机场场面多点定位利用S模式信号到达时间差实现目标定位。针对S模式信号易受接收系统内部非线性影响和机场场面复杂电磁干扰的问题,研究S模式信号失真恢复方法。根据S模式信号频谱特征和接收基站弱非线性记忆系统特征简化Volterra级数,...机场场面多点定位利用S模式信号到达时间差实现目标定位。针对S模式信号易受接收系统内部非线性影响和机场场面复杂电磁干扰的问题,研究S模式信号失真恢复方法。根据S模式信号频谱特征和接收基站弱非线性记忆系统特征简化Volterra级数,降低计算量的同时满足Volterra级数关键核函数对S模式信号非线性失真表示能力,得到S模式信号失真恢复模型。仿真结果表明:3阶简化Volterra级数模型恢复15 dB和0 dB S模式信号前导脉冲的失真前波形,误差仅有2.23%和12.59%,且模型在典型运用环境下满足一定的适用性、抗干扰性和稳定性,为S模式信号到达时间戳的准确提取提供基础。展开更多
Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves ...Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order. Keywords Model predictive control - Volterra series - process control - nonlinear control Yun Li is a senior lecturer at University of Glasgow, UK, where has taught and researched in evolutionary computation and control engineering since 1991. He worked in the UK National Engineering Laboratory and Industrial Systems and Control Ltd, Glasgow in 1989 and 1990. In 1998, he established the IEEE CACSD Evolutionary Computation Working Group and the European Network of Excellence in Evolutionary Computing (EvoNet) Workgroup on Systems, Control, and Drives. In summer 2002, he served as a visiting professor to Kumamoto University, Japan. He is also a visiting professor at University of Electronic Science and Technology of China. His research interests are in parallel processing, design automation and discovery of engineering systems using evolutionary learning and intelligent search techniques. Applications include control, system modelling and prediction, circuit design, microwave engineering, and operations management. He has advised 12 Ph.D.s in evolutionary computation and has 140 publications.Hiroshi Kashiwagi received B.E, M.E. and Ph.D. degrees in measurement and control engineering from the University of Tokyo, Japan, in 1962, 1964 and 1967 respectively. In 1967 he became an Associate Professor and in 1976 a Professor at Kumamoto University. From 1973 to 1974, he served as a visiting Associate Professor at Purdue University, Indiana, USA. From 1990 to 1994, he was the Director at Computer Center of Kumamoto University. He has also served as a member of Board of Trustees of Society of Instrument and Control Engineers (SICE), Japan, Chairman of Kyushu Branch of SICE and General Chair of many international conferences held in Japan, Korea, Chin and India. In 1994, he was awarded SICE Fellow for his contributions to the field of measurement and control engineering through his various academic activities. He also received the Gold Medal Prize at ICAUTO’95 held in India. In 1997, he received the “Best Book Award” from SICE for his new book entitled “M-sequence and its application” written in Japanese and published in 1996 by Shoukoudou Publishing Co. in Japan. In 1999, he received the “Best Paper Award” from SICE for his paper “M-transform and its application to system identification”. His research interests include signal processing and applications, especially pseudorandom sequence and its applications to measurement and control engineering.展开更多
A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear...A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear systems is studied in this paper.The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function(GFRF).For a class of nonlinear systems,the growing exponential method is used to determine the first 3 rd-order GFRFs.The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input.The relationship between the peak of PSD and the parameters of the nonlinear system is discussed.By using the proposed method,the nonlinear characteristics of multi-band output via single-band input can be well predicted.The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD.This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.展开更多
It is important to solve the nth-order Volterra kernel or nonlinear transfer function indescribing a nonlinear network by the Volterra series.Based on an auxiliary algebraic expression ofthe Volterra series,an algebra...It is important to solve the nth-order Volterra kernel or nonlinear transfer function indescribing a nonlinear network by the Volterra series.Based on an auxiliary algebraic expression ofthe Volterra series,an algebraic algorithm is proposed to evaluate the nth-order Volterra kernel andnonlinear transfer function in regular,triangular and symmetric forms.In addition,the complexity ofthe algebraic algorithm is improved.展开更多
In this work, we present a computational method for solving nonlinear Fredholm-Volterra integral equations of the second kind which is based on replacement of the unknown function by truncated series of well known Blo...In this work, we present a computational method for solving nonlinear Fredholm-Volterra integral equations of the second kind which is based on replacement of the unknown function by truncated series of well known Block-Pulse functions (BPfs) expansion. Error analysis is worked out that shows efficiency of the method. Finally, we also give some numerical examples.展开更多
The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was c...The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.展开更多
In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a sy...In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a system of nonlinear Volterra integral equations. Runge-Kutta method (RKM) and Bolck by block method (BBM) are used to solve the system of nonlinear Volterra integral equations of the second kind (SNVIEs) with continuous kernel. The error in each case is calculated.展开更多
This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear syst...This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear system, if its derived linear system is a damped dissipative system, the steady response obtained through the regular perturbation method is exactly identical to the response given by the Volterra series. On the other hand, if the derived linear system is an undamped conservative system, then the Volterra series is incapable of modeling the forced polynomial nonlinear system. Numerical examples are further presented to illustrate these points. The results provide a new criterion for quickly judging whether the Volterra series is applicable for modeling a given polynomial nonlinear system.展开更多
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^+ in Banach spaces.By the use of a new comparison res...In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.展开更多
A fully discrete version of a piecewise polynomial collocation method based on new collocation points, is constructed to solve nonlinear Volterra-Fredholm integral equations. In this paper, we obtain existence and uni...A fully discrete version of a piecewise polynomial collocation method based on new collocation points, is constructed to solve nonlinear Volterra-Fredholm integral equations. In this paper, we obtain existence and uniqueness results and analyze the convergence properties of the collocation method when used to approximate smooth solutions of Volterra- Fredholm integral equations.展开更多
We consider a class of doubly nonlinear history-dependent problems having a convection term and a pseudomonotone nonlinear diffusion operator associated an equation of the type ?<sub>t</sub>(k * (b(v) - b(...We consider a class of doubly nonlinear history-dependent problems having a convection term and a pseudomonotone nonlinear diffusion operator associated an equation of the type ?<sub>t</sub>(k * (b(v) - b(v<sub>0</sub>))) - div(a(x,Dv) + F(v)) = f where the right hand side belongs to L<sup>1</sup>. The kernel k belongs to the large class of PC kernels. In particular, the case of fractional time derivatives of order α ∈ (0,1) is included. Assuming b nondecreasing with L<sup>1</sup>-data, we prove existence in the framework of entropy solutions. The approach adopted for the proof is based on a several step approximation method and by using a result in the case of a strictly increasing b.展开更多
文摘机场场面多点定位利用S模式信号到达时间差实现目标定位。针对S模式信号易受接收系统内部非线性影响和机场场面复杂电磁干扰的问题,研究S模式信号失真恢复方法。根据S模式信号频谱特征和接收基站弱非线性记忆系统特征简化Volterra级数,降低计算量的同时满足Volterra级数关键核函数对S模式信号非线性失真表示能力,得到S模式信号失真恢复模型。仿真结果表明:3阶简化Volterra级数模型恢复15 dB和0 dB S模式信号前导脉冲的失真前波形,误差仅有2.23%和12.59%,且模型在典型运用环境下满足一定的适用性、抗干扰性和稳定性,为S模式信号到达时间戳的准确提取提供基础。
文摘Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order. Keywords Model predictive control - Volterra series - process control - nonlinear control Yun Li is a senior lecturer at University of Glasgow, UK, where has taught and researched in evolutionary computation and control engineering since 1991. He worked in the UK National Engineering Laboratory and Industrial Systems and Control Ltd, Glasgow in 1989 and 1990. In 1998, he established the IEEE CACSD Evolutionary Computation Working Group and the European Network of Excellence in Evolutionary Computing (EvoNet) Workgroup on Systems, Control, and Drives. In summer 2002, he served as a visiting professor to Kumamoto University, Japan. He is also a visiting professor at University of Electronic Science and Technology of China. His research interests are in parallel processing, design automation and discovery of engineering systems using evolutionary learning and intelligent search techniques. Applications include control, system modelling and prediction, circuit design, microwave engineering, and operations management. He has advised 12 Ph.D.s in evolutionary computation and has 140 publications.Hiroshi Kashiwagi received B.E, M.E. and Ph.D. degrees in measurement and control engineering from the University of Tokyo, Japan, in 1962, 1964 and 1967 respectively. In 1967 he became an Associate Professor and in 1976 a Professor at Kumamoto University. From 1973 to 1974, he served as a visiting Associate Professor at Purdue University, Indiana, USA. From 1990 to 1994, he was the Director at Computer Center of Kumamoto University. He has also served as a member of Board of Trustees of Society of Instrument and Control Engineers (SICE), Japan, Chairman of Kyushu Branch of SICE and General Chair of many international conferences held in Japan, Korea, Chin and India. In 1994, he was awarded SICE Fellow for his contributions to the field of measurement and control engineering through his various academic activities. He also received the Gold Medal Prize at ICAUTO’95 held in India. In 1997, he received the “Best Book Award” from SICE for his new book entitled “M-sequence and its application” written in Japanese and published in 1996 by Shoukoudou Publishing Co. in Japan. In 1999, he received the “Best Paper Award” from SICE for his paper “M-transform and its application to system identification”. His research interests include signal processing and applications, especially pseudorandom sequence and its applications to measurement and control engineering.
基金the National Natural Science Foundation of China(Nos.11772084 and U1906233)the National High Technology Research and Development Program of China(No.2017YFC0307203)the Key Technology Research and Development Program of Shandong Province of China(No.2019JZZY010801)。
文摘A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear systems is studied in this paper.The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function(GFRF).For a class of nonlinear systems,the growing exponential method is used to determine the first 3 rd-order GFRFs.The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input.The relationship between the peak of PSD and the parameters of the nonlinear system is discussed.By using the proposed method,the nonlinear characteristics of multi-band output via single-band input can be well predicted.The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD.This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.
文摘It is important to solve the nth-order Volterra kernel or nonlinear transfer function indescribing a nonlinear network by the Volterra series.Based on an auxiliary algebraic expression ofthe Volterra series,an algebraic algorithm is proposed to evaluate the nth-order Volterra kernel andnonlinear transfer function in regular,triangular and symmetric forms.In addition,the complexity ofthe algebraic algorithm is improved.
文摘In this work, we present a computational method for solving nonlinear Fredholm-Volterra integral equations of the second kind which is based on replacement of the unknown function by truncated series of well known Block-Pulse functions (BPfs) expansion. Error analysis is worked out that shows efficiency of the method. Finally, we also give some numerical examples.
文摘The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.
文摘In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a system of nonlinear Volterra integral equations. Runge-Kutta method (RKM) and Bolck by block method (BBM) are used to solve the system of nonlinear Volterra integral equations of the second kind (SNVIEs) with continuous kernel. The error in each case is calculated.
基金supported by the National Science Fund for Distinguished Young Scholars(11125209)the National Natural Science Foundation of China(51121063 and 10702039)
文摘This paper is concerned with the connection between the Volterra series and the regular perturbation method in nonlinear systems analyses. It is revealed for the first time that, for a forced polynomial nonlinear system, if its derived linear system is a damped dissipative system, the steady response obtained through the regular perturbation method is exactly identical to the response given by the Volterra series. On the other hand, if the derived linear system is an undamped conservative system, then the Volterra series is incapable of modeling the forced polynomial nonlinear system. Numerical examples are further presented to illustrate these points. The results provide a new criterion for quickly judging whether the Volterra series is applicable for modeling a given polynomial nonlinear system.
文摘In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.
文摘A fully discrete version of a piecewise polynomial collocation method based on new collocation points, is constructed to solve nonlinear Volterra-Fredholm integral equations. In this paper, we obtain existence and uniqueness results and analyze the convergence properties of the collocation method when used to approximate smooth solutions of Volterra- Fredholm integral equations.
文摘We consider a class of doubly nonlinear history-dependent problems having a convection term and a pseudomonotone nonlinear diffusion operator associated an equation of the type ?<sub>t</sub>(k * (b(v) - b(v<sub>0</sub>))) - div(a(x,Dv) + F(v)) = f where the right hand side belongs to L<sup>1</sup>. The kernel k belongs to the large class of PC kernels. In particular, the case of fractional time derivatives of order α ∈ (0,1) is included. Assuming b nondecreasing with L<sup>1</sup>-data, we prove existence in the framework of entropy solutions. The approach adopted for the proof is based on a several step approximation method and by using a result in the case of a strictly increasing b.