proposes an improved frequency adaptive phase-locked loop structure for SOGI.Firstly,an amplitude compensation branch is introduced to compensate for the SOGI tracking fundamental frequency signal,ensuring the accuracy of the SOGI output orthogonal signal under frequency fluctuation conditions.Secondly,by cascading two adaptive SOGI modules,the suppression capability of low-order harmonics and Direct Current(DC)components has been improved.Finally,the positive and negative sequence separation method of orthogonal signals is introduced to eliminate the influence of unbalanced components on the phase-locked loop.The comparative experiment with the classic SOGI-PLL method shows that the proposed phase-locked loop structure effectively improves the accuracy of power grid synchronization detection under complex working conditions such as harmonic components,unbalanced components,and frequency fluctuations.It can complete frequency detection within 1.5 power frequency cycles,and the detected fundamental frequency positive sequence voltage has a higher sinuosity and harmonic distortion rate within 0.5%.展开更多
As oil and gas exploration moves into deeper waters,marine risers are subjected to increasingly complex service conditions,including vessel motions,ocean currents,seabed-soil interactions,and internal flow effects.Thi...As oil and gas exploration moves into deeper waters,marine risers are subjected to increasingly complex service conditions,including vessel motions,ocean currents,seabed-soil interactions,and internal flow effects.This work establishes a dynamic behavior model of steel catenary risers(SCRs)with varying curvatures subjected to internal flow and external currents and considers the effects of pipe-soil interactions on the curvature profile.The governing equation is solved via the generalized integral transform technique(GITT),which yields a semi-analytical solution of a high-order nonlinear partial differential equation.Parametric studies are then performed to analyze the effects of varying curvature on the vibration frequency and amplitude of SCRs.The vibration frequency and amplitude increase with the touchdown angle and hang-off angle,although the effect of the hang-off angle is negligible.Additionally,as the curvature increases along the centerline axis,the position of the maximum amplitude of the SCR moves upward.展开更多
To handle input and output time delays that commonly exist in many networked control systems(NCSs), a new robust continuous sliding mode control(CSMC) scheme is proposed for the output tracking in uncertain single inp...To handle input and output time delays that commonly exist in many networked control systems(NCSs), a new robust continuous sliding mode control(CSMC) scheme is proposed for the output tracking in uncertain single input-single-output(SISO) networked control systems. This scheme consists of three consecutive steps. First, although the network-induced delay in those systems can be effectively handled by using Pade approximation(PA), the unmatched disturbance cames out as another difficulty in the control design. Second, to actively estimate this unmatched disturbance, a generalized proportional integral observer(GPIO) technique is utilized based on only one measured state. Third, by constructing a new sliding manifold with the aid of the estimated unmatched disturbance and states, a GPIO-based CSMC is synthesized, which is employed to cope with not only matched and unmatched disturbances, but also networkinduced delays. The stability of the entire closed-loop system under the proposed GPIO-based CSMC is detailedly analyzed.The promising tracking efficiency and feasibility of the proposed control methodology are verified through simulations and experiments on Quanser's servo module for motion control under various test conditions.展开更多
Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2...Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.展开更多
In this paper, we study the boundedness of higher order commutators of gen- eralized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.
Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almo...Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.展开更多
This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z =...This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.展开更多
In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generali...In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generalized convexity and concavity of these functions.In particular,some Turán type inequalities are given.Finally,we also show some new series representations of these functions by applying Alzer and Richard's methods.展开更多
In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalga...In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional operators.Meanwhile,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional operator.In order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional order.Meanwhile,some special cases are apprehended and the new outcomes are also illustrated.The obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering.展开更多
Active Magnetic Bearing(AMB)levitates rotor by magnetic force without friction,and it can provide active control force to suppress vibration while rotating.Most of vibration suppressing methods need angular speed sens...Active Magnetic Bearing(AMB)levitates rotor by magnetic force without friction,and it can provide active control force to suppress vibration while rotating.Most of vibration suppressing methods need angular speed sensors to obtain rotating speed,but in many occasions,angular speed sensor is difficult to install or is difficult to guarantee reliability.This paper proposed a vibration suppressing strategy without angular speed sensor based on generalized integrator and frequency locked loop(GI-FLL)and phase shift generalized integrator(PSGI).GI-FLL and high-pass filter estimate frequency from control current,PSGI is applied to generate compensating signal.Firstly,model of AMB system expressed by transfer function is established and effect of centrifugal force is analyzed.Then,principle and process of vibration suppressing strategy is introduced.Influence of parameters are analyzed by root locus and bode diagram.Simulation results display the process of frequency estimation and performance of displacement.Experiments are carried on a test rig,results of simulations and experiments demonstrate the effectiveness of proposed vibration suppressing strategy.展开更多
The stator flux and electromagnetic torque observation is the basis of direct torque controlled permanent magnet synchronous motor( PMSM) drive system. However,the traditional stator flux observer based on voltage mod...The stator flux and electromagnetic torque observation is the basis of direct torque controlled permanent magnet synchronous motor( PMSM) drive system. However,the traditional stator flux observer based on voltage model is affected by integral initial values and integral drift,that based on current model is affected by the parameters of PMSM,so a new stator flux observation method is proposed based on an improved secondorder generalized integrator( SOGI). Compared to the stator flux observation method based on the conventional SOGI,the proposed method can not only overcome the influence of integral initial values and integral drift,but also completely eliminate the DC offset's influence. Therefore,the observation accuracy of stator flux is further improved. The simulation and experimental results both show that the proposed method has a higher stator flux and electromagnetic torque observation precision.展开更多
In predictive direct power control(PDPC)system of three-phase pulse width modulation(PWM)rectifier,grid voltage sensor makes the whole system more complex and costly.Therefore,third-order generalized integrator(TOGI)i...In predictive direct power control(PDPC)system of three-phase pulse width modulation(PWM)rectifier,grid voltage sensor makes the whole system more complex and costly.Therefore,third-order generalized integrator(TOGI)is used to generate orthogonal signals with the same frequency to estimate the grid voltage.In addition,in view of the deviation between actual and reference power in the three-phase PWM rectifier traditional PDPC strategy,a power correction link is designed to correct the power reference value.The grid voltage sensor free algorithm based on TOGI and the corrected PDPC strategy are applied to three-phase PWM rectifier and simulated on the simulation platform.Simulation results show that the proposed method can effectively eliminate the power tracking deviation and the grid voltage.The effectiveness of the proposed method is verified by comparing the simulation results.展开更多
Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. T...Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.展开更多
To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive co...To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity （ARIMA-GARCH） model. In which, the ARIMA model is used as the mean equation of the GARCH model to model the travel time levels and the GARCH model is used to model the conditional variances of travel time. The proposed method is validated and evaluated using actual traffic flow data collected from the traffic monitoring system of Kunshan city. The evaluation results show that, compared with the conventional ARIMA model, the proposed model cannot significantly improve the forecasting performance of travel time levels but has advantage in travel time volatility forecasting. The proposed model can well capture the travel time heteroskedasticity and forecast the time-varying confidence intervals of travel time which can better reflect the volatility of observed travel times than the fixed confidence interval provided by the ARIMA model.展开更多
Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nons...Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nonsmooth kernel related to L,or Tj,1=I, Tj,2,Tj,4 be the linear operators,which are bounded on Lp(Rn)for 1<p<∞,and Tj,3=±I(j=1,2,···,m),where I is the identity operator.For b∈L 1 loc (Rn),denote the Toeplitz-type operator byΘαbfmj=1(Tj,1MbIαTj,2 + Tj,3MbIαTj,4),where Mb is a multiplication ope...展开更多
Fruit classification is found to be one of the rising fields in computer and machine vision.Many deep learning-based procedures worked out so far to classify images may have some ill-posed issues.The performance of th...Fruit classification is found to be one of the rising fields in computer and machine vision.Many deep learning-based procedures worked out so far to classify images may have some ill-posed issues.The performance of the classification scheme depends on the range of captured images,the volume of features,types of characters,choice of features from extracted features,and type of classifiers used.This paper aims to propose a novel deep learning approach consisting of Convolution Neural Network(CNN),Recurrent Neural Network(RNN),and Long Short-TermMemory(LSTM)application to classify the fruit images.Classification accuracy depends on the extracted and selected optimal features.Deep learning applications CNN,RNN,and LSTM were collectively involved to classify the fruits.CNN is used to extract the image features.RNN is used to select the extracted optimal features and LSTM is used to classify the fruits based on extracted and selected images features by CNN and RNN.Empirical study shows the supremacy of proposed over existing Support Vector Machine(SVM),Feed-forwardNeural Network(FFNN),and Adaptive Neuro-Fuzzy Inference System(ANFIS)competitive techniques for fruit images classification.The accuracy rate of the proposed approach is quite better than the SVM,FFNN,and ANFIS schemes.It has been concluded that the proposed technique outperforms existing schemes.展开更多
Based on the Euler-Bernoulli beam theory and Kelvin-Voigt model,a nonlinear model for the transverse vibration of a pipe under the combined action of base motion and pulsating internal flow is established.The governin...Based on the Euler-Bernoulli beam theory and Kelvin-Voigt model,a nonlinear model for the transverse vibration of a pipe under the combined action of base motion and pulsating internal flow is established.The governing partial differential equation is transformed into a nonlinear system of fourth-order ordinary differential equations by using the generalized integral transform technique(GITT).The effects of the combined excitation of base motion and pulsating internal flow on the nonlinear dynamic behavior of the pipe are investigated using a bifurcation diagram,phase trajectory diagram,power spectrum diagram,time-domain diagram,and Poincare map.The results show that the base excitation amplitude and frequency significantly affect the dynamic behavior of the pipe system.Some new resonance phenomena can be observed,such as the period-1 motion under the base excitation or the pulsating internal flow alone becomes the multi-periodic motion,quasi-periodic motion or even chaotic motion due to the combined excitation action.展开更多
In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentiall...In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.展开更多
文摘This paper presents a novel active disturbance rejection control(ADRC)scheme based on a cascade connection of generalized proportional integral observers(GPIOs)with internal models designed to estimate both polynomial and resonant disturbances.In this estimator structure,referred to as Cascade GPIO(CGPIO),the total disturbance sensitivity is the product of the sensitivities at each cascade level.This approach improves system performance against both periodic and non-periodic disturbances and enhances robustness under frequency variations in harmonic components.Additionally,the decoupled nature of the estimator reduces the order of the GPIOs,thereby simplifying tuning and limiting observer gains.The proposed control scheme is supported by a frequency-domain analysis and is experimentally validated in the current control of a grid-connected converter subject to control gain uncertainties,harmonic distortion,frequency deviations,and measurement noise.Experimental results demonstrate that the CGPIO-based ADRC outperforms benchmark solutions,including proportional-integral(PI)and proportional-resonant(PR)controllers.
基金supported by the Deanship of Research at Jordan University of Science and Technology (Grant number:20210333).
文摘Fast and accurate monitoring of the phase,amplitude,and frequency of the grid voltage is essential for single-phase grid-connected converters.The presence of DC offset in the grid voltage is detrimental to not only grid synchronization but also the closed-loop stability of the grid-connected converters.In this paper,a new synchronization method to mitigate the effect of DC offset is presented using arbitrarily delayed signal cancelation(ADSC)in a second-order generalized integrator(SOGI)phase-locked loop(PLL).A frequency-fixed SOGI-based PLL(FFSOGI-PLL)is adopted to ensure better stability and to reduce the complexity compared with other SOGI-based PLLs.A small-signal model of the proposed PLL is derived for the systematic design of proportional-integral(PI)controller gains.The effects of frequency variation and ADSC on the proposed PLL are considered,and correction methods are adopted to accurately estimate grid information.The simulation results are presented,along with comparisons to other single-phase PLLs in terms of settling time,peak frequency,and phase error to validate the proposed PLL.The dynamic performance of the proposed PLL is also experimentally validated.Overall,the proposed PLL has the fastest transient response and better dynamic performance than the other PLLs for almost all performance indices,offering an improved solution for precise grid synchronization in single-phase applications.
基金supported by the Science and Technology Project of China Southern Power Grid Co.,Ltd.(Grant No.ZBKJXM20232471)the National Key R&D Program of China(Grant No.2021YFB1600200)the Innovation Capability Support Program of Shaanxi(Grant No.2022KXJ-144)。
文摘In response to the complex working conditions of the power grid caused by the high proportion of new energy access,which leads to insufficient output accuracy of the second-order generalized integrator(SOGI)phaselocked loop,this article proposes an improved frequency adaptive phase-locked loop structure for SOGI.Firstly,an amplitude compensation branch is introduced to compensate for the SOGI tracking fundamental frequency signal,ensuring the accuracy of the SOGI output orthogonal signal under frequency fluctuation conditions.Secondly,by cascading two adaptive SOGI modules,the suppression capability of low-order harmonics and Direct Current(DC)components has been improved.Finally,the positive and negative sequence separation method of orthogonal signals is introduced to eliminate the influence of unbalanced components on the phase-locked loop.The comparative experiment with the classic SOGI-PLL method shows that the proposed phase-locked loop structure effectively improves the accuracy of power grid synchronization detection under complex working conditions such as harmonic components,unbalanced components,and frequency fluctuations.It can complete frequency detection within 1.5 power frequency cycles,and the detected fundamental frequency positive sequence voltage has a higher sinuosity and harmonic distortion rate within 0.5%.
基金financially supported by the National Natural Science Foundation of China(Grant No.52201312).
文摘As oil and gas exploration moves into deeper waters,marine risers are subjected to increasingly complex service conditions,including vessel motions,ocean currents,seabed-soil interactions,and internal flow effects.This work establishes a dynamic behavior model of steel catenary risers(SCRs)with varying curvatures subjected to internal flow and external currents and considers the effects of pipe-soil interactions on the curvature profile.The governing equation is solved via the generalized integral transform technique(GITT),which yields a semi-analytical solution of a high-order nonlinear partial differential equation.Parametric studies are then performed to analyze the effects of varying curvature on the vibration frequency and amplitude of SCRs.The vibration frequency and amplitude increase with the touchdown angle and hang-off angle,although the effect of the hang-off angle is negligible.Additionally,as the curvature increases along the centerline axis,the position of the maximum amplitude of the SCR moves upward.
基金supported in part by the Australian Research Council Discovery Project(DP190101557)
文摘To handle input and output time delays that commonly exist in many networked control systems(NCSs), a new robust continuous sliding mode control(CSMC) scheme is proposed for the output tracking in uncertain single input-single-output(SISO) networked control systems. This scheme consists of three consecutive steps. First, although the network-induced delay in those systems can be effectively handled by using Pade approximation(PA), the unmatched disturbance cames out as another difficulty in the control design. Second, to actively estimate this unmatched disturbance, a generalized proportional integral observer(GPIO) technique is utilized based on only one measured state. Third, by constructing a new sliding manifold with the aid of the estimated unmatched disturbance and states, a GPIO-based CSMC is synthesized, which is employed to cope with not only matched and unmatched disturbances, but also networkinduced delays. The stability of the entire closed-loop system under the proposed GPIO-based CSMC is detailedly analyzed.The promising tracking efficiency and feasibility of the proposed control methodology are verified through simulations and experiments on Quanser's servo module for motion control under various test conditions.
基金Supported by National 973 Project(G.19990751)the SEDF of China(20040027001)
文摘Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.
基金Supported by the NSF of China (10371087)NSF of Anhui Province (07021019)+2 种基金Education Committee ofAnhui Province (KJ2007A009Kj2008B244)the Grant for Younth of Anhui Normal University (2009xqn58)
文摘In this paper, we study the boundedness of higher order commutators of gen- eralized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.
文摘Littlewood-Paley operators and Marcinkiewicz integral on generalized Campanula spaces ερ,φ are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in ερ,φ.
文摘This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.
基金supported by the Natural Science Foundation of Shandong Province (ZR2019QA003 and ZR2018MF023)by the National Natural Science Foundation of China (11601036)by the Major Project of Binzhou University (2020ZD02)
文摘In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generalized convexity and concavity of these functions.In particular,some Turán type inequalities are given.Finally,we also show some new series representations of these functions by applying Alzer and Richard's methods.
基金supported by the National Natural Science Foundation of China(Grant No.61673169).
文摘In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional operators.Meanwhile,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional operator.In order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional order.Meanwhile,some special cases are apprehended and the new outcomes are also illustrated.The obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering.
基金the National Natural Science Foundation of China(NSFC)under Grant 51877091.
文摘Active Magnetic Bearing(AMB)levitates rotor by magnetic force without friction,and it can provide active control force to suppress vibration while rotating.Most of vibration suppressing methods need angular speed sensors to obtain rotating speed,but in many occasions,angular speed sensor is difficult to install or is difficult to guarantee reliability.This paper proposed a vibration suppressing strategy without angular speed sensor based on generalized integrator and frequency locked loop(GI-FLL)and phase shift generalized integrator(PSGI).GI-FLL and high-pass filter estimate frequency from control current,PSGI is applied to generate compensating signal.Firstly,model of AMB system expressed by transfer function is established and effect of centrifugal force is analyzed.Then,principle and process of vibration suppressing strategy is introduced.Influence of parameters are analyzed by root locus and bode diagram.Simulation results display the process of frequency estimation and performance of displacement.Experiments are carried on a test rig,results of simulations and experiments demonstrate the effectiveness of proposed vibration suppressing strategy.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51377041)
文摘The stator flux and electromagnetic torque observation is the basis of direct torque controlled permanent magnet synchronous motor( PMSM) drive system. However,the traditional stator flux observer based on voltage model is affected by integral initial values and integral drift,that based on current model is affected by the parameters of PMSM,so a new stator flux observation method is proposed based on an improved secondorder generalized integrator( SOGI). Compared to the stator flux observation method based on the conventional SOGI,the proposed method can not only overcome the influence of integral initial values and integral drift,but also completely eliminate the DC offset's influence. Therefore,the observation accuracy of stator flux is further improved. The simulation and experimental results both show that the proposed method has a higher stator flux and electromagnetic torque observation precision.
基金National Natural Science Foundation of China(Nos.51767013,52067013)。
文摘In predictive direct power control(PDPC)system of three-phase pulse width modulation(PWM)rectifier,grid voltage sensor makes the whole system more complex and costly.Therefore,third-order generalized integrator(TOGI)is used to generate orthogonal signals with the same frequency to estimate the grid voltage.In addition,in view of the deviation between actual and reference power in the three-phase PWM rectifier traditional PDPC strategy,a power correction link is designed to correct the power reference value.The grid voltage sensor free algorithm based on TOGI and the corrected PDPC strategy are applied to three-phase PWM rectifier and simulated on the simulation platform.Simulation results show that the proposed method can effectively eliminate the power tracking deviation and the grid voltage.The effectiveness of the proposed method is verified by comparing the simulation results.
文摘Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.
基金The National Natural Science Foundation of China(No.51108079)
文摘To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity （ARIMA-GARCH） model. In which, the ARIMA model is used as the mean equation of the GARCH model to model the travel time levels and the GARCH model is used to model the conditional variances of travel time. The proposed method is validated and evaluated using actual traffic flow data collected from the traffic monitoring system of Kunshan city. The evaluation results show that, compared with the conventional ARIMA model, the proposed model cannot significantly improve the forecasting performance of travel time levels but has advantage in travel time volatility forecasting. The proposed model can well capture the travel time heteroskedasticity and forecast the time-varying confidence intervals of travel time which can better reflect the volatility of observed travel times than the fixed confidence interval provided by the ARIMA model.
基金Supported by the NNSF of China(10571014)SEDF of China(20040027001)
文摘Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α<n.Let Tj,1 be the singular integral with nonsmooth kernel related to L,or Tj,1=I, Tj,2,Tj,4 be the linear operators,which are bounded on Lp(Rn)for 1<p<∞,and Tj,3=±I(j=1,2,···,m),where I is the identity operator.For b∈L 1 loc (Rn),denote the Toeplitz-type operator byΘαbfmj=1(Tj,1MbIαTj,2 + Tj,3MbIαTj,4),where Mb is a multiplication ope...
基金This research is funded by Taif University,TURSP-2020/150.
文摘Fruit classification is found to be one of the rising fields in computer and machine vision.Many deep learning-based procedures worked out so far to classify images may have some ill-posed issues.The performance of the classification scheme depends on the range of captured images,the volume of features,types of characters,choice of features from extracted features,and type of classifiers used.This paper aims to propose a novel deep learning approach consisting of Convolution Neural Network(CNN),Recurrent Neural Network(RNN),and Long Short-TermMemory(LSTM)application to classify the fruit images.Classification accuracy depends on the extracted and selected optimal features.Deep learning applications CNN,RNN,and LSTM were collectively involved to classify the fruits.CNN is used to extract the image features.RNN is used to select the extracted optimal features and LSTM is used to classify the fruits based on extracted and selected images features by CNN and RNN.Empirical study shows the supremacy of proposed over existing Support Vector Machine(SVM),Feed-forwardNeural Network(FFNN),and Adaptive Neuro-Fuzzy Inference System(ANFIS)competitive techniques for fruit images classification.The accuracy rate of the proposed approach is quite better than the SVM,FFNN,and ANFIS schemes.It has been concluded that the proposed technique outperforms existing schemes.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52171288,51890914)the Key Research and Development Program of Shandong Province(Major Innovation Project)(Grant No.2022CXGC020405)+1 种基金the National Ministry of Industry and Information Technology Innovation Special Project-Engineering Demonstration Application of Subsea Oil and Gas Production SystemSubject 4:Research on Subsea Christmas Tree and Wellhead Offshore Testing Technology(Grant No.MC-201901-S01-04)CNPq,CAPES and FAPERJ of Brazil。
文摘Based on the Euler-Bernoulli beam theory and Kelvin-Voigt model,a nonlinear model for the transverse vibration of a pipe under the combined action of base motion and pulsating internal flow is established.The governing partial differential equation is transformed into a nonlinear system of fourth-order ordinary differential equations by using the generalized integral transform technique(GITT).The effects of the combined excitation of base motion and pulsating internal flow on the nonlinear dynamic behavior of the pipe are investigated using a bifurcation diagram,phase trajectory diagram,power spectrum diagram,time-domain diagram,and Poincare map.The results show that the base excitation amplitude and frequency significantly affect the dynamic behavior of the pipe system.Some new resonance phenomena can be observed,such as the period-1 motion under the base excitation or the pulsating internal flow alone becomes the multi-periodic motion,quasi-periodic motion or even chaotic motion due to the combined excitation action.
基金This project is supported by the National Science Foundation of China.
文摘In this paper, by Laplace transform version of the Trotter-Kato approximation theorem and the integrated C-semigroup introduced by Myadera, the authors obtained some Trotter-Kato approximation theorems on exponentially bounded C-semigroups, where the range of C (and so the domain of the generator) may not be dense. The authors deduced the corresponding results on exponentially bounded integrated semigroups with nondensely generators. The results of this paper extended and perfected the results given by Lizama, Park and Zheng.
