Adaptive Volterra Filter Research Articles

A class of robust nonlinear quaternion volterra adaptive filter based on recursive Tukey’s Biweight M-estimate and its performance analysis

A class of robust nonlinear quaternion volterra adaptive filter based on recursive Tukey’s Biweight M-estimate and its performance analysis

A Volterra Adaptive Filtering Method for Polar Motion Prediction Based on Chaotic Time Series

In consideration of the complex time-varying characteristics of polar motion (PM), this paper takes PM as chaotic time series. A Volterra adaptive filter is employed for predicting PM based on the state space reconstruction of delay-coordinate embedding of dynamic system. This method first uses the Least Squares (LS) technology to estimate the harmonic models for the linear trend, Annual and Chandler Wobbles (AW and CW) in PM. The selected LS deterministic models are subsequently used to extrapolate the linear trend, AW, and CW, and obtain the LS residues (the difference between the LS model and PM data themselves). Secondly, the phase space and largest Lyapunov exponent of the LS residues are reconstructed, and calculated by means of the C-C and small data-set algorithm, respectively. Further, a Volterra adaptive filter is designed for generating the extrapolations of the LS residues. The extrapolated LS residues are then added to the LS deterministic models in order to obtain the predicted PM values. The EOP C04 time series released by the International Earth Rotation and Reference Systems Service (IERS) are selected as data base to generate the PM predictions up to 60 days in the future. The results of the predictions are analyzed and compared with those obtained by the Earth Orientation Parameters Prediction Comparison Campaign (EOP PCC) and IERS Bulletin A. The results show that the accuracy of the predictions up to 30 days is comparable with that by the most accurate prediction techniques participating in the EOP PCC for PM, but worse than that by those most accurate techniques beyond 30 days in the future. The results also illustrate that the short-term predictions are better than those published by the IERS Bulletin A. However, the errors of the predictions rapidly increase with the prediction days. It is therefore concluded that the proposed method is a potential technology for short-term PM prediction.

SOC prediction of Volterra adaptive filter based on chaotic time series

This paper presents an SOC (State of Charge) prediction method based on a chaotic time series Volterra adaptive filter. This method first verifies the chaotic characteristics of the SOC time series of lithium-ion batteries and then implements the phase space reconstruction method to reorganize the voltage and current data into multi-dimensional data. Furthermore, we use the Volterra adaptive filter to predict the SOC of the lithium-ion battery pack on the reconstructed multi-dimensional data. This method can effectively solve the problem that the SOC estimation error increases due to the poor real-time performance of battery voltage, current, and other parameters of vehicular lithium-ion battery packs in electric vehicles obtained by the battery management system. According to the simulation and test results, the error of the SOC estimation algorithm studied in this paper is less than 0.6%, which indicates that the Volterra adaptive filter based on chaotic time series comprehensively uses the linear and non-linear parameter characteristics of lithium-ion batteries and recombines the voltage and current data into multi-dimensional data through phase space reconstruction technology. It can reveal the relationship between the battery SOC and other variables better, achieve higher precision lithium-ion battery SOC prediction, and have better realizability.

ROBUSTNESS ANALYSIS OF THE DATA-SELECTIVE VOLTERRA NLMS ALGORITHM

Recently, the data-selective adaptive Volterra filters have been proposed;however, up to now, there are not any theoretical analyses on its behavior rather than numerical simulations. Therefore, in this paper, we analyze the robustness (in the sense of l_2-stability) of the data-selective Volterra normalized least-mean-square (DSVNLMS) algorithm. First, we study the local robustness of this algorithm at any iteration, then we propose a global bound for the error/discrepancy in the coefficient vector. Also, we demonstrate that the DS-VNLMS algorithm improves the parameter estimation for the majority of the iterations that an update is implemented. Moreover, we also prove that if the noise bound is known, then we can set the DS-VNLMS so that it never degrades the estimate. The simulation results corroborate the validity of the executed analysis and demonstrate that the DS-VNLMS algorithm is robust against noise, no matter how its parameters are adopted.

A family of quaternion-valued pipelined second-order Volterra adaptive filters for nonlinear system identification

This paper primarily proposes a family of quaternion Volterra filters based on the feedforward pipelined structure (QPSOVAFs) for nonlinear quaternion system identification to reduce the computational complexity. Then, the strictly nonlinear QPSOVAF (SNL-QPSOVAF), semi-widely nonlinear QPSOVAF(SWNL-QPSOVAF) and widely nonlinear QPSOVAF (WNL-QPSOVAF) are proposed. This architecture consists of several quaternion-valued second-order Volterra (SOV) modules. The structure’s nonlinear subsection executes a nonlinear mapping from the input space to an intermediate space using the feedforward SOV; the linear combiner subsection performs a linear mapping from the intermediate space to the output space. Moreover, the theoretical analysis expresses the effectiveness of the proposed QPSOVAFs in a specific condition. Finally, simulation results further prove that the proposed QPSOVAFs have good performance in identifying the quaternion-valued nonlinear system.

A Robust Fully Arctangent Adaptive Interpolated Volterra Filtering Algorithm Against Impulsive Noise

The applicability of adaptive Volterra filter is greatly limited by the high computational complexity and notable performance degradation when encountering the impulsive noise. Although the existing interpolated adaptive Volterra filter has reduced the computational complexity, its performance is still significantly degraded while the impulsive noise occurs. This brief proposes a robust fully arctangent adaptive fully interpolated Volterra (RFAAFIV) filtering algorithm by using the novel arctangent function. The proposed algorithm can effectively improve the robustness against impulsive noise while requiring the low computational cost. Moreover, the computational complexity and the steady-state mean square performance of the proposed RFAAFIV algorithm are analyzed. Simulations on nonlinear system identification further evaluate the effectiveness of the RFAAFIV algorithm against impulsive noise and verify the theoretical analysis.

Network traffic prediction method based on autoregressive integrated moving average and adaptive Volterra filter

SummaryIn the process of controlling network congestion and network management, how to accurately predict network traffic is very important. A network traffic prediction method based on autoregressive integrated moving average (ARIMA) model and adaptive Volterra filter model is proposed in this study. Firstly, ARIMA model is utilized to capture and predict the linear features of network traffic time series. The residual sequence is generated by network traffic sequence minus ARIMA predictive value sequence. The residual sequence only contains the nonlinear characteristics of original network traffic. Then an adaptive Volterra filter is used to train and predict the nonlinear residual sequence of original network traffic. The optimal parameters of adaptive Volterra filter are obtained by improved particle swarm optimization algorithm. Add the linear value predicted by ARIMA and the nonlinear value predicted by adaptive Volterra filter to get the final predicted value. The simulation results show that the proposed prediction method has high accuracy, small prediction error, and high reliability.

Design of quaternion-valued second-order Volterra adaptive filters for nonlinear 3-D and 4-D signals

In this paper, the quaternion-valued second-order Volterra adaptive filters (QSOVAFs) are designed for the processing of nonlinear three-dimensional (3-D) and four-dimensional (4-D) signals. In the proposed frameworks, the structure of the strictly nonlinear (SNL), semi-widely nonlinear (SWNL), and widely nonlinear (WNL) QSOVAFs are primarily constructed in the quaternion domain. Then, their loss functions defined by the instantaneous error signals are minimized in the quaternion domain by using the recent generalized Hamilton-real (GHR) calculus. Thus, novel weight update equations are obtained for training the proposed SNL-QSOVAF, SWNL-QSOVAF, and WNL-QSOVAF. Furthermore, the stability bounds for each quaternion-valued kernel functions of them are derived from the convergence in the mean analysis. The comprehensive simulations on the nonlinear system identification and one-step-ahead prediction experiments support that the proposed SWNL-QSOVAF and WNL-QSOVAF can be effectively used in the processing of nonlinear noncircular quaternion signals, whereas that their SNL version can produce optimal results for nonlinear circular quaternion signals.

Physical configuration-based feedforward active noise control using adaptive second-order truncated Volterra filter

This paper presents a physical configuration-based feedforward active noise control scheme with an adaptive second-order truncated Volterra filter for point source cancellation in three-dimensional free-field acoustic environment. The inertial particle swarm optimization (PSO) algorithm is used as the parameter adjustment mechanism for tuning the coefficients of the adaptive Volterra filter. The first motivation of this paper is to provide a precise description of the relationship between the degree of cancellation and the physical distances between system components. The second motivation is to improve the cancellation performance in the presence of nonlinearities with the adaptive Volterra filter in light of the characteristics of sensing microphone and actuating loudspeaker. The reason for choosing the inertial PSO algorithm is that it can avoid the trap of local optima. The work thus presented makes two main contributions. The first is using the degree of cancellation as a function of the physical distances between system components to provide a quantitative analysis of system performance. The second is the application of the adaptive Volterra filter, which achieves improvements in the cancellation performance of the system under different physical configurations with a reasonable compromise with complexity. For consistency with the numerical analysis, several simulation experiments are conducted using MATLAB/Simulink.

Short-term natural gas consumption prediction based on Volterra adaptive filter and improved whale optimization algorithm

Short-term natural gas consumption prediction is an important indicator of natural gas pipeline network planning and design, which is of great significance. The purpose of this study is to propose a novel hybrid forecast model in view of the Volterra adaptive filter and an improved whale optimization algorithm to predict the short-term natural gas consumption. Firstly, Gauss smoothing and C–C method is adopted to pretreat and reconstruct short-term natural gas consumption time series; secondly, to improve the performance of whale optimization algorithm, adaptive search-surround mechanism and spiral position and jumping behavior are introduced into it; Thirdly, Volterra adaptive filter is used to predict the short-term natural gas consumption, and the important parameters (e.g. embedding dimension) is optimized by improved whale optimization algorithm. Finally, an actual example is given to test the performance of the developed prediction model. The results indicate that (1) short-term natural gas consumption time series has chaotic characteristics; (2) performance of the improved whale optimization algorithm is better than some comparative algorithms (i.e. cuckoo optimization algorithm, etc. ) based on the different evaluation indicators; (3) exploration factor is the main operational factor; (4) the performance of the proposed prediction model is better than some advanced prediction models (e.g. back propagation neural network). It can be concluded that such an innovative hybrid prediction model may provide a reference for natural gas companies to achieve intelligent scheduling.

Numerical Investigation of Long-Haul Coherent Optical Generalized Frequency Division Multiplexing Signal

Generalized frequency division multiplexing (GFDM) is a recent physical layer scheme proposed for next-generation cellular systems. Like orthogonal frequency division multiplexing (OFDM), it is based on multicarrier modulation, but the filter shape is no longer rectangular (roll off ≠ 0) and the orthogonality between subcarriers is lost. With higher flexibility, low peak to average power ratio (PAPR) and reduced out-of-band emissions compared with OFDM, GFDM modulation is an attractive candidate for 5G application scenarios. This paper explores the performance of 10 Gb/s GFDM system over the optical link in terms of PAPR, quality factor ( Q factor), and mean squared error using a third-order adaptive Volterra filter with 3 and 5 taps. The impact of linear impairments (chromatic dispersion, polarization mode dispersion), laser line width, and Mach–Zehnder non-linearity have been addressed. The results of our simulations indicate that the transmitted 10 Gb/s GFDM signal through an optical fiber can reach 930 Km and Q = 11.9 dB after 700 Km at –8 dBm of launch power using 5 taps third-order adaptive Volterra equalizer with an improvement of approximately 210 Km and 1.25 dB compared with the same equalizer with 3 taps.

Extraction of Opening and Closing States of Cracked Structure using Adaptive Volterra Filter Model

Fatigue cracks often exist in structures during the service life of the structure and need to detect at its earliest stage before it leads to catastrophic failure. The fatigue breathing crack problem exhibits an instantaneous change in the stiffness of the structure due to change in the state of the cracked domain from open to close and vice versa. Therefore these fatigue cracks exhibit breathing like phenomena, hence widely referred as breathing cracks. The present work attempts to separate the opening and closing of the cracked structure from the global response using adaptive Volterra Filter Model. Adaptive Volterra Filter model is a generalization of the linear convolution and the impulse response function to nonlinear structures in discrete form. The dynamical properties of the nonlinear system in the Volterra series representation or adaptive Volterra Filter Model are completely characterized by a sequence of multi-dimensional weighting function called Volterra kernels. These Volterra kernels are the backbone of adaptive Volterra filter approach in nonlinear analysis and system identification and diverse range of techniques are reported in the literature for Volterra kernel estimation. Adaptive Volterra series based Least square is used in the present work to estimate Volterra kernels. The various states of the cracked structure are then estimated using these Volterra kernels. Numerical simulation studies are carried out on a simple beam example to demonstrate the capability of the proposed adaptive Volterra filter in extracting the opening and closing state response from the global response of the cracked structure.

Nonlinear Structural Damage Detection Based on Adaptive Volterra Filter Model

The majority of the existing damage diagnostic techniques are based on linear models. Changes in the state of the dynamics of these models, before and after damage in the structure based on the vibration measurements, are popularly used as damage indicators. However, the system may initially behave linearly and subsequently exhibit nonlinearity due to the incipience of damage. Breathing cracks that exhibit bilinear behavior are one such example of the damage induced due to nonlinearity. Further many real world structures even in their undamaged state are nonlinear. Hence, in this paper, we present a nonlinear damage detection technique based on the adaptive Volterra filter using the nonlinear time history response. Three damage indices based on the adaptive Volterra filter are proposed and their sensitiveness to damage and noise is assessed through two numerically simulated examples. Numerical investigations demonstrate the effectiveness of the adaptive Volterra filter model to detect damage in nonlinear structures even with measurement noise.

Data-Selective Volterra Adaptive Filters

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.

Yellow River runoff forecast based on Volterra adaptive filter

Yellow River runoff forecast based on Volterra adaptive filter

Partially Decoupled Adaptive Filter Based Multifunctional Three-Phase GPV System

This paper deals with partially decoupled adaptive Volterra filter (PDAVF) based control for a three-phase two-stage grid-interfaced photovoltaic (GPV) system. Besides maximum power extraction, the proposed control is having the potential of grid currents balancing, harmonics currents mitigation, reactive power compensation, and adaptive adjustment of DC bus voltage. The control technique is efficient in extraction of weight component of reference grid currents and an adaptation routine of filter weights uses the principle of fifth-order PDAVF with single-element observation vector implemented by using the method of least mean squares (LMS). An increased order of partial filter assures accurate estimation of filter weights by adaptive weight update at each filter step. The convergence is ensured by providing bounds on algorithm's step size. The algorithm overcomes drawbacks of Adaline-based LMS and LMF (least mean fourth) based weight estimations without imposing high computational burden. The switching losses in voltage source converter are minimized using adaptive DC bus voltage. Effectiveness of PDAVF is presented through simulation and test results. These results are found satisfactory with improved steady state and dynamic performances and total harmonic distortion of grid currents meet an IEEE-519 standard.

Nonlinear Adaptive Volterra Filter for Control of Distribution Static Compensator

This paper presents nonlinear adaptive Volterra filter for control of three-phase four wires Distribution Static Compensator under mixed type linear and nonlinear load. The proposed adaptive filter identifies and measures active and reactive weights of the fundamental components of load currents. These weights are used to generate the reference signals such that the currents drawn from a supply are close to balanced and sinusoidal. The performance of the proposed control algorithm is observed under nonlinear load in the laboratory environment. The test results are found satisfactory as total harmonic distortion in supply currents are within the 5% levels specified by the IEEE Standard 519-1992.

Adaptive filtering for white-light LED visible light communication

White-light phosphor-based light-emitting diode (LED) can be used to provide lighting and visible light communication (VLC) simultaneously. However, the long relaxation time of phosphor can reduce the modulation bandwidth and limit the VLC data rate. Recent VLC works focus on improving the LED modulation bandwidths. Here, we propose and demonstrate the use of adaptive Volterra filtering (AVF) to increase the data rate of a white-light LED VLC system. The detailed algorithm and implementation of the AVF for the VLC system have been discussed. Using our proposed electrical frontend circuit and the proposed AVF, a significant data rate enhancement to 700.68 Mbit / s is achieved after 1-m free-space transmission using a single white-light phosphor-based LED.

Collaborative adaptive Volterra filters for nonlinear system identification in α-stable noise environments

The least mean pth power (LMP) and normalized LMP (NLMP) algorithms of adaptive Volterra filter have been successfully developed for nonlinear system identification in α-stable noise environments. However, there exists an inherent tradeoff between the convergence rate and steady-state performance. To address this compromise, a collaborative adaptive Volterra filter based on the convex combination scheme is proposed under the α-stable noise in this paper. By utilizing the convex combination which performs at least as well as the best component filter, the proposed algorithms achieve fast convergence rate and small misadjustment. Furthermore, by following a frame of the generalized combination scheme, two novel combination structures of Volterra filter are presented. Simulations in nonlinear system identification contexts demonstrate that the performances of the proposed algorithms are superior to the existing algorithms under the α-stable noise in terms of the convergence speed and steady state kernel error.

Drought class transition analysis through different models: a case study in North China

The standardized precipitation index (SPI) and standardized runoff index (SRI) are computed for several gauge stations in Panjiakou Reservoir catchment of Luanhe Basin, a drought prone region of North China. Based on the SPI and SRI time series, two different models, a weighted Markov chain model and a Volterra adaptive filter model for chaotic time series, were established to predict drought classes and achieve both short- and long-term drought forecasting. These approaches were compared with a three-dimensional (3D) loglinear model, reported in our previous work. It was observed that all the three models have pros and cons when applied to drought prediction in Panjiakou Reservoir catchment. The 3D loglinear model is able to forecast drought class within 1 month. However, its predicting accuracy declines with the increase of prediction time scale, and this confines its application. The weighted Markov chain model is a useful tool for drought early warning. Its precision, which is significantly related to the stable condition of drought classes, is highest for Non-drought, followed by Moderate and Severe/Extreme drought, and lowest for Near-normal. The Volterra adaptive filter model for chaotic time series combined the phase space reconstruction technique, Volterra series expansion technique and adaptive filter optimization technique, and was for the first time used in a drought class transition study. This model is effective and highly precise in long-term drought prediction (for example, 12 months). It is able to provide reliable information for the medium- and long-term decisions and plans for water resources systems.