Air combat target maneuver trajectory prediction based on robust regularized Volterra series and adaptive ensemble online transfer learning

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.

Power spectral density analysis for nonlinear systems based on Volterra series

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.

Volterra series based predistortion for broadband RF power amplifiers with memory effects

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.

THE PARALLEL RECURSIVE AP ADAPTIVE ALGORITHM BASED ON VOLTERRA SERIES

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.

Connection between Volterra series and perturbation method in nonlinear systems analyses

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.

High-Order Volterra Model Predictive Control and Its Application to a Nonlinear Polymerisation Process

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.

CHARACTERISTIC FUNCTIONS OF BILINEAR TIME SERIES MODEL

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.

子集优化在非线性系统辨识中的应用

提出了一种基于子集优化的非线性系统辨识方法．该方法没有对非线性系统激励信号的统计特性作任何假设，但它的计算量比现有的方法低，而对非线性系统输入输出数据量的要求也比现有的方法少．仿真结果表明。

Reducing force transmissibility in multiple degrees of freedom structures through anti-symmetric nonlinear viscous damping

In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom （MDOF） structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force trans- missibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.

Adaptive control method for nonlinear time-delay processes

Two complex properties, varying time-delay and block-oriented nonlinearity, are very common in chemical engineering processes and not easy to be controlled by routine control methods. Aimed at these two complex properties, a novel adaptive control algorithm the basis of nonlinear OFS （orthonormal functional series） model is proposed. First, the hybrid model which combines OFS and Volterra series is introduced. Then, a stable state feedback strategy is used to construct a nonlinear adaptive control algorithm that can guarantee the closed-loop stability and can track the set point curve without steady-state errors. Finally, control simulations and experiments on a nonlinear process with varying time-delay are presented. A number of experimental results validate the efficiency and superiority of this algorithm.

Effects of anti-symmetric nonlinear viscous damping on the force transmissibility of multi-degree of freedom structures

In the present study, the concept of the output frequency response function is applied to theoretically investigate the force transmissibility of multi-degree of freedom (MDOF) structures with a nonlinear anti-symmetric viscous damping. The results reveal that an anti-symmetric nonlinear viscous damping can significantly reduce the transmissibility over all resonance regions for MDOF structures while it has almost no effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to overcome the dilemma in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant region but increases the transmissibility over non-resonant regions.

Detection and classification of multiple power signal patterns with Volterra series and interval type-2 fuzzy logic system

The paper deals with the application of Volterra bound Interval type−2 fuzzy logic techniques in power quality assessment.This work proposes a new layout for detection,localization and classification of various types of power quality events.The proposed method exploits Volterra series for the extraction of relevant features,which are used to recognize different PQ events by Interval type-2 fuzzy logic based classifier.Numerous single as well as multiple powers signal disturbances have been simulated to testify the efficiency of the proposed technique.This time–frequency analysis results in the clear visual detection,localization,and classification of the different power quality events.The simulation results signify that the proposed scheme has a higher recognition rate while classifying single and multiple power quality events unlike other methods.Finally,the proposed method is compared with SVM,feed forward neural network and type−1 Fuzzy logic system based classifier to show the efficacy of the proposed technique in classifying the Power quality events.

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

An approach of dynamic response analysis of nonlinear structures based on least square Volterra kernel function identification

Analysis of the dynamic response of a complex nonlinear system is always a difficult problem.By using Volterra functional series to describe a nonlinear system,its response analysis can be similar to using Fourier/Laplace transform and linear transfer function method to analyse a linear system’s response.In this paper,a dynamic response analysis method for nonlinear systems based on Volterra series is developed.Firstly,the recursive formula of the least square method is established to solve the Volterra kernel function vector,and the corresponding MATLAB programme is compiled.Then,the Volterra kernel vector corresponding to the nonlinear response of a structure under seismic excitation is identified,and the accuracy and applicability of using the kernel vector to predict the response of a nonlinear structure are analysed.The results show that the Volterra kernel function identified by the derived recursive formula can accurately describe the nonlinear response characteristics of a structure under an excitation.For a general nonlinear system,the first three order Volterra kernel function can relatively accurately express its nonlinear response characteristics.In addition,the obtained Volterra kernel function can be used to accurately predict the nonlinear response of a structure under the similar type of dynamic load.

An overview of vortex-induced vibration(VIV)of bridge decks

A brief overview of vortex-induced vibration(VIV)of circular cylinders is first given as most of VIVstudies have been focused on this particular bluff cross-section.A critical literature review of VIV of bridge decks thathighlights physical mechanisms central to VIV from a renewed perspective is provided.The discussion focuses on VIVofbridge decks from wind-tunnel experiments,full-scale observations,semi-empirical models and computational fluidsdynamics(CFD)perspectives.Finally,a recently developed reduced order model(ROM)based on truncated Volterraseries is introduced to model VIVof long-span bridges.This model captures successfully salient features of VIVat“lockin”and unlike most phenomenological models offers physical significance of the model kernels.

A Behavior Level Analytical Method of Electromagnetic Susceptibility for Radio Frequency Receiver

Based on simplified Volterra model, a behavior-level simulation analysis approach of electromagnetic susceptibility （EMS） for radio frequency （RF） receiver is presented in this article. Third order simplified Volterra model is adopted to analyze receiver EMS. A general criterion for EMS is proposed according to EMS response characteristics in frequency domain, and then the simulation flow charts for calculating susceptibility thresholds are given. This approach is superior to the previous EMS analysis method on receiver, which mainly relies on experiments but lack simulation analysis. Take the dual frequency GPS receiver and zero IF receiver interfered by continue wave as examples for in-band and out-of-band susceptibility threshold calculation. Simulation results show that the proposed method is not only valid and effective, but also reduces the internal storage and simulation time, which is suitable to RF receiver EMS analysis and practical in engineering and technology field.

Diagnosis of soft faults in analog integrated circuits based on fractional correlation

Aiming at the problem of diagnosing soft faults in analog integrated circuits, an approach based on fractional correlation is proposed. First, the Volterra series of the circuit under test （CUT） decomposed by the fractional wavelet packet are used to calculate the fractional correlation functions. Then, the calculated fractional correlation functions are used to form the fault signatures of the CUT. By comparing the fault signatures, the different soft faulty conditions of the CUT are identified and the faults are located. Simulations of benchmark circuits illustrate the proposed method and validate its effectiveness in diagnosing soft faults in analog integrated circuits.

Parameter estimation of analog circuits based on the fractional wavelet method

Aiming at the problem of parameter estimation in analog circuits, a new approach is proposed. The approach is based on the fractional wavelet to derive the Volterra series model of the circuit under test （CUT）. By the gradient search algorithm used in the Volterra model, the unknown parameters in the CUT are estimated and the Volterra model is identified. The simulations show that the parameter estimation results of the proposed method in the paper are better than those of other parameter estimation methods.

Digital post-calibration of a 5-bit 1.25 GS/s flash ADC

We report a high-speed flash analog to digital converter（ADC） linearization technique employing the inverse Volterra model and digital post processing.First,a 1.25 GS/s 5-bit flash ADC is designed using a 0.18μm CMOS,and the signal is quantized by a distributed track-and-hold circuit.Second,based on the Volterra series, a proposed digital post-calibration model is introduced.Then,the model is applied to estimate and compensate the nonlinearity of the high-speed flash ADC.Simulation results indicate that the distortion is reduced effectively. Specifically,the ADC achieves gains of 4.83 effective bits for a 117.1 MHz frequency input and 4.74 effective bits for a Nyquist input at 1.25 GS/s.