基于数据驱动随机子空间识别(SSI)算法,引入Hankel矩阵行块数i和列数j经验确定方法和模态传递范数(Modal Transfer Norm),采用奇异熵进行系统自动定阶方法,使识别过程自动化,实现工程模态参数的实时识别。应用Choleshy分解求解下三角矩...基于数据驱动随机子空间识别(SSI)算法,引入Hankel矩阵行块数i和列数j经验确定方法和模态传递范数(Modal Transfer Norm),采用奇异熵进行系统自动定阶方法,使识别过程自动化,实现工程模态参数的实时识别。应用Choleshy分解求解下三角矩阵R,缩减了计算量,特别是连续两个时刻的窗口数据大量重叠时,大大减小了计算时间,从而满足实时识别时间上的要求。三跨连续梁桥数值算例和一座实桥测试数据结果表明,每次识别均在移动步长时间内完成,速度快、精度高,可有效运用于大型结构模态参数的实时识别。展开更多
The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,...The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.展开更多
This paper concerns about the frequency domain stability criteria for fractional-order control systems. On the base of characteristics of the fractional-order equations solutions, we consider the Nyquist stability cri...This paper concerns about the frequency domain stability criteria for fractional-order control systems. On the base of characteristics of the fractional-order equations solutions, we consider the Nyquist stability criterion in a wider sense and obtain a more common means to analyze the stability of fractional-order systems conveniently. Finally, this paper illustrates the generalized stability criteria with an example to show the effect of the parameters variation on the fractional-order control systems.展开更多
Autonomous underwater vehicles(AUV) work in a complex marine environment. Its system reliability and autonomous fault diagnosis are particularly important and can provide the basis for underwater vehicles to take corr...Autonomous underwater vehicles(AUV) work in a complex marine environment. Its system reliability and autonomous fault diagnosis are particularly important and can provide the basis for underwater vehicles to take corresponding security policy in a failure. Aiming at the characteristics of the underwater vehicle which has uncertain system and modeling difficulty, an improved Elman neural network is introduced which is applied to the underwater vehicle motion modeling. Through designing self-feedback connection with fixed gain in the unit connection as well as increasing the feedback of the output layer node, improved Elman network has faster convergence speed and generalization ability. This method for high-order nonlinear system has stronger identification ability. Firstly, the residual is calculated by comparing the output of the underwater vehicle model(estimation in the motion state) with the actual measured values. Secondly, characteristics of the residual are analyzed on the basis of fault judging criteria. Finally, actuator fault diagnosis of the autonomous underwater vehicle is carried out. The results of the simulation experiment show that the method is effective.展开更多
The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By...The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By using coupled amplitude-phase formulation, a series of new exact cnoidal and solitary wave solutions with different parameters are obtained, which may have potential application in optical communication.展开更多
In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical co...In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper, without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.展开更多
Here we introduce generalized momentum and coordinate to transform seismic wave displacement equations into Hamiltonian system.We define the Lie operators associated with kinetic and potential energy,and construct a n...Here we introduce generalized momentum and coordinate to transform seismic wave displacement equations into Hamiltonian system.We define the Lie operators associated with kinetic and potential energy,and construct a new kind of second order symplectic scheme,which is extremely suitable for high efficient and long-term seismic wave simulations.Three sets of optimal coefficients are obtained based on the principle of minimum truncation error.We investigate the stability conditions for elastic wave simulation in homogeneous media.These newly developed symplectic schemes are compared with common symplectic schemes to verify the high precision and efficiency in theory and numerical experiments.One of the schemes presented here is compared with the classical Newmark algorithm and third order symplectic scheme to test the long-term computational ability.The scheme gets the same synthetic surface seismic records and single channel record as third order symplectic scheme in the seismic modeling in the heterogeneous model.展开更多
We investigate the low regularity local and global well-posedness of the Cauchy problem for the coupled Klein-Gordon-Schr¨odinger system with fractional Laplacian in the Schr¨odinger equation in R^（1＋1）. ...We investigate the low regularity local and global well-posedness of the Cauchy problem for the coupled Klein-Gordon-Schr¨odinger system with fractional Laplacian in the Schr¨odinger equation in R^（1＋1）. We use Bourgain space method to study this problem and prove that this system is locally well-posed for Schr¨odinger data in H^（s_1） and wave data in H^（s_2） × H^（s_2-1）for 3/4- α ＆lt; s_1≤0 and-1/2 ＆lt; s_2 ＆lt; 3/2, where α is the fractional power of Laplacian which satisfies 3/4 ＆lt; α≤1. Based on this local well-posedness result, we also obtain the global well-posedness of this system for s_1 = 0 and-1/2 ＆lt; s_2 ＆lt; 1/2 by using the conservation law for the L^2 norm of u.展开更多
Ionospheric delay is one of the major error sources in GNSS navigation and positioning.Nowadays,the dual-frequency technique is the most widely used in ionospheric refraction correction.However,dual-frequency measurem...Ionospheric delay is one of the major error sources in GNSS navigation and positioning.Nowadays,the dual-frequency technique is the most widely used in ionospheric refraction correction.However,dual-frequency measurements can only eliminate the first-order term of ionospheric delay,while the effect of the second-order term on GNSS observations may be several centimeters.In this paper,two models,the International Reference Ionosphere (IRI) 2007 and International Geomagnetic Reference Field (IGRF) 11 are used to estimate the second-order term through the integral calculation method.Besides,the simplified single layer ionosphere model in a dipole moment approximation for the earth magnetic field is used.Since the traditional integral calculation method requires large calculation load and takes much time,it is not convenient for practical use.Additionally,although the simplified single layer ionosphere model is simple to implement,it results in larger errors.In this study,second-order term ionospheric correction formula proposed by Hoque (2007) is improved for estimating the second-order term at a global scale.Thus,it is more practicable to estimate the second-order term.More importantly,its results have a higher precision of the sub-millimeter level for a global scale in normal conditions.Compared with Hoque's original regional correction model,which calculates coefficients through polynomial fitting of elevation and latitudes,this study proposes a piece-wise look-up table and interpolation technique to modify Hoque model.Through utilizing a table file,the modified Hoque model can be conveniently implemented in an engineering software package,like as PANDA in this study.Through applying the proposed scheme for the second-order ionospheric correction into GNSS precise positioning in both PPP daily and epoch solutions,the results have shown south-shift characteristics in daily solution at a global scale and periodic change with VTEC daily variation in epoch positioning solution.展开更多
This paper deals with a coupled system of fourth-order parabolic inequalities ｜u｜t ≥ -△2^u＋｜v｜^q, ｜v｜t ≥-△2v＋｜u｜p^ in S=R^n ×R^＋ withp, q 〉 1, n ≥1. AFujita- Liouville type theorem is establishe...This paper deals with a coupled system of fourth-order parabolic inequalities ｜u｜t ≥ -△2^u＋｜v｜^q, ｜v｜t ≥-△2v＋｜u｜p^ in S=R^n ×R^＋ withp, q 〉 1, n ≥1. AFujita- Liouville type theorem is established that the inequality system does not admit nontrivial nonnegative global solutions on S whenever n/4≤ max（ p＋1/pq-1, q＋1/pq-1 ）. Since the general maximum-comparison principle does not hold for the fourth-order problem, the authors use the test function method to get the global non-existence of nontrivial solutions.展开更多
文摘基于数据驱动随机子空间识别(SSI)算法,引入Hankel矩阵行块数i和列数j经验确定方法和模态传递范数(Modal Transfer Norm),采用奇异熵进行系统自动定阶方法,使识别过程自动化,实现工程模态参数的实时识别。应用Choleshy分解求解下三角矩阵R,缩减了计算量,特别是连续两个时刻的窗口数据大量重叠时,大大减小了计算时间,从而满足实时识别时间上的要求。三跨连续梁桥数值算例和一座实桥测试数据结果表明,每次识别均在移动步长时间内完成,速度快、精度高,可有效运用于大型结构模态参数的实时识别。
文摘The existence of high energy periodic solutions for the second-order Hamiltonian system -ü（t）＋A（t）u（t）=▽F（t,u（t）） with convex and concave nonlinearities is studied, where F（t, u） = F1（t,u）＋F2（t,u）. Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.
基金Supported by the Natural Science Foundation of Chongqing City (No. CSTC2004BB2165) and Research Foundation of Chongqing University of Posts and Telecommunications (No. A2005-47)
文摘This paper concerns about the frequency domain stability criteria for fractional-order control systems. On the base of characteristics of the fractional-order equations solutions, we consider the Nyquist stability criterion in a wider sense and obtain a more common means to analyze the stability of fractional-order systems conveniently. Finally, this paper illustrates the generalized stability criteria with an example to show the effect of the parameters variation on the fractional-order control systems.
基金Project(2012T50331)supported by China Postdoctoral Science FoundationProject(2008AA092301-2)supported by the High-Tech Research and Development Program of China
文摘Autonomous underwater vehicles(AUV) work in a complex marine environment. Its system reliability and autonomous fault diagnosis are particularly important and can provide the basis for underwater vehicles to take corresponding security policy in a failure. Aiming at the characteristics of the underwater vehicle which has uncertain system and modeling difficulty, an improved Elman neural network is introduced which is applied to the underwater vehicle motion modeling. Through designing self-feedback connection with fixed gain in the unit connection as well as increasing the feedback of the output layer node, improved Elman network has faster convergence speed and generalization ability. This method for high-order nonlinear system has stronger identification ability. Firstly, the residual is calculated by comparing the output of the underwater vehicle model(estimation in the motion state) with the actual measured values. Secondly, characteristics of the residual are analyzed on the basis of fault judging criteria. Finally, actuator fault diagnosis of the autonomous underwater vehicle is carried out. The results of the simulation experiment show that the method is effective.
文摘The coupled higher-order nonlinear Schroedinger system is a major subject in nonlinear optics as one of the nonlinear partial differential equation which describes the propagation of optical pulses in optic fibers. By using coupled amplitude-phase formulation, a series of new exact cnoidal and solitary wave solutions with different parameters are obtained, which may have potential application in optical communication.
基金The work is supported by the National Natural Science Foundation of China under Grants No.60304002 No.60674036the Science and Technical Development Plan of Shandong Province under Grant No.2004GG4204014.
文摘In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper, without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.41174047,40874024&41204041)
文摘Here we introduce generalized momentum and coordinate to transform seismic wave displacement equations into Hamiltonian system.We define the Lie operators associated with kinetic and potential energy,and construct a new kind of second order symplectic scheme,which is extremely suitable for high efficient and long-term seismic wave simulations.Three sets of optimal coefficients are obtained based on the principle of minimum truncation error.We investigate the stability conditions for elastic wave simulation in homogeneous media.These newly developed symplectic schemes are compared with common symplectic schemes to verify the high precision and efficiency in theory and numerical experiments.One of the schemes presented here is compared with the classical Newmark algorithm and third order symplectic scheme to test the long-term computational ability.The scheme gets the same synthetic surface seismic records and single channel record as third order symplectic scheme in the seismic modeling in the heterogeneous model.
基金supported by National Natural Science Foundation of China (Grant No. 11201498)
文摘We investigate the low regularity local and global well-posedness of the Cauchy problem for the coupled Klein-Gordon-Schr¨odinger system with fractional Laplacian in the Schr¨odinger equation in R^（1＋1）. We use Bourgain space method to study this problem and prove that this system is locally well-posed for Schr¨odinger data in H^（s_1） and wave data in H^（s_2） × H^（s_2-1）for 3/4- α ＆lt; s_1≤0 and-1/2 ＆lt; s_2 ＆lt; 3/2, where α is the fractional power of Laplacian which satisfies 3/4 ＆lt; α≤1. Based on this local well-posedness result, we also obtain the global well-posedness of this system for s_1 = 0 and-1/2 ＆lt; s_2 ＆lt; 1/2 by using the conservation law for the L^2 norm of u.
基金supported by the National Basic Research Project of China (Grant No.2009CB72400205)the National Natural Science Foundation of China (Grant No.40804005)the National High Technology Research and Development Program of China (Grant No.2009AA121401)
文摘Ionospheric delay is one of the major error sources in GNSS navigation and positioning.Nowadays,the dual-frequency technique is the most widely used in ionospheric refraction correction.However,dual-frequency measurements can only eliminate the first-order term of ionospheric delay,while the effect of the second-order term on GNSS observations may be several centimeters.In this paper,two models,the International Reference Ionosphere (IRI) 2007 and International Geomagnetic Reference Field (IGRF) 11 are used to estimate the second-order term through the integral calculation method.Besides,the simplified single layer ionosphere model in a dipole moment approximation for the earth magnetic field is used.Since the traditional integral calculation method requires large calculation load and takes much time,it is not convenient for practical use.Additionally,although the simplified single layer ionosphere model is simple to implement,it results in larger errors.In this study,second-order term ionospheric correction formula proposed by Hoque (2007) is improved for estimating the second-order term at a global scale.Thus,it is more practicable to estimate the second-order term.More importantly,its results have a higher precision of the sub-millimeter level for a global scale in normal conditions.Compared with Hoque's original regional correction model,which calculates coefficients through polynomial fitting of elevation and latitudes,this study proposes a piece-wise look-up table and interpolation technique to modify Hoque model.Through utilizing a table file,the modified Hoque model can be conveniently implemented in an engineering software package,like as PANDA in this study.Through applying the proposed scheme for the second-order ionospheric correction into GNSS precise positioning in both PPP daily and epoch solutions,the results have shown south-shift characteristics in daily solution at a global scale and periodic change with VTEC daily variation in epoch positioning solution.
基金supported by the National Natural Science Foundation of China (Nos. 10771024,11171048)the Fundamental Research Funds for the Central Universities (No. 851011)
文摘This paper deals with a coupled system of fourth-order parabolic inequalities ｜u｜t ≥ -△2^u＋｜v｜^q, ｜v｜t ≥-△2v＋｜u｜p^ in S=R^n ×R^＋ withp, q 〉 1, n ≥1. AFujita- Liouville type theorem is established that the inequality system does not admit nontrivial nonnegative global solutions on S whenever n/4≤ max（ p＋1/pq-1, q＋1/pq-1 ）. Since the general maximum-comparison principle does not hold for the fourth-order problem, the authors use the test function method to get the global non-existence of nontrivial solutions.
