Showing papers on "Volterra series published in 2017"
TL;DR: In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts derived from the VOLTERRA series, including the general frequency response function (GFRF), the nonlinear output frequency response functions (NOFRF) and associated frequency response (AFRF), and a detailed review is then given on the applications of Volterras in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.
137 citations
TL;DR: The most critical points related to high-speed Volterra filter design and implementation are investigated and a simple guidance for filter complexity reduction and useful hints for channel acquisition are provided.
Abstract: Unlike ultralong coherent optical systems that seriously suffer from fiber nonlinearities, short-reach noncoherent systems such as data center interconnections, which utilize small, cheap, and low-bandwidth components, are sensitive to nonlinearities that are mainly produced by devices responsible for electrical signal amplification, modulation, and demodulation. One of the most promising schemes for these applications is the four-level pulse amplitude modulation format combined with intensity modulation and direct detection; however, it can be significantly degraded by linear and nonlinear intersymbol interference. Linear and nonlinear signal degradation can efficiently be handled by different types of equalizers. In many cases, the straightforward linear equalizer cannot lower the error rate at the acceptable level. Therefore, much stronger equalizers based on nonlinear models such as the Volterra series are proposed. Volterra filter that can also be orthogonalized by the Wiener model is well described in the existing literature, and, in this paper, we investigate the most critical points related to high-speed Volterra filter design and implementation. Several experiments are carried out in order to indicate filter requirements/complexity, acquisition, and stability. We also provide a simple guidance for filter complexity reduction and useful hints for channel acquisition.
106 citations
TL;DR: The regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modeled as Volterra series, where the kernels of order higher than one, representing higher dimensional impulse responses in the series, are considered to be realizations of multidimensional Gaussian processes.
61 citations
TL;DR: The CAPD method can outperform the Volterra series based nonlinear equalizer with a lower BER value and relatively lower complexity and to the best of the knowledge, this is the first time that the clustering algorithm in machine learning is successfully applied to VLC systems.
Abstract: Nonlinearities induced by the electrical amplifiers and the optoelectronic devices can be detrimental effects in visible light communication (VLC) systems. In this paper, clustering algorithm based perception decision (CAPD) is proposed to mitigate the nonlinear distortion in a VLC system. Aided by CAPD nonlinear compensation, we experimentally demonstrate a multiband CAP modulated VLC system consisting of a red light-emitting diode as a transmitter and a p-i-n photodiode based differential receiver. The system performances including the Q factor, bit error rate (BER), and computational complexity are thoroughly investigated when using a pure linear blind equalization scheme (modified cascaded multimodulus algorithm, M-CMMA) and when using hybrid linear and nonlinear equalizers (M-CMMA + Volterra series based nonlinear equalizer). The experiment results show that compared to pure linear equalizer case, the measured BER can be enhanced up to 1e−6, correspondingly the Q factor of each subband can be improved for around 1.6–2.5 dB by employing CAPD. The CAPD method can outperform the Volterra series based nonlinear equalizer with a lower BER value (at least 10% reduction) and relatively lower complexity. To the best of our knowledge, this is the first time that the clustering algorithm in machine learning is successfully applied to VLC systems.
48 citations
TL;DR: A technique for reducing the number of basis waveforms used in a Volterra series model for digital predistortion of radio frequency power amplifiers is proposed, and it is shown that grouping and pruning produce similar ACLR results when the coefficient estimator notch filters the linear signal bandwidth and applies regularization.
Abstract: A technique for reducing the number of basis waveforms used in a Volterra series model for digital predistortion (DPD) of radio frequency power amplifiers is proposed. An effective delay is defined for each basis waveform. The DPD model is constrained so that the basis waveforms used have unique delays. When several of the original Volterra terms have a common delay, they are either grouped together to form a single basis waveform or pruned to discard all but the dominant term. It is shown that grouping and pruning produce similar ACLR results when the coefficient estimator notch filters the linear signal bandwidth and applies regularization. Unique delay DPD basis sets are compatible with a fractionally sampled memory polynomial estimator. The basis waveforms within the estimator are specified in the frequency domain as a function of memoryless waveforms and delay operators, thereby reducing the number of fast Fourier transforms needed and allowing for fractional tap spacing that matches the effective delays of Volterra basis waveforms used within the DPD basis set. The approximation associated with using a memory polynomial estimator is sufficiently accurate for a closed-loop estimator to converge to a desired steady state.
44 citations
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TL;DR: This paper proposes algebraic Gramians for QB systems based on the underlying Volterra series representation of QB systems and their Hilbert adjoint systems and investigates the Lyapunov stability of the reduced-order systems.
Abstract: We discuss balanced truncation model order reduction for large-scale quadratic-bilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and observability Gramians. These Gramians are extended to a general nonlinear setting in Scherpen (1993), where it is shown that Gramians for nonlinear systems are the solutions of state-dependent nonlinear Hamilton-Jacobi equations. Therefore, they are not only difficult to compute for large-scale systems but also hard to utilize in the model reduction framework. In this paper, we propose algebraic Gramians for QB systems based on the underlying Volterra series representation of QB systems and their Hilbert adjoint systems. We then show their relations with a certain type of generalized quadratic Lyapunov equation. Furthermore, we present how these algebraic Gramians and energy functionals relate to each other. Moreover, we characterize the reachability and observability of QB systems based on the proposed algebraic Gramians. This allows us to find those states that are hard to control and hard to observe via an appropriate transformation based on the Gramians. Truncating such states yields reduced-order systems. Additionally, we present a truncated version of the Gramians for QB systems and discuss their advantages in the model reduction framework. We also investigate the Lyapunov stability of the reduced-order systems. We finally illustrate the efficiency of the proposed balancing-type model reduction for QB systems by means of various semi-discretized nonlinear partial differential equations and show its competitiveness with the existing moment-matching methods for QB systems.
33 citations
TL;DR: In this paper, the adaptive filter concept is used for nonlinear identification of multi-degree of freedom systems, without sacrificing the benefits associated with the traditional Volterra series approach.
29 citations
TL;DR: The prognostic results show that the proposed approach can predict the RUL of IGBT modules with small error and achieve higher prediction precision and lower time cost than some classic prediction approaches.
Abstract: The insulated gate bipolar transistor (IGBT) is a kind of excellent performance switching device used widely in power electronic systems. How to estimate the remaining useful life (RUL) of an IGBT to ensure the safety and reliability of the power electronics system is currently a challenging issue in the field of IGBT reliability. The aim of this paper is to develop a prognostic technique for estimating IGBTs' RUL. There is a need for an efficient prognostic algorithm that is able to support in-situ decision-making. In this paper, a novel prediction model with a complete structure based on optimally pruned extreme learning machine (OPELM) and Volterra series is proposed to track the IGBT's degradation trace and estimate its RUL; we refer to this model as Volterra k-nearest neighbor OPELM prediction (VKOPP) model. This model uses the minimum entropy rate method and Volterra series to reconstruct phase space for IGBTs' ageing samples, and a new weight update algorithm, which can effectively reduce the influence of the outliers and noises, is utilized to establish the VKOPP network; then a combination of the k-nearest neighbor method (KNN) and least squares estimation (LSE) method is used to calculate the output weights of OPELM and predict the RUL of the IGBT. The prognostic results show that the proposed approach can predict the RUL of IGBT modules with small error and achieve higher prediction precision and lower time cost than some classic prediction approaches.
27 citations
TL;DR: In this paper, a discrete Volterra model is used to monitor the prediction error of a reference model representing the healthy structure, which can separate the linear and nonlinear components of the response of a system.
Abstract: Nonlinearities in the dynamical behavior of mechanical systems can degrade the performance of damage detection features based on a linearity assumption. In this article, a discrete Volterra model is used to monitor the prediction error of a reference model representing the healthy structure. This kind of model can separate the linear and nonlinear components of the response of a system. This property of the model is used to compare the consequences of assuming a nonlinear model during the nonlinear regime of a magneto-elastic system. Hypothesis tests are then employed to detect variations in the statistical properties of the damage features. After these analyses, conclusions are made about the application of Volterra series in damage detection.
26 citations
TL;DR: In this paper, a complex-valued orthogonal least squares algorithm is developed to estimate the Volterra series kernels of a weakly nonlinear system and the physical parameters of the system.
22 citations
TL;DR: In this article, the Volterra theory-based reduced-order modeling (ROM) technique was used for simulating fluid-structure interactions of bridge decks during vortex-induced vibration (VIV).
26 Jun 2017
TL;DR: A new method of hyperparameter tuning based on expectation-maximization (EM) is proposed, which allows the global optimization to be split into smaller components such that the search space of any given optimization problem is not prohibitively large.
Abstract: In nonlinear system identification, Volterra kernel estimation based on regularized least squares can be performed by taking a Bayesian approach. In this framework, covariance structures which describe the Gaussian kernels are represented by a set of hyperparameters. The hyperparameters are traditionally tuned through a global optimization which maximizes their marginal likelihood with respect to the measured data. The global optimization is computationally intensive for high-order estimates, as the number of hyperparameters increases quadratically with the Volterra series order. In this letter, we propose a new method of hyperparameter tuning based on expectation-maximization (EM). The technique allows the global optimization to be split into smaller components such that the search space of any given optimization problem is not prohibitively large. The main advantage of the proposed EM method is improved computation time scaling with respect to Volterra series order. The computation time benefits of the EM-based method are demonstrated through a numerical example for the case where the maximum nonlinear order is known.
TL;DR: This paper demonstrates a general model for nonlinear systems with complex-valued inputs and its application to communication systems modeling based on Wirtinger calculus and a double Volterra series approach.
TL;DR: The theoretical analysis of the effects of nonlinear viscous damping on vibration isolation using the output frequency response function approach reveals that the force transmissibility of the oscillator is suppressed due to the existence of the fractional order damping, but the results can be used as designing parameters for vibration isolation systems.
Abstract: Motivated by the theoretical analysis of the effects of nonlinear viscous damping on vibration isolation using the output frequency response function approach, the output frequency response function approach is employed to investigate the effects of the nonlinear fractional order damping on vibration isolation based on Volterra series in the frequency domain. First, the recursive algorithm which is proposed by Billings et al. is extended to deal with the system with fractional order terms. Then, the analytical relationships are established among the force transmissibility, nonlinear characteristic coefficients and fractional order parameters for the single degree of freedom oscillator. Consequently, the effects of the nonlinear system parameters on the force transmissibility are discussed in detail. The theoretical analysis reveals that the force transmissibility of the oscillator is suppressed due to the existence of the fractional order damping, but presents different effects on suppressing the ...
TL;DR: A new interpolatory framework for model reduction of large-scale bilinear systems is proposed that reduces the computational costs as it involves computations associated with solving linear systems only.
TL;DR: In this article, a systematic approach that enables a convenient extraction of Volterra kernels from X-parameters is presented, and a concise and general representation of the output response due to arbitrary number of input tones is given.
Abstract: Volterra series (VS) representation is a powerful mathematical model for nonlinear circuits. However, the difficulties in determining higher order Volterra kernels limited its broader applications. In this paper, a systematic approach that enables a convenient extraction of Volterra kernels from X-parameters is presented. A concise and general representation of the output response due to arbitrary number of input tones is given. The relationship between Volterra kernels and X-parameters is explicitly formulated. An efficient frequency sweep scheme and an output frequency indexing scheme are provided. The least square linear regression method is employed to separate different orders of Volterra kernels at the same frequency, which leads to the obtained Volterra kernels complete. The proposed VS representation based on X-parameters is further validated for time-domain verification. The proposed method is systematic and general-purpose. It paves the way for time-domain simulation with X-parameters and constitutes a powerful supplement to the existing blackbox macromodeling methods for nonlinear circuits.
01 Jun 2017
TL;DR: It is shown that the proposed system achieves transmission distance of 3 meters, which exceeds the longest reported in the organic VLC literature, and can mitigate both inter-symbol interference (ISI) and nonlinearity more effectively than other equalizers.
Abstract: Organic light emitting diodes (OLEDs) show promising applications due to their unique advantages compared with conventional commercial LEDs. In OLED-base visible light communication (VLC), the nonlinearity may severely degrade the system performance, especially for modulation format with high peak to average power ratio (PAPR) such as orthogonal frequency-division multiplexing (OFDM). We experimentally analyze the OLED nonlinearity by Volterra series and apply the Volterra-based nonlinear equalizer to demodulate the signal. It is shown that the proposed system achieves transmission distance of 3 meters, which exceeds the longest reported in the organic VLC literature. It can mitigate both inter-symbol interference (ISI) and nonlinearity more effectively than other equalizers. Experimental results at different distance and driving voltage are also reported.
TL;DR: In this article, a joint chromatic dispersion (CD) and nonlinearity compensation technique using super-Nyquist image-induced aliasing and a Volterra series-based simplified nonlinear equalizer (SNE) was investigated in a decision feedback manner.
Abstract: For long reach passive optical networks, double-sideband intensity modulation and direct detection can offer the advantages of low cost and low complexity. In this paper, we investigate a joint chromatic dispersion (CD) and nonlinearity compensation technique using super-Nyquist image-induced aliasing and a Volterra series-based simplified nonlinear equalizer (SNE) in a decision feedback manner. The SNE employed in our experiments offers signal-to-noise ratio (SNR) performance comparable to the conventional nonlinear equalizers (NE), but with much fewer coefficients. The distribution of the nonlinear coefficients and the memory length of the SNE/NE are also investigated. Experimental results show that with the proposed aliasing-based CD compensation technique combined with SNE used in each down-sampled signal before per-subcarrier maximum ratio combining, the SNR can be significantly improved. The data rate of the 10-GHz optical OFDM signals is increased by 45%, 52%, and 51% after 48.8, 79.2, and 99.6 km of standard single mode fiber transmission, respectively, compared with those without CD/nonlinearity compensation.
TL;DR: Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two point nonlinear boundary value problem, and, the second explores theApplication of the Volterra series in characterizing the controls.
TL;DR: In this article, a simple non-linear system modelling algorithm designed to work with limited a priori knowledge and short data records is examined, which creates an empirical Volterra series-based model of a system using an l q -constrained least squares algorithm with q ≥ 1.
Abstract: A simple non-linear system modelling algorithm designed to work with limited 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 ≥ 1 . If the system m ⋅ is a continuous and bounded map with a finite memory no longer than some known τ , 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 N − 1 ln D , even for D ≥ 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 characterise the nature of the system, while the sparse solutions obtained for q = 1 yield smaller error values in terms of input-output behaviour.
TL;DR: A novel support vector machine robust version, specifically adapted to a 100 Gb/s CO-OFDM data structure for long haul distance, is proposed and demonstrates that SVM-NLE upgrades the system performance by about 10−1 in terms of bit-error rate and can double the transmission distance up to 1600 km over single mode fibre channel.
Abstract: Classifiers, such as artificial neural networks non-linear equaliser (ANN-NLE), Wiener–Hammerstein non-linear equaliser, Volterra non-linear equaliser (Volterra-NLE) and support vector machine non-linear equaliser (SVM-NLE), can play a significant role in compensating non-linear imperfections in the optical communications context. Using classifiers to mitigate the non-linear effects in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems is an interesting idea to be investigated. In this study, a novel support vector machine robust version, specifically adapted to a 100 Gb/s CO-OFDM data structure for long haul distance, is proposed. Firstly, the authors demonstrate that SVM-NLE upgrades the system performance by about 10−1 in terms of bit-error rate compared to Volterra-NLE at optical signal-to-noise ratio equal to 14 dB. Then, they show that it can double the transmission distance up to 1600 km over single mode fibre channel. Furthermore, a performance comparison is performed using 16 quadrature amplitude modulation and 40 Gb/s bit rate for SVM-NLE, ANN-NLE and inverse Volterra series transfer function non-linear equaliser, respectively.
TL;DR: Experimental results of the predistortion of a commercial power amplifier are given, showing equivalent performance to the pruning with the reference algorithm while further reducing the number of components.
Abstract: Digital predistortion has become an attractive technique for power amplifier linearisation whose limiting factor for using Volterra series as the underlying model is its computational complexity, since the number of components rapidly grows with the non-linear order and memory. Based on a previous reference algorithm, which consists on applying the orthogonal matching pursuit for the sorting of the model components and a Bayesian information criterion for the selection of the optimum number of components, a new technique to reduce the size of the support set taking into account the structural information within a model is presented. Experimental results of the predistortion of a commercial power amplifier are given as a proof of its capabilities, showing equivalent performance to the pruning with the reference algorithm while further reducing the number of components.
TL;DR: The proposed scheme has a higher recognition rate while classifying single and multiple power quality events unlike other methods, and is compared with SVM, feed forward neural network and type −1 Fuzzy logic system based classifier to show the efficacy of the method.
Abstract: 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.
TL;DR: In this article, a data-driven identification method, based on polynomial nonlinear autoregressive models with exogenous inputs (NARX) and the Volterra series, is proposed to describe the dynamic and nonlinear voltage and current characteristics of polymer electrolyte membrane fuel cells (PEMFCs).
TL;DR: In this article, the authors developed a lumped parameter model for the entire electromechanical system, developed an approach to non-destructively determine these parameters, and predict the nonlinear response of the shaker.
TL;DR: In this paper, an efficient nonparametric time domain nonlinear system identification method applied to the measurement benchmark data of the cascaded water tanks is presented, where the transients are removed by a special regularization method based on the novel ideas of transient removal for linear time-varying (LTV) systems.
01 Jul 2017
TL;DR: It is shown that the fifth-order VNLE better combats the fiber nonlinearity in comparison with the third- order VLNE and exhibits closer performance to the DBP.
Abstract: In the context of long-haul Nyquist wavelength division multiplexed (WDM) superchannel system, a fifth-order Volterra-based nonlinear equalizer (VNLE) is proposed to compensate for the optical fiber nonlinear effects, which represent the major fiber impairment in such high data rate systems. A performance comparison of the fifth-order VNLE with the benchmark digital-back propagation (DBP) and the third-order VNLE is provided. We show that the fifth-order VNLE better combats the fiber nonlinearity in comparison with the third-order VLNE and exhibits closer performance to the DBP. A significant improvement of the performance in terms of the Q factor, nonlinear threshold, and transmission reach is observed when compared with the third-order VNLE.
TL;DR: In this paper, a combined first-and second-order theory accounting for the first-order wave loads and nonlinear secondorder slowly varying loads, is established to predict the deckwetness occurrence.
TL;DR: This paper is a survey of the literature about the nonlinear updating process focused on the computation of the difference between the numerical model and the reference data as well as the algorithm uses to find the optimal parameters.
Abstract: This paper is a survey of the literature about the nonlinear updating process. It is focused on the computation of the difference between the numerical model and the reference data as well as the algorithm uses to find the optimal parameters. In both parts of the nonlinear updating process, the popular approaches are presented. Special emphasis is given to methods based on Volterra series.
TL;DR: In this article, a new methodology to analyze non-linear components in perturbative transport experiments is introduced, which has been experimentally validated in the Large Helical Device for the electron heat transport channel.
Abstract: A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.