In this paper,we survey some recent progress in the study of time fractional equations and its interplay with anomalous sub-diffusions,with some improvements and extensions.
The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of co...The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.展开更多
Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional p...Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional power spectra（FrFT moment） of the linear chirp signal.This method can adaptively determine the optimum FrFT order by maximizing the second-order central FrFT moment.This makes the desired chirp signal substantially concentrated whereas the noise is rejected considerably.This improves the mean square error minimization beamformer by reducing effectively the signal-noise cross terms due to the finite data length de-correlation operation.Simulation results show that the new method works well under a wide range of signal to noise ratio and signal to interference ratio.展开更多
Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problem...Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization(PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste(MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.展开更多
A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult ...A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult problem in the s-domain that needs to be solved, i.e. how to calculate fractional derivatives and integrals efficiently and quickly. Our scheme adopts the time domain that is well suited for Z-transform analysis and digital implementation. The main idea of the scheme is based on the definition of Grünwald-Letnicov fractional calculus. In this case some limited terms of the definition are taken so that it is much easier and faster to calculate fractional derivatives and integrals in the time domain or z-domain without loss much of the precision. Its effectiveness is illustrated by discretization of half-order fractional differential and integral operators compared with that of the analytical scheme. An example of designing fractional order digital controllers is included for illustration, in which different fractional order PID controllers are designed for the control of a nonlinear dynamic system containing one of the four different kinds of nonlinear blocks: saturation, deadzone, hysteresis, and relay.展开更多
The controllability for a class of fractional-order linear control systems is mainly investigated. The generalizations of the usual complete solution formulae of the fractional-order linear control systems are derived...The controllability for a class of fractional-order linear control systems is mainly investigated. The generalizations of the usual complete solution formulae of the fractional-order linear control systems are derived not only for time-invariant case but also for time-varying case. Several sufficient and necessary conditions for state controllability of such systems are established and the corresponding criteria for fractional-order time-invariant continuous-time systems are also obtained. The results obtained will be help for future study of fractional-order control systems.展开更多
To improve the data rate of underwater acoustic frequency-hopped communications, frequency hopping is applied to different orders of fractional Fourier domain (FrFD), to enable non-intrusive, bandwidth-limited acousti...To improve the data rate of underwater acoustic frequency-hopped communications, frequency hopping is applied to different orders of fractional Fourier domain (FrFD), to enable non-intrusive, bandwidth-limited acoustic communications. An FrFD frequency-hopped communication method based on chirp modulation, namely multiple chirp shift keying-FrFD hopping (MCSK-FrFDH), is proposed for underwater acoustic channels. Validated by both simulations and experimental results, this method can reach a bandwidth efficiency twice more than conventional frequency-hopped methods with the same data rate and anti-multipath capability, suggesting that the proposed method achieves a better performance than the traditional frequency hopped communication in underwater acoustic communication channels. Results also show that in practical scenarios, the MCSK-FrFDH system with longer symbol length performs better at the low signal-to-noise ratio (SNR), while the system with larger frequency sweeping range performs better at a high SNR.展开更多
Aiming at dealing with the difficulty for traditional emergency rescue vehicle(ECV)to enter into limited rescue scenes,the electro-hydraulic steer-by-wire(SBW)system is introduced to achieve the multi-mode steering of...Aiming at dealing with the difficulty for traditional emergency rescue vehicle(ECV)to enter into limited rescue scenes,the electro-hydraulic steer-by-wire(SBW)system is introduced to achieve the multi-mode steering of the ECV.The overall structure and mathematical model of the SBW system are described at length.The fractional order proportional-integral-derivative(FOPID)controller based on fractional calculus theory is designed to control the steering cylinder’s movement in SBW system.The anti-windup problem is considered in the FOPID controller design to reduce the bad influence of saturation.Five parameters of the FOPID controller are optimized using the genetic algorithm by maximizing the fitness function which involves integral of time by absolute value error(ITAE),peak overshoot,as well as settling time.The time-domain simulations are implemented to identify the performance of the raised FOPID controller.The simulation results indicate the presented FOPID controller possesses more effective control properties than classical proportional-integral-derivative(PID)controller on the part of transient response,tracking capability and robustness.展开更多
To further investigate the one-dimensional(1D)rheological consolidation mechanism of double-layered soil,the fractional derivative Merchant model(FDMM)and the non-Darcian flow model with the non-Newtonian index are re...To further investigate the one-dimensional(1D)rheological consolidation mechanism of double-layered soil,the fractional derivative Merchant model(FDMM)and the non-Darcian flow model with the non-Newtonian index are respectively introduced to describe the deformation of viscoelastic soil and the flow of pore water in the process of consolidation.Accordingly,an 1D rheological consolidation equation of double-layered soil is obtained,and its numerical analysis is performed by the implicit finite difference method.In order to verify its validity,the numerical solutions by the present method for some simplified cases are compared with the results in the related literature.Then,the influence of the revelent parameters on the rheological consolidation of double-layered soil are investigated.Numerical results indicate that the parameters of non-Darcian flow and FDMM of the first soil layer greatly influence the consolidation rate of double-layered soil.As the decrease of relative compressibility or the increase of relative permeability between the lower soil and the upper soil,the dissipation rate of excess pore water pressure and the settlement rate of the ground will be accelerated.Increasing the relative thickness of soil layer with high permeability or low compressibility will also accelerate the consolidation rate of double-layered soil.展开更多
The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governi...The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials(FGM)(i.e., material with spatially varying material properties) are established. The analytical solution in the transform domain is obtained by using the eigenvalue approach.The inversion of Laplace transform is done numerically. The graphical results indicate that the fractional parameter has significant effects on all the physical quantities. Thus, we can consider the theory of fractional order generalized thermoelasticity an improvement on studying elastic materials.展开更多
An approach is proposed to realize a digital channelized receiver in the fractional Fourier domain （FRFD） for signal intercept applications. The presented architecture can be considered as a generalization of that i...An approach is proposed to realize a digital channelized receiver in the fractional Fourier domain （FRFD） for signal intercept applications. The presented architecture can be considered as a generalization of that in the traditional Fourier domain. Since the linear frequency modulation （LFM） signal has a good energy concentration in the FRFD, by choosing an appropriate fractional Fourier transform （FRFT） order, the presented architecture can concentrate the broadband LFM signal into only one sub-channel and that will prevent it from crossing several sub-channels. Thus the performance of the signal detection and parameter estimation after the sub-channel output will be improved significantly. The computational complexity is reduced enormously due to the implementation of the polyphase filter bank decomposition, thus the proposed architecture can be realized as efficiently as in the Fourier domain. The related simulation results are presented to verify the validity of the theories and methods involved in this paper.展开更多
Adaptive digital self-interference cancellation(ADSIC)is a significant method to suppress self-interference and improve the performance of the linear frequency modulated continuous wave(LFMCW)radar.Due to efficient im...Adaptive digital self-interference cancellation(ADSIC)is a significant method to suppress self-interference and improve the performance of the linear frequency modulated continuous wave(LFMCW)radar.Due to efficient implementation structure,the conventional method based on least mean square(LMS)is widely used,but its performance is not sufficient for LFMCW radar.To achieve a better self-interference cancellation(SIC)result and more optimal radar performance,we present an ADSIC method based on fractional order LMS(FOLMS),which utilizes the multi-path cancellation structure and adaptively updates the weight coefficients of the cancellation system.First,we derive the iterative expression of the weight coefficients by using the fractional order derivative and short-term memory principle.Then,to solve the problem that it is difficult to select the parameters of the proposed method due to the non-stationary characteristics of radar transmitted signals,we construct the performance evaluation model of LFMCW radar,and analyze the relationship between the mean square deviation and the parameters of FOLMS.Finally,the theoretical analysis and simulation results show that the proposed method has a better SIC performance than the conventional methods.展开更多
To fully display the modeling mechanism of the novelfractional order grey model （FGM （q,1））, this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and...To fully display the modeling mechanism of the novelfractional order grey model （FGM （q,1））, this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and the raw data matrix, whichare consistent with the fractional order accumulative grey model（FAGM （1,1））. Following this, this paper decomposes the accumulativedata difference matrix into the accumulative generationmatrix, the q-order reductive accumulative matrix and the rawdata matrix, and then combines the least square method, findingthat the differential order affects the model parameters only byaffecting the formation of differential sequences. This paper thensummarizes matrix decomposition of some special sequences,such as the sequence generated by the strengthening and weakeningoperators, the jumping sequence, and the non-equidistancesequence. Finally, this paper expresses the influences of the rawdata transformation, the accumulation sequence transformation,and the differential matrix transformation on the model parametersas matrices, and takes the non-equidistance sequence as an exampleto show the modeling mechanism.展开更多
Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributio...Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributions,and it is difficult to identify such signals using traditional time-frequency analysis methods.To solve this problem,this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis.First of all,fractional Fourier transform and the Wigner-Ville distribution(WVD)are used to determine the number of main ridgelines and the tilt angle of the target component in WVD.Next,the standard deviation of the target component's width in the signal's WVD is calculated.Finally,an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features.Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17%under 0 dB.When the training data set and the test data set are mixed with noise,the recognition rate reaches 89.93%.The best recognition accuracy is achieved when the size of the training set is taken as 400.The algorithm complexity can meet the requirements of real-time recognition.展开更多
To remove the scalar ambiguity in conventional blind channel estimation algorithms, totally blind channel estimation （TBCE） is proposed by using multiple constellations. To estimate the unknown scalar, its phase is ...To remove the scalar ambiguity in conventional blind channel estimation algorithms, totally blind channel estimation （TBCE） is proposed by using multiple constellations. To estimate the unknown scalar, its phase is decomposed into a fractional phase and an integer phase. However, the maximum-likelihood （ML） algorithm for the fractional phase does not have closed-form solutions and suffers from high computational complexity. By ex- ploring the structures of widely used constellations, this paper proposes a low-complexity fractional phase estimation algorithm which requires no exhaustive search. Analytical expressions of the asymptotic mean squared error （MSE） are also derived. The theo- retical analysis and simulation results indicate that the proposed fractional phase estimation algorithm exhibits almost the same performance as the ML algorithm but with significantly reduced computational burden.展开更多
Motion estimation is an important and intensive task in video coding applications. Since the complexity of integer pixel search has been greatly reduced by the numerous fast ME algorithm, the computation overhead requ...Motion estimation is an important and intensive task in video coding applications. Since the complexity of integer pixel search has been greatly reduced by the numerous fast ME algorithm, the computation overhead required by fractional pixel ME has become relatively significant. To reduce the complexity of the fractional pixel ME algorithm, a directionality-based fractional pixel ME algorithm is proposed. The proposed algorithm efficiently explores the neighborhood positions which with high probability to be the best matching around the minimum one and skips over other unlikely ones. Thus, the proposed algorithm can complete the search by examining only 3 points on appropriate condition instead of 17 search points in the search algorithm of reference software. The simulation results show that the proposed algorithm successfully optimizes the fractional-pixel motion search on both half and quarter-pixel accuracy and improves the processing speed with low PSNR penalty.展开更多
In this paper,we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform.With this system,we aim to achieve the subNyquist sampling an...In this paper,we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform.With this system,we aim to achieve the subNyquist sampling and accurate reconstruction for chirp-like signals containing time-varying characteristics.Under the proposed scheme,we introduce the fractional Gabor transform to make a stable expansion for signals in the joint time-fractional-frequency domain.Then the compressive sampling and reconstruction system is constructed under the compressive sensing and shift-invariant space theory.We establish the reconstruction model and propose a block multiple response extension of sparse Bayesian learning algorithm to improve the reconstruction effect.The reconstruction error for the proposed system is analyzed.We show that,with considerations of noises and mismatches,the total error is bounded.The effectiveness of the proposed system is verified by numerical experiments.It is shown that our proposed system outperforms the other systems state-of-the-art.展开更多
The modified three-step sequential extraction procedure proposed by the BCR was used to predict Pb and Cd fractional distribution in sewage sludge and tomato soil amended with sludge compost. There was no significant ...The modified three-step sequential extraction procedure proposed by the BCR was used to predict Pb and Cd fractional distribution in sewage sludge and tomato soil amended with sludge compost. There was no significant increasing of Pb and Cd contents in the soil with sludge application as compared with that in the reference soil. The Pb contents were much lower for the soil samples than for the National Soil Standards of Environmental Quality, but Cd contents in soil were much more than background mean Cd contents. Pb content in soil fractions was followed with residual Pb 〉 reducible Pb 〉 exchangeable and weak acid soluble Pb〉 oxidizable Pb. In all soil samples, the partitioning of Cd had the same extractability in the first two steps of the procedure and the residual fraction. Only a small fraction or almost zero extractability was observed at the oxidation step for Pb and Cd.展开更多
文摘In this paper,we survey some recent progress in the study of time fractional equations and its interplay with anomalous sub-diffusions,with some improvements and extensions.
基金Supported by the National Natural Science Foundation of China(12101004)the Natural Science Research Project of Anhui Educational Committee(2023AH030021)the Research Startup Foundation for Introducing Talent of Anhui Polytechnic University(2020YQQ064)。
文摘The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.
基金supported by the National Natural Science Foundation of China (606720846060203760736006)
文摘Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional power spectra（FrFT moment） of the linear chirp signal.This method can adaptively determine the optimum FrFT order by maximizing the second-order central FrFT moment.This makes the desired chirp signal substantially concentrated whereas the noise is rejected considerably.This improves the mean square error minimization beamformer by reducing effectively the signal-noise cross terms due to the finite data length de-correlation operation.Simulation results show that the new method works well under a wide range of signal to noise ratio and signal to interference ratio.
基金supported by the National Natural Science Foundation of China (51479151,61403288)。
文摘Most of the existing multivariable grey models are based on the 1-order derivative and 1-order accumulation, which makes the parameters unable to be adjusted according to the data characteristics of the actual problems. The results about fractional derivative multivariable grey models are very few at present. In this paper, a multivariable Caputo fractional derivative grey model with convolution integral CFGMC(q, N) is proposed. First, the Caputo fractional difference is used to discretize the model, and the least square method is used to solve the parameters. The orders of accumulations and differential equations are determined by using particle swarm optimization(PSO). Then, the analytical solution of the model is obtained by using the Laplace transform, and the convergence and divergence of series in analytical solutions are also discussed. Finally, the CFGMC(q, N) model is used to predict the municipal solid waste(MSW). Compared with other competition models, the model has the best prediction effect. This study enriches the model form of the multivariable grey model, expands the scope of application, and provides a new idea for the development of fractional derivative grey model.
文摘A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult problem in the s-domain that needs to be solved, i.e. how to calculate fractional derivatives and integrals efficiently and quickly. Our scheme adopts the time domain that is well suited for Z-transform analysis and digital implementation. The main idea of the scheme is based on the definition of Grünwald-Letnicov fractional calculus. In this case some limited terms of the definition are taken so that it is much easier and faster to calculate fractional derivatives and integrals in the time domain or z-domain without loss much of the precision. Its effectiveness is illustrated by discretization of half-order fractional differential and integral operators compared with that of the analytical scheme. An example of designing fractional order digital controllers is included for illustration, in which different fractional order PID controllers are designed for the control of a nonlinear dynamic system containing one of the four different kinds of nonlinear blocks: saturation, deadzone, hysteresis, and relay.
文摘The controllability for a class of fractional-order linear control systems is mainly investigated. The generalizations of the usual complete solution formulae of the fractional-order linear control systems are derived not only for time-invariant case but also for time-varying case. Several sufficient and necessary conditions for state controllability of such systems are established and the corresponding criteria for fractional-order time-invariant continuous-time systems are also obtained. The results obtained will be help for future study of fractional-order control systems.
基金supported by the National Natural Science Foundation of China(4137604041676024)
文摘To improve the data rate of underwater acoustic frequency-hopped communications, frequency hopping is applied to different orders of fractional Fourier domain (FrFD), to enable non-intrusive, bandwidth-limited acoustic communications. An FrFD frequency-hopped communication method based on chirp modulation, namely multiple chirp shift keying-FrFD hopping (MCSK-FrFDH), is proposed for underwater acoustic channels. Validated by both simulations and experimental results, this method can reach a bandwidth efficiency twice more than conventional frequency-hopped methods with the same data rate and anti-multipath capability, suggesting that the proposed method achieves a better performance than the traditional frequency hopped communication in underwater acoustic communication channels. Results also show that in practical scenarios, the MCSK-FrFDH system with longer symbol length performs better at the low signal-to-noise ratio (SNR), while the system with larger frequency sweeping range performs better at a high SNR.
基金Project(2016YFC0802904)supported by the National Key Research and Development Program of China
文摘Aiming at dealing with the difficulty for traditional emergency rescue vehicle(ECV)to enter into limited rescue scenes,the electro-hydraulic steer-by-wire(SBW)system is introduced to achieve the multi-mode steering of the ECV.The overall structure and mathematical model of the SBW system are described at length.The fractional order proportional-integral-derivative(FOPID)controller based on fractional calculus theory is designed to control the steering cylinder’s movement in SBW system.The anti-windup problem is considered in the FOPID controller design to reduce the bad influence of saturation.Five parameters of the FOPID controller are optimized using the genetic algorithm by maximizing the fitness function which involves integral of time by absolute value error(ITAE),peak overshoot,as well as settling time.The time-domain simulations are implemented to identify the performance of the raised FOPID controller.The simulation results indicate the presented FOPID controller possesses more effective control properties than classical proportional-integral-derivative(PID)controller on the part of transient response,tracking capability and robustness.
基金Project(51578511)supported by the National Natural Science Foundation of China。
文摘To further investigate the one-dimensional(1D)rheological consolidation mechanism of double-layered soil,the fractional derivative Merchant model(FDMM)and the non-Darcian flow model with the non-Newtonian index are respectively introduced to describe the deformation of viscoelastic soil and the flow of pore water in the process of consolidation.Accordingly,an 1D rheological consolidation equation of double-layered soil is obtained,and its numerical analysis is performed by the implicit finite difference method.In order to verify its validity,the numerical solutions by the present method for some simplified cases are compared with the results in the related literature.Then,the influence of the revelent parameters on the rheological consolidation of double-layered soil are investigated.Numerical results indicate that the parameters of non-Darcian flow and FDMM of the first soil layer greatly influence the consolidation rate of double-layered soil.As the decrease of relative compressibility or the increase of relative permeability between the lower soil and the upper soil,the dissipation rate of excess pore water pressure and the settlement rate of the ground will be accelerated.Increasing the relative thickness of soil layer with high permeability or low compressibility will also accelerate the consolidation rate of double-layered soil.
文摘The present work is concerned with the solution of a problem on thermoelastic interactions in a functional graded material due to thermal shock in the context of the fractional order three-phase lag model. The governing equations of fractional order generalized thermoelasticity with three-phase lag model for functionally graded materials(FGM)(i.e., material with spatially varying material properties) are established. The analytical solution in the transform domain is obtained by using the eigenvalue approach.The inversion of Laplace transform is done numerically. The graphical results indicate that the fractional parameter has significant effects on all the physical quantities. Thus, we can consider the theory of fractional order generalized thermoelasticity an improvement on studying elastic materials.
基金supported by the Program for New Century Excellent Talents in University(NCET-06-0921)
文摘An approach is proposed to realize a digital channelized receiver in the fractional Fourier domain （FRFD） for signal intercept applications. The presented architecture can be considered as a generalization of that in the traditional Fourier domain. Since the linear frequency modulation （LFM） signal has a good energy concentration in the FRFD, by choosing an appropriate fractional Fourier transform （FRFT） order, the presented architecture can concentrate the broadband LFM signal into only one sub-channel and that will prevent it from crossing several sub-channels. Thus the performance of the signal detection and parameter estimation after the sub-channel output will be improved significantly. The computational complexity is reduced enormously due to the implementation of the polyphase filter bank decomposition, thus the proposed architecture can be realized as efficiently as in the Fourier domain. The related simulation results are presented to verify the validity of the theories and methods involved in this paper.
文摘Adaptive digital self-interference cancellation(ADSIC)is a significant method to suppress self-interference and improve the performance of the linear frequency modulated continuous wave(LFMCW)radar.Due to efficient implementation structure,the conventional method based on least mean square(LMS)is widely used,but its performance is not sufficient for LFMCW radar.To achieve a better self-interference cancellation(SIC)result and more optimal radar performance,we present an ADSIC method based on fractional order LMS(FOLMS),which utilizes the multi-path cancellation structure and adaptively updates the weight coefficients of the cancellation system.First,we derive the iterative expression of the weight coefficients by using the fractional order derivative and short-term memory principle.Then,to solve the problem that it is difficult to select the parameters of the proposed method due to the non-stationary characteristics of radar transmitted signals,we construct the performance evaluation model of LFMCW radar,and analyze the relationship between the mean square deviation and the parameters of FOLMS.Finally,the theoretical analysis and simulation results show that the proposed method has a better SIC performance than the conventional methods.
基金supported by the National Natural Science Foundation of China(5147915151279149+2 种基金71540027)the China Postdoctoral Science Foundation Special Foundation Project(2013T607552012M521487)
文摘To fully display the modeling mechanism of the novelfractional order grey model （FGM （q,1））, this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and the raw data matrix, whichare consistent with the fractional order accumulative grey model（FAGM （1,1））. Following this, this paper decomposes the accumulativedata difference matrix into the accumulative generationmatrix, the q-order reductive accumulative matrix and the rawdata matrix, and then combines the least square method, findingthat the differential order affects the model parameters only byaffecting the formation of differential sequences. This paper thensummarizes matrix decomposition of some special sequences,such as the sequence generated by the strengthening and weakeningoperators, the jumping sequence, and the non-equidistancesequence. Finally, this paper expresses the influences of the rawdata transformation, the accumulation sequence transformation,and the differential matrix transformation on the model parametersas matrices, and takes the non-equidistance sequence as an exampleto show the modeling mechanism.
基金This work was supported by the National Natural Science Foundation of China(91538201)the Taishan Scholar Project of Shandong Province(ts201511020)the project supported by Chinese National Key Laboratory of Science and Technology on Information System Security(6142111190404).
文摘Recent advances in electronics have increased the complexity of radar signal modulation.The quasi-linear frequency modulation(quasi-LFM)radar waveforms(LFM,Frank code,P1−P4 code)have similar time-frequency distributions,and it is difficult to identify such signals using traditional time-frequency analysis methods.To solve this problem,this paper proposes an algorithm for automatic recognition of quasi-LFM radar waveforms based on fractional Fourier transform and time-frequency analysis.First of all,fractional Fourier transform and the Wigner-Ville distribution(WVD)are used to determine the number of main ridgelines and the tilt angle of the target component in WVD.Next,the standard deviation of the target component's width in the signal's WVD is calculated.Finally,an assembled classifier using neural network is built to recognize different waveforms by automatically combining the three features.Simulation results show that the overall recognition rate of the proposed algorithm reaches 94.17%under 0 dB.When the training data set and the test data set are mixed with noise,the recognition rate reaches 89.93%.The best recognition accuracy is achieved when the size of the training set is taken as 400.The algorithm complexity can meet the requirements of real-time recognition.
基金supported by the National Science and Technology Major Project of China(2013ZX03003006-003)
文摘To remove the scalar ambiguity in conventional blind channel estimation algorithms, totally blind channel estimation （TBCE） is proposed by using multiple constellations. To estimate the unknown scalar, its phase is decomposed into a fractional phase and an integer phase. However, the maximum-likelihood （ML） algorithm for the fractional phase does not have closed-form solutions and suffers from high computational complexity. By ex- ploring the structures of widely used constellations, this paper proposes a low-complexity fractional phase estimation algorithm which requires no exhaustive search. Analytical expressions of the asymptotic mean squared error （MSE） are also derived. The theo- retical analysis and simulation results indicate that the proposed fractional phase estimation algorithm exhibits almost the same performance as the ML algorithm but with significantly reduced computational burden.
文摘Motion estimation is an important and intensive task in video coding applications. Since the complexity of integer pixel search has been greatly reduced by the numerous fast ME algorithm, the computation overhead required by fractional pixel ME has become relatively significant. To reduce the complexity of the fractional pixel ME algorithm, a directionality-based fractional pixel ME algorithm is proposed. The proposed algorithm efficiently explores the neighborhood positions which with high probability to be the best matching around the minimum one and skips over other unlikely ones. Thus, the proposed algorithm can complete the search by examining only 3 points on appropriate condition instead of 17 search points in the search algorithm of reference software. The simulation results show that the proposed algorithm successfully optimizes the fractional-pixel motion search on both half and quarter-pixel accuracy and improves the processing speed with low PSNR penalty.
基金supported by National Natural Science Foundation of China(Grant No.61501493)。
文摘In this paper,we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform.With this system,we aim to achieve the subNyquist sampling and accurate reconstruction for chirp-like signals containing time-varying characteristics.Under the proposed scheme,we introduce the fractional Gabor transform to make a stable expansion for signals in the joint time-fractional-frequency domain.Then the compressive sampling and reconstruction system is constructed under the compressive sensing and shift-invariant space theory.We establish the reconstruction model and propose a block multiple response extension of sparse Bayesian learning algorithm to improve the reconstruction effect.The reconstruction error for the proposed system is analyzed.We show that,with considerations of noises and mismatches,the total error is bounded.The effectiveness of the proposed system is verified by numerical experiments.It is shown that our proposed system outperforms the other systems state-of-the-art.
文摘The modified three-step sequential extraction procedure proposed by the BCR was used to predict Pb and Cd fractional distribution in sewage sludge and tomato soil amended with sludge compost. There was no significant increasing of Pb and Cd contents in the soil with sludge application as compared with that in the reference soil. The Pb contents were much lower for the soil samples than for the National Soil Standards of Environmental Quality, but Cd contents in soil were much more than background mean Cd contents. Pb content in soil fractions was followed with residual Pb 〉 reducible Pb 〉 exchangeable and weak acid soluble Pb〉 oxidizable Pb. In all soil samples, the partitioning of Cd had the same extractability in the first two steps of the procedure and the residual fraction. Only a small fraction or almost zero extractability was observed at the oxidation step for Pb and Cd.
