Target maneuver trajectory prediction is an important prerequisite for air combat situation awareness and maneuver decision-making.However,how to use a large amount of trajectory data generated by air combat confronta...Target maneuver trajectory prediction is an important prerequisite for air combat situation awareness and maneuver decision-making.However,how to use a large amount of trajectory data generated by air combat confrontation training to achieve real-time and accurate prediction of target maneuver trajectory is an urgent problem to be solved.To solve this problem,in this paper,a hybrid algorithm based on transfer learning,online learning,ensemble learning,regularization technology,target maneuvering segmentation point recognition algorithm,and Volterra series,abbreviated as AERTrOS-Volterra is proposed.Firstly,the model makes full use of a large number of trajectory sample data generated by air combat confrontation training,and constructs a Tr-Volterra algorithm framework suitable for air combat target maneuver trajectory prediction,which realizes the extraction of effective information from the historical trajectory data.Secondly,in order to improve the real-time online prediction accuracy and robustness of the prediction model in complex electromagnetic environments,on the basis of the TrVolterra algorithm framework,a robust regularized online Sequential Volterra prediction model is proposed by integrating online learning method,regularization technology and inverse weighting calculation method based on the priori error.Finally,inspired by the preferable performance of models ensemble,ensemble learning scheme is also incorporated into our proposed algorithm,which adaptively updates the ensemble prediction model according to the performance of the model on real-time samples and the recognition results of target maneuvering segmentation points,including the adaptation of model weights;adaptation of parameters;and dynamic inclusion and removal of models.Compared with many existing time series prediction methods,the newly proposed target maneuver trajectory prediction algorithm can fully mine the prior knowledge contained in the historical data to assist the current prediction.The rationality and effectiveness of the proposed algorithm are verified by simulation on three sets of chaotic time series data sets and a set of real target maneuver trajectory data sets.展开更多
A new second-order neural Volterra filter (SONVF) with conjugate gradient (CG) algorithm is proposed to predict chaotic time series based on phase space delay-coordinate reconstruction of chaotic dynamics system i...A new second-order neural Volterra filter (SONVF) with conjugate gradient (CG) algorithm is proposed to predict chaotic time series based on phase space delay-coordinate reconstruction of chaotic dynamics system in this paper, where the neuron activation functions are introduced to constraint Volterra series terms for improving the nonlinear approximation of second-order Volterra filter (SOVF). The SONVF with CG algorithm improves the accuracy of prediction without increasing the computation complexity. Meanwhile, the difficulty of neuron number determination does not exist here. Experimental results show that the proposed filter can predict chaotic time series effectively, and one-step and multi-step prediction performances are obviously superior to those of SOVF, which demonstrate that the proposed SONVF is feasible and effective.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
RF power amplifiers (PAs) are usually considered as memoryless devices in most existing predistortion techniques. However, in broadband communication systems, such as WCDMA, the PA memory effects are significant, an...RF power amplifiers (PAs) are usually considered as memoryless devices in most existing predistortion techniques. However, in broadband communication systems, such as WCDMA, the PA memory effects are significant, and memoryless predistortion cannot linearize the PAs effectively. After analyzing the PA memory effects, a novel predistortion method based on the simplified Volterra series is proposed to linearize broadband RF PAs with memory effects. The indirect learning architecture is adopted to design the predistortion scheme and the reeursive least squares algorithm with forgetting factor is applied to identify the parameters of the predistorter. Simulation results show that the proposed predistortion method can compensate the nonlinear distortion and memory effects of broadband RF PAs effectively.展开更多
Aiming at the nonlinear system identification problem, a parallel recursive affine projection (AP) adaptive algorithm for the nonlinear system based on Volterra series is presented in this paper. The algorithm identif...Aiming at the nonlinear system identification problem, a parallel recursive affine projection (AP) adaptive algorithm for the nonlinear system based on Volterra series is presented in this paper. The algorithm identifies in parallel the Volterra kernel of each order, recursively estimate the inverse of the autocorrelation matrix for the Volterra input of each order, and remarkably improve the convergence speed of the identification process compared with the NLMS and conventional AP adaptive algorithm based on Volterra series. Simulation results indicate that the proposed method in this paper is efficient.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 the paper, perturbed stochastic Volterra Equations with noise terms driven by series of independent scalar Wiener processes are considered. In the study, the resolvent approach to the equations under consideration ...In the paper, perturbed stochastic Volterra Equations with noise terms driven by series of independent scalar Wiener processes are considered. In the study, the resolvent approach to the equations under consideration is used. Sufficient conditions for the existence of strong solution to the class of perturbed stochastic Volterra Equations of convolution type are given. Regularity of stochastic convolution is supplied, as well.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
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
Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help...Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help of Volterra seriesexpansion,the impulse response function and frequency characteristic function of thegeneral bilinear time series model are also derived.展开更多
基金the support of the Fundamental Research Funds for the Air Force Engineering University under Grant No.XZJK2019040。
文摘Target maneuver trajectory prediction is an important prerequisite for air combat situation awareness and maneuver decision-making.However,how to use a large amount of trajectory data generated by air combat confrontation training to achieve real-time and accurate prediction of target maneuver trajectory is an urgent problem to be solved.To solve this problem,in this paper,a hybrid algorithm based on transfer learning,online learning,ensemble learning,regularization technology,target maneuvering segmentation point recognition algorithm,and Volterra series,abbreviated as AERTrOS-Volterra is proposed.Firstly,the model makes full use of a large number of trajectory sample data generated by air combat confrontation training,and constructs a Tr-Volterra algorithm framework suitable for air combat target maneuver trajectory prediction,which realizes the extraction of effective information from the historical trajectory data.Secondly,in order to improve the real-time online prediction accuracy and robustness of the prediction model in complex electromagnetic environments,on the basis of the TrVolterra algorithm framework,a robust regularized online Sequential Volterra prediction model is proposed by integrating online learning method,regularization technology and inverse weighting calculation method based on the priori error.Finally,inspired by the preferable performance of models ensemble,ensemble learning scheme is also incorporated into our proposed algorithm,which adaptively updates the ensemble prediction model according to the performance of the model on real-time samples and the recognition results of target maneuvering segmentation points,including the adaptation of model weights;adaptation of parameters;and dynamic inclusion and removal of models.Compared with many existing time series prediction methods,the newly proposed target maneuver trajectory prediction algorithm can fully mine the prior knowledge contained in the historical data to assist the current prediction.The rationality and effectiveness of the proposed algorithm are verified by simulation on three sets of chaotic time series data sets and a set of real target maneuver trajectory data sets.
基金Project supported by the National Natural Science Foundation of China (Grant No 60276096), the National Ministry Foundation of China (Grant No 51430804QT2201).
文摘A new second-order neural Volterra filter (SONVF) with conjugate gradient (CG) algorithm is proposed to predict chaotic time series based on phase space delay-coordinate reconstruction of chaotic dynamics system in this paper, where the neuron activation functions are introduced to constraint Volterra series terms for improving the nonlinear approximation of second-order Volterra filter (SOVF). The SONVF with CG algorithm improves the accuracy of prediction without increasing the computation complexity. Meanwhile, the difficulty of neuron number determination does not exist here. Experimental results show that the proposed filter can predict chaotic time series effectively, and one-step and multi-step prediction performances are obviously superior to those of SOVF, which demonstrate that the proposed SONVF is feasible and effective.
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.
基金the National Natural Science Foundation of China (60671037).
文摘RF power amplifiers (PAs) are usually considered as memoryless devices in most existing predistortion techniques. However, in broadband communication systems, such as WCDMA, the PA memory effects are significant, and memoryless predistortion cannot linearize the PAs effectively. After analyzing the PA memory effects, a novel predistortion method based on the simplified Volterra series is proposed to linearize broadband RF PAs with memory effects. The indirect learning architecture is adopted to design the predistortion scheme and the reeursive least squares algorithm with forgetting factor is applied to identify the parameters of the predistorter. Simulation results show that the proposed predistortion method can compensate the nonlinear distortion and memory effects of broadband RF PAs effectively.
文摘Aiming at the nonlinear system identification problem, a parallel recursive affine projection (AP) adaptive algorithm for the nonlinear system based on Volterra series is presented in this paper. The algorithm identifies in parallel the Volterra kernel of each order, recursively estimate the inverse of the autocorrelation matrix for the Volterra input of each order, and remarkably improve the convergence speed of the identification process compared with the NLMS and conventional AP adaptive algorithm based on Volterra series. Simulation results indicate that the proposed method in this paper is efficient.
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 the paper, perturbed stochastic Volterra Equations with noise terms driven by series of independent scalar Wiener processes are considered. In the study, the resolvent approach to the equations under consideration is used. Sufficient conditions for the existence of strong solution to the class of perturbed stochastic Volterra Equations of convolution type are given. Regularity of stochastic convolution is supplied, as well.
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Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help of Volterra seriesexpansion,the impulse response function and frequency characteristic function of thegeneral bilinear time series model are also derived.