Showing papers on "Volterra series published in 2018"

Sparse Modeling of Nonlinear Secondary Path for Nonlinear Active Noise Control

Abstract: In many practical active noise control systems, the nonlinear secondary path (NSP) model can offer broader applications than the linear secondary path (LSP) model for the widespread existence of nonlinearities in the secondary path. However, the computational burden often limits the application of the NSP algorithms. In this paper, we apply a sparse Volterra model for the LSP and NSP instead of the complete Volterra model, which may be over parameterized for the nonlinear active noise control (NANC) system. The developed new control algorithms greatly result in reduction of computational complexity. We also provide an analysis of the NANC system to show that the noise at the canceling point could be approximated by the function expansion filters when the secondary path is modeled as the second-order Volterra series. In addition, two new function expansion forms, the even mirror Fourier nonlinear filter with a linear finite-impulse response section and the Chebyshev filter, are explored to process the nonlinearities in the NANC system using the filtered-x least mean square and filtered-error least mean square algorithm structures. The computational complexity analysis and the computer simulations validate that the new control algorithms with a sparse Volterra model for the secondary path can significantly reduce computational load without sacrificing the control performance.

Policy Approximation in Policy Iteration Approximate Dynamic Programming for Discrete-Time Nonlinear Systems

Abstract: Policy iteration approximate dynamic programming (DP) is an important algorithm for solving optimal decision and control problems. In this paper, we focus on the problem associated with policy approximation in policy iteration approximate DP for discrete-time nonlinear systems using infinite-horizon undiscounted value functions. Taking policy approximation error into account, we demonstrate asymptotic stability of the control policy under our problem setting, show boundedness of the value function during each policy iteration step, and introduce a new sufficient condition for the value function to converge to a bounded neighborhood of the optimal value function. Aiming for practical implementation of an approximate policy, we consider using Volterra series, which has been extensively covered in controls literature for its good theoretical properties and for its success in practical applications. We illustrate the effectiveness of the main ideas developed in this paper using several examples including a practical problem of excitation control of a hydrogenerator.

Diagnosis of Inter-Turn Short Circuit of Synchronous Generator Rotor Winding Based on Volterra Kernel Identification

Abstract: The inter-turn short circuit is a common fault in the synchronous generator This fault is not easily detected at early stage However, with the development of the fault, it will pose a threat to the safe operation of the generator To detect the inter-turn short circuit of rotor winding, the feasibility of identifying the stator branch characteristics of synchronous generator during inter-turn short circuit was analyzed In this paper, an on-line fault identification method based on Volterra kernel identification is presented This method uses the stator branch voltage and stator unbalance branch current collected from the generator as input and output signals of the series model Recursive batch least squares method is applied to calculate the three kernels of Volterra series When the generator is in normal state or fault state, the Volterra kernel will change accordingly Through the identification of the time-domain kernel of the nonlinear transfer model, the inter-turn short circuit fault of the synchronous generator is diagnosed The correctness and effectiveness of this method is verified by using the data of fault experimental synchronous generator

Modeling and Cancellation of Self-Interference in Full-Duplex Radio Transceivers: Volterra Series-Based Approach

Abstract: This paper presents a novel digital self-interference canceller for inband full-duplex radio transceivers. The proposed digital canceller utilizes a Volterra series with sparse memory to model the residual SI signal, and it can thereby accurately reconstruct the self-interference even under a heavily nonlinear transmitter power amplifier. To the best of our knowledge, this is the first time such a sparse-memory Volterra series has been used to model the self-interference within an inband full-duplex device. The performance of the Volterra-based canceller is evaluated with real-life measurements that incorporate also an active analog canceller. The results show that the novel digital canceller suppresses the SI by 34 dB in the digital domain, outperforming the state- of-the-art memory polynomial-based solution by a margin of 5 dB. The total amount of cancellation is nearly 110 dB with a transmit power of +30 dBm, even though a shared transmit/receive antenna is used. To the best of our knowledge, this is the highest reported cancellation performance for a shared-antenna full-duplex device with such a high transmit power level.

Definition of Simplified Frequency-Domain Volterra Models With Quasi-Sinusoidal Input

Abstract: The Volterra approach to the modeling of nonlinear systems has been employed for a long time thanks to its conceptual simplicity and flexibility. Its main drawback lies in the number of coefficients, which rapidly grows with memory length and nonlinearity order. In some important cases, such as power system applications, the input signal is periodic and contains a fundamental component that is much larger with respect to the others. This peculiarity can be exploited in order to dramatically reduce the number of coefficients defining the frequency-domain Volterra model with slight drawbacks in terms of accuracy. A systematic procedure for the definition of simplified, frequency-domain models of arbitrary order is proposed. Thanks to the simplification, very high orders of nonlinearity can be managed. The proposed approach has been employed to model the behavior of two electrical devices with different amount of nonlinearity, and that of a power grid containing linear and nonlinear loads. Accuracy is discussed and compared with that obtained with a conventional Volterra model defined by a similar number of coefficients. Results show the effectiveness of the approach, which is particularly suitable to model and test voltage and current transducers as well as other ac power system devices.

Computational-Complexity Comparison of Artificial Neural Network and Volterra Series Transfer Function for Optical Nonlinearity Compensation with Time- and Frequency-Domain Dispersion Equalization

Abstract: We evaluated the number of complex multiplications in an ANN and a VSTF for optical nonlinearity compensation. The results show that the ANN involved lower computational complexity than the VSTF when additional time-domain nonlinear processing is required.

Modeling the Nonlinear Cortical Response in EEG Evoked by Wrist Joint Manipulation

Abstract: Joint manipulation elicits a response from the sensors in the periphery which, via the spinal cord, arrives in the cortex. The average evoked cortical response recorded using electroencephalography was shown to be highly nonlinear; a linear model can only explain 10% of the variance of the evoked response, and over 80% of the response is generated by nonlinear behavior. The goal of this paper is to obtain a nonparametric nonlinear dynamic model, which can consistently explain the recorded cortical response requiring little a priori assumptions about model structure. Wrist joint manipulation was applied in ten healthy participants during which their cortical activity was recorded and modeled using a truncated Volterra series. The obtained models could explain 46% of the variance of the evoked cortical response, thereby demonstrating the relevance of nonlinear modeling. The high similarity of the obtained models across participants indicates that the models reveal common characteristics of the underlying system. The models show predominantly high-pass behavior, which suggests that velocity-related information originating from the muscle spindles governs the cortical response. In conclusion, the nonlinear modeling approach using a truncated Volterra series with regularization, provides a quantitative way of investigating the sensorimotor system, offering insight into the underlying physiology.

Volterra bound interval type-2 fuzzy logic-based approach for multiple power quality events analysis

Abstract: This study demonstrates detection and classification of power quality (PQ) events utilising Volterra series for feature extraction and interval type-2 fuzzy logic system (IT2FLS) for classification of PQ events. The Volterra series represented in the form of infinite power series with memory which provides a convenient and strong platform for representation of input–output relationship for non-linear systems. IT2FLS uses the concept of membership functions to perform classification of multiple PQ events. When supply power is distorted by additive noise where signal-to-noise ratio is low and uncertain, IT2FLS has shown improved performance over support vector machine, neural networks (NNs), probabilistic NN and type-1 fuzzy logic system classifiers, which makes an IT2FLS favourable for real-time applications.

Nonlinear system modeling based on constrained Volterra series estimates

Abstract: A simple nonlinear system modeling algorithm designed to work with limited \emph{a priori }knowledge and short data records, is examined. It creates an empirical Volterra series-based model of a system using an $l_{q}$-constrained least squares algorithm with $q\geq 1$. If the system $m\left( \cdot \right) $ is a continuous and bounded map with a finite memory no longer than some known $\tau$, then (for a $D$ parameter model and for a number of measurements $N$) the difference between the resulting model of the system and the best possible theoretical one is guaranteed to be of order $\sqrt{N^{-1}\ln D}$, even for $D\geq N$. The performance of models obtained for $q=1,1.5$ and $2$ is tested on the Wiener-Hammerstein benchmark system. The results suggest that the models obtained for $q>1$ are better suited to characterize the nature of the system, while the sparse solutions obtained for $q=1$ yield smaller error values in terms of input-output behavior.

Sparsity-Aware Distributed Adaptive Filtering Algorithms for Nonlinear System Identification

Abstract: In this work we consider a scenario in which several dispersed nodes intend to identify a nonlinear Volterra system. Such system is represented by a series that has sparse kernels, with few non-zero coefficients. This sparse feature of Volterra series allows us to propose distributed and sparsity- aware adaptive filtering algorithms, that aim at identifying such nonlinear system. We consider a network composed by agents, called Wireless Sensor Network (WSN), containing sensor nodes that have energy and computational constraints. We evaluate the performance of the proposed algorithm by means of the Mean-Squared Deviation (MSD) metric, and we verified that the distributed scheme provides a higher convergence rate and steady-state performance.

A new adaptive sliding mode control of nonlinear systems using Volterra series: application to hydraulic system

Abstract: In this paper, we propose a new adaptive sliding mode control for nonlinear systems which are affine with respect to control and where the free term of state representation is assumed to be unknown and modelled using Volterra series The proposed control law depends on the estimated parameters of Volterra series The Lyapunov function was defined based on the sliding surface and the errors between the Volterra model parameters and their estimated values The Lyapunov function is defined as positive and decreasing which shows the systems studied An example of simulation and a validation on a real system are performed at the end of this paper to show the effectiveness of this approach

Nonlinearity Mitigation for VLC with an Artificial Neural Network Based Equalizer

Abstract: Light emitting diode (LED) is a major source of nonlinearity in visible light communication (VLC). In this work, we introduce a Wiener-Hammerstein model considering the LED nonlinearity and memory effect of an indoor channel. The VLC nonlinearity belongs to dynamic-range-limited nonlinearities. Considering the impact of nonlinearity strength in different dynamic regions, we design three types of signals for both weak and strong nonlinearity regions. Moreover, in order to well compensate the nonlinearity, an artificial neural network (ANN) based equalizer is compared with the conventional Volterra series-based equalizer and the memory orthogonal polynomial-based equalizer. The results show that the proposed equalizer significantly outperforms conventional nonlinear equalizers, up to two orders of magnitude in high SNR region.

A Two-Port Nonlinear Dynamic Behavioral Model of RF PAs Subject to Wideband Load Modulation

Abstract: This work presents a full two-port, i.e., double input-double output, behavioral modeling approach suitable for radio frequency power amplifiers (PAs) in the presence of dynamic load modulation (DLM). The formulation of the model, based on a first-order approximation of a modified Volterra series, accounts for the nonlinear distortion determined by large-signal operation under mismatched conditions, and also for the memory effects stimulated by a modulated PA input signal, or by the dynamic variations of the PA load. By following an exhaustive procedure defined in the frequency domain, the model of a general purpose commercial PA is extracted over 160 MHz of modulation bandwidth (BW) with nonlinear vector network analyzer measurements. Validation results under 20-MHz BW multisine excitation and injected 80-MHz BW multisine load modulation show improved prediction capabilities with respect to quasi-static or single-input descriptions, allowing for reliable system-level simulations in the presence of DLM.

Behavioral modeling of VCSELs for high-speed optical interconnects

Abstract: Transition from on-off keying to 4-level pulse amplitude modulation (PAM) in VCSEL based optical interconnects allows for an increase of data rates, at the cost of 4.8 dB sensitivity penalty. The resulting strained link budget creates a need for accurate VCSEL models for driver integrated circuit (IC) design and system level simulations. Rate equation based equivalent circuit models are convenient for the IC design, but system level analysis requires computationally efficient closed form behavioral models based Volterra series and neural networks. In this paper we present and compare these models.

Comparison of Nonlinear Compensation Techniques for 400-Gb/s Coherent Multi-Band OFDM Super-Channels

Abstract: The last few years, many studies have been published on the 3rd-order inverse Volterra series transfer function nonlinear equalizer (IVSTF-NLE) in long-haul optical communication systems. Nonetheless, no experimental work has been published on investigating the potential of the 3rd-order IVSTF-NLE for the compensation of Kerr nonlinearities in a long-haul wavelength division multiplexing (WDM) system consisting of high-bit rate super-channels, as high as 400 Gb/s. In this paper, we study experimentally the performance of a 3rd-order IVSTF-NLE in a coherent optical WDM system, with a central, 400-Gb/s, 4-band, dual-polarization (DP), 16-ary quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) super-channel. We compare its performance against the performance of the digital back-propagation split-step Fourier (DBP-SSF) method for the compensation of nonlinearities after 10 × 100 km of ITU-T G.652 standard single mode fiber (SSMF). In the second part of this paper, we compare, via Monte Carlo simulations, the performance of the 3rd-order IVSTF-NLE and the DBP-SSF method, in terms of reach extension and computational complexity, after propagation through ITU-T G.652 SSMF and a ITU-T G.655 large effective area fiber (LEAF). By means of both experimental evaluation and simulations, we show that, in the presence of strong nonlinear effects, the 3rd-order IVSTF-NLE, which uses a single step per span, performs similarly with the two-steps-per-span DBP-SSF, whereas the eight-steps-per-span DBP-SSF is only marginally better but at the vast expense of computational complexity.

Computational-Complexity Comparison of Artificial Neural Network and Volterra Series Transfer Function for Optical Nonlinearity Compensation

Abstract: We evaluated the number of multiplications of ANN and VSTF for optical nonlinearity compensation. The results revealed that ANN improves the computational-complexity of VSTF in case that dispersion compensation is required at the same time.

Real Time Emulation of Parametric Guitar Tube Amplifier with Long Short Term Memory Neural Network

Abstract: Numerous audio systems for musicians are expensive and bulky. Therefore, it could be advantageous to model them and to replace them by computer emulation. In guitar players' world, audio systems could have a desirable nonlinear behavior (distortion effects). It is thus difficult to find a simple model to emulate them in real time. Volterra series model and its subclass are usual ways to model nonlinear systems. Unfortunately, these systems are difficult to identify in an analytic way. In this paper we propose to take advantage of the new progress made in neural networks to emulate them in real time. We show that an accurate emulation can be reached with less than 1% of root mean square error between the signal coming from a tube amplifier and the output of the neural network. Moreover, the research has been extended to model the Gain parameter of the amplifier.

Turbo Equalization Based on a Combined VMP-BP Algorithm for Nonlinear Satellite Channels

Abstract: Close to saturation operation of high power amplifier (HPA) leads to strong nonlinear and dispersive characteristic of satellite channels. At the receiver, the observation signals are distorted by not only the linear inter-symbol interference (ISI) but also the nonlinear ones, which makes it challenge to perform optimal detection. In this paper, we study factor graph (FG)-based turbo equalization for nonlinear satellite channels characterized by Volterra series. Factor nodes on FG are classified into belief propagation (BP) set and variational message passing (VMP) set to enable low complexity combined message passing implementation while with high performance. BP is used on the hard constraint nodes, such as demapping and decoding, while VMP is employed to update messages of the likelihood function node. It is shown that, without any approximation on the Volterra series channel model, messages can be expressed in a closed form via canonical parameters, and the extrinsic information from equalizer to decoder is derived in an explicit way. Simulation results demonstrate the superior performance of the proposed combined VMP-BP algorithm with low computational complexity.

Nonlinear system identification using Kautz basis expansion-based Volterra–PARAFAC model

Abstract: Volterra series is a powerful mathematical tool for nonlinear system analysis, which extends the convolution integral for linear systems to nonlinear systems. There is a wide range of nonlinear engineering systems and structures which can be modeled as Volterra series. The usefulness of Volterra models is mainly because of their ability to approximate any fading memory nonlinear systems to an arbitrary accuracy. One question involved in modeling a functional relationship between the input and output of a system using Volterra series is to identify the Volterra kernel functions, the number of which increases rapidly with the system nonlinearity order and the kernels memory. In this paper, a Kautz basis expansion-based Volterra–PARAFAC model is proposed to identify the Volterra nonlinear system from observations of the in- and outgoing signals. In addition, based on the best linear approximation, an effective method for the choice of initial values of pole parameters is presented, and based on the back propagation through-time technique and the Levenberg–Marquardt algorithm, an optimization algorithm for pole and nonlinear parameters is presented in this paper. The simulation studies verify the effectiveness of the proposed novel Kautz basis expansion-based Volterra–PARAFAC modeling method.

pth-order inverse of the Volterra series for multiple-input multiple-output non-linear dynamic systems

Abstract: A method to determine the pth-order inverse of the Volterra series of multiple-input multiple-output non-linear dynamic systems is presented; it combines time- and frequency-domain techniques to determine the Volterra series of the inverse as a function of the forward system's Volterra series. The method can be used for continuous and discrete time systems. Each operator of non-linear order n of the inverse is a function of the forward system's operators of non-linear order n and lower. It is shown that the p th-order post-inverse is equal to the pth-order preinverse. For the special case that there are no linear cross terms and that the linear memory effects are negligible the kernels of the forward and inverse models are approximately the same. In an example, an approximate inverse model of a model of a concurrent dual band radio frequency amplifier is derived.

Real Time Emulation of Parametric Guitar Tube Amplifier With Long Short Term Memory Neural Network

Abstract: Numerous audio systems for musicians are expensive and bulky. Therefore, it could be advantageous to model them and to replace them by computer emulation. In guitar players' world, audio systems could have a desirable nonlinear behavior (distortion effects). It is thus difficult to find a simple model to emulate them in real time. Volterra series model and its subclass are usual ways to model nonlinear systems. Unfortunately, these systems are difficult to identify in an analytic way. In this paper we propose to take advantage of the new progress made in neural networks to emulate them in real time. We show that an accurate emulation can be reached with less than 1% of root mean square error between the signal coming from a tube amplifier and the output of the neural network. Moreover, the research has been extended to model the Gain parameter of the amplifier.

Unsteady aerodynamics modeling using Volterra series expansed by basis function

Abstract: Unsteady aerodynamics modeling must accurately describe nonlinear aerodynamic characteristics in addition to unsteady aerodynamic characteristics. The Volterra series has attracted increasing attention as a powerful tool for nonlinear system modeling. It is essential to incorporate the influence of the second-order Volterra kernel or higher-order kernels to build a nonlinear unsteady aerodynamics model. The main difficulty in the identification of higher-order kernels is that the number of parameters to be identified increases exponentially with the order of a kernel. This paper expands the Volterra kernels with the four-order B-spline wavelet on the interval as the basis function, converts the problem into the solution of low-dimensional equations, and obtains a stable solution. A nonlinear unsteady aerodynamics model is built by identifying the second-order and third-order kernels of the lift, drag, and pitching moment coefficients of the NACA0012 airfoil. Then the model is verified at different reduced frequencies using CFD.

Volterra Kernel Identification using Regularized Orthonormal Basis Functions.

Abstract: The Volterra series is a powerful tool in modelling a broad range of nonlinear dynamic systems. However, due to its nonparametric nature, the number of parameters in the series increases rapidly with memory length and series order, with the uncertainty in resulting model estimates increasing accordingly. In this paper, we propose an identification method where the Volterra kernels are estimated indirectly through orthonormal basis function expansions, with regularization applied directly to the expansion coefficients to reduce variance in the final model estimate and provide access to useful models at previously unfeasible series orders. The higher dimensional kernel expansions are regularized using a method that allows smoothness and decay to be imposed on the entire hyper-surface. Numerical examples demonstrate improved Volterra series estimation up to the 4th order using the regularized basis function method.

Data-Selective Volterra Adaptive Filters

Abstract: This work proposes the use of data-selective schemes in Volterra adaptive filters. By working only with input data that brings novelty to the system, thus avoiding unnecessary parameter updates, one can reduce drastically the high computational burden associated with the use of Volterra series. Considering a nonlinear system identification setup, results show that the proposed data-selective Volterra filters update in only 7.5% of the iterations, whereas in a nonlinear channel equalization setup the update rate is around 27%, without compromising the performance in terms of mean squared error or bit-error rate.