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When a probe particle immersed in a fluid with nonlinear interactions is subject to strong driving, the cumulants of the stochastic force acting on the probe are nonlinear functionals of the driving protocol. We present a Volterra series for these nonlinear functionals by applying nonlinear response theory in a path integral formalism, where the emerging kernels are shown to be expressed in terms of connected equilibrium correlation functions. The first cumulant is the mean force, the second cumulant characterizes the non-equilibrium force fluctuations (noise), and higher order cumulants quantify non-Gaussian fluctuations. We discuss the interpretation of this formalism in relation to Langevin dynamics. We highlight two example scenarios of this formalism. (i) For a particle driven with the prescribed trajectory, the formalism yields the non-equilibrium statistics of the interaction force with the fluid. (ii) For a particle confined in a moving trapping potential, the formalism yields the non-equilibrium statistics of the trapping force. In simulations of a model of nonlinearly interacting Brownian particles, we find that nonlinear phenomena, such as shear-thinning and oscillating noise covariance, appear in third- or second-order response, respectively. [ABSTRACT FROM AUTHOR]

Machine learning and artificial intelligence algorithms typically require a large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden associated with generating data, the usability of such methods has been limited to highly simplified aeroelastic systems. This paper presents a novel approach for the identification of optimized sparse higher-order polynomial-based aeroelastic reduced order models (ROMs) to significantly reduce the amount of training data needed without sacrificing fidelity. Several sparsity promoting algorithms are considered, including rigid sparsity, least absolute shrinkage and selection operator (LASSO) regression, and orthogonal matching pursuit (OMP). The study demonstrates that through OMP, it is possible to efficiently identify optimized s-sparse nonlinear aerodynamic ROMs using only aerodynamic response information. This approach is exemplified in a three-dimensional aeroelastic stabilator model experiencing high-amplitude freeplay-induced limit cycles. The comparison shows excellent agreement between the ROM and the full-order aeroelastic response, including the ability to generalize to new freeplay and velocity index values, with online computational savings of several orders of magnitude. The development of an optimally sparse ROM extends previous higher-order polynomial-based ROM approaches for feasible application to complex three-dimensional nonlinear aeroelastic problems, without incurring significant computational burdens or loss of accuracy. [ABSTRACT FROM AUTHOR]

This paper applied the fuzzy function approach, combined with the ridge regression model, to produce daily rainfall projections from large-scale climate variables. This study developed a statistical downscaling model based on principal components, c-means fuzzy clustering, Volterra series, and ridge regression. The model is known, hereafter as SDC2R2. In the developed downscaling model, the use of ridge regression, instead of multiple linear regression, is proposed to downscale daily rainfall with wide range (WR) predictors. The WR predictors were applied to sufficiently incorporate climate change signals. The developed model also captured the non-linear interactions of the climate variables by applying the transformation of Volterra series realization over WR predictors. This transformation was performed by applying principal components as orthogonal filters. Further, these principal components were clustered by using c-means clustering and non-linear transformations were applied on these membership functions, to improve the prediction ability of the model. The reanalysis of climate data from the National Centres for Environmental Prediction (NCEP) was used to develop the model and was validated by using the Global Climate Model (GCM) for four locations in the Manawatu River basin. The developed model was used to obtain future daily rainfall projections from three Representative Concentrative Pathways (RCP 2.6, RCP 4.5, and RCP 8.5) scenarios from the Canadian Earth System Model (CanESM2) GCM. The performance of the model was compared with a widely used statistical downscaling model (SDSM). It was observed that the model performed better than SDSM in downscaling rainfall on a daily basis. Every scenario indicated that there is a probability of obtaining high future rainfall frequency. The results of this study provide valuable information for decision-makers since climate change may potentially impact the Manawatu basin. [ABSTRACT FROM AUTHOR]

【Objective】The non-linear characteristics of Light Emitting Diodes (LEDs) contribute to the degradation of Bit Error Rate (BER) performance in Visible Light Communication (VLC) systems, particularly in Optical Orthogonal Frequency Division Multiplexing (O-OFDM) systems with high Peak-to-Average Power Ratio (PAPR). A single-stage equalizer based on the Volterra series can handle the high-order non-linear distortions of LEDs with low latency. However, solving the traditional Volterra series necessitates multiple integration operations, resulting in the high implementation complexity of the Volterra-based equalizer. Additionally, the single-stage equalizer accumulates errors with limited performance improvements.【Methods】Firstly, to address the issue of high computational complexity in the traditional calculations of the Volterra series, a proposition is made to retain only the high-order power series terms of the various nonlinear terms and kernel coefficients within the Volterra series. This approach, known as the Memory Polynomial-based Volterra Series (MPVS), not only reduces the computational complexity compared to the traditional Volterra series but also enhances the accuracy of nonlinear system modeling by considering all input signals at the current moment. Subsequently, the design of channel equalizer considers the Memory Polynomial-based Volterra (MPV) equalizer and the Memory Polynomial-based Volterra Decision Feedback Equalizer (MPV-DFE). For a single-stage MPV-DFE, if an error occurs in the decision part leading to an incorrect symbol decoding, this error tends to manifest as a consecutive series of errors, thereby impacting the entire symbol sequence. To mitigate this, a proposal is made to cascade the two non-linear equalizers, MPV and MPV-DFE, forming a hybrid equalizer called MPV+MPV-DFE. The MPV equalizer performs a primary equalization on the LED's nonlinear distortion signal, effectively suppressing a portion of the non-linear distortions and thereby reducing symbol decoding errors in the MPV-DFE. Subsequently, a secondary equalization is carried out by the MPV-DFE, leading to improved suppression of residual nonlinear distortions.【Results】Finally, the effectiveness of the system design was validated using Monte Carlo simulation to analyze the BER. The results demonstrate that compared to the single-stage MPV equalizer and the linear-cascade nonlinear hybrid equalizer (LMS+MPV-DFE), the proposed hybrid equalizer achieves approximately 7 dB and 2 dB Signal-to-Noise Ratio (SNR) gains, respectively, in a 4 Quadrature Amplitude Modulation (QAM) -modulated Asymmetrically Clipped Optical OFDM (ACO-OFDM) system at a BER of 10-4.【Conclusion】In conclusion, the implementation of the MPV equalizer is straightforward, and the cascaded design of the two-stage nonlinear equalizers as a hybrid equalizer enables better mitigation of the LED’s nonlinearity.

The practical implementation of many quantum algorithms known today is limited by the coherence time of the executing quantum hardware and quantum sampling noise. Here we present a machine learning algorithm, NISQRC, for qubit-based quantum systems that enables inference on temporal data over durations unconstrained by decoherence. NISQRC leverages mid-circuit measurements and deterministic reset operations to reduce circuit executions, while still maintaining an appropriate length persistent temporal memory in the quantum system, confirmed through the proposed Volterra Series analysis. This enables NISQRC to overcome not only limitations imposed by finite coherence, but also information scrambling in monitored circuits and sampling noise, problems that persist even in hypothetical fault-tolerant quantum computers that have yet to be realized. To validate our approach, we consider the channel equalization task to recover test signal symbols that are subject to a distorting channel. Through simulations and experiments on a 7-qubit quantum processor we demonstrate that NISQRC can recover arbitrarily long test signals, not limited by coherence time. Inherent limitations on continuously measured quantum systems calls into question whether they could even in principle be used for online learning. Here, the authors experimentally demonstrate a quantum machine learning framework for inference on streaming data of arbitrary length, and provide a theory with criteria for the utility of their algorithm for inference on streaming data. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear Volterra series expansion is extended and used to describe certain types of nonautonomous differential equations related to the inverse scattering problem in nuclear physics. The nonautonomous Volterra series expansion lets us determine a dynamic, polynomial approximation of the variable phase approximation (VPA), which is used to determine the phase shifts from nuclear potentials through first-order nonlinear differential equations. By using the first-order Volterra expansion, a robust approximation is formulated to the inverse scattering problem for weak potentials and/or high energies. The method is then extended with the help of radial basis function neural networks by applying a nonlinear transformation on the measured phase shifts to be able to model the scattering system with a linear approximation given by the first-order Volterra expansion. The method is applied to describe the |${}^1S_0$| NN potentials in neutron+proton scattering below 200 MeV laboratory kinetic energies, giving physically sensible potentials and below |$1\%$| averaged relative error between the recalculated and the measured phase shifts. [ABSTRACT FROM AUTHOR]

The existing sparse adversarial attack methods for color images often overlook the interplay between RGB channels. In saliency analysis, only the individual impact of each input variable on the output is considered, while their interaction effects are disregarded. In order to overcome the lack of sparsity caused by inaccurate saliency analysis methods, we propose a sparse adversarial example generation method for color images based on Volterra expansion of color channels. Firstly, Volterra expansion is performed on different RGB channels, and a saliency analysis method is implemented to relate the interaction effects of different RGB channels. Then, the sparse adversarial perturbation is generated by a heuristic method with multiple iterations. Compared with the existing sparse adversarial attack methods for white-box color images, our proposed method can obtain sparser results with the same attack effect. [ABSTRACT FROM AUTHOR]

This article proposes a new nonlinear behavioral analysis of the Spice diode model by using Volterra series theory, in which the expression of the third‐order intermodulation was expressed. Moreover, the impact on the behavior of diode CV characteristic parameters Zero‐bias Junction capacitance Cjo, gradient coefficient M, and built‐in potential Vj are discussed. Two‐tones harmonic balance simulations are performed with the hpeesofsim circuit simulator. Results are consistent with the Volterra series analysis, showing the rationality and validity of this behavioral modeling method. [ABSTRACT FROM AUTHOR]

The evolution of Digital Predistortion (DPD) for Power Amplifier (PA) linearization in wireless communications has seen a natural progression towards increasingly complex DPD models. This complexity directly correlates with improved accuracy in modeling PAs, thereby enhancing the linearization performance of DPD systems. As the demand for bandwidth and PA operation frequencies continues to rise, there is a growing trend towards achieving higher accuracy at the expense of increased complexity. This trend poses challenges for DPD design, necessitating the introduction of more complex algorithms to ensure effective PA linearization. This phenomenon is especially apparent in Volterra Series DPD algorithms, which are widely used for modelling nonlinear systems like PAs. This paper showcases the steps of reducing the modelling operations complexity of the Simplified Volterra (SV) method. The treated SV method presented in this paper is compared against the original SV method through simulation. The DPD model operations complexity is evaluated using the number of required multiplication operations. The DPD PA linearization performance is evaluated with respective model’s Normalized Mean Square Error (NMSE). A 57% reduction on the number of multiplication operations is observed in the treated SV against the original SV. Measured NMSE is similar for both models, indicating the treated SV model achieves this reduction in complexity without sacrificing linearization performance. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of quantifying nonlinear output frequency response components of different orders of nonlinear dynamical systems for a general excitation. An alternative approach is presented based on Volterra series and conditioned spectral analysis (CSA) theories. Firstly, a multiple-input/single-output (MISO) linear system with a series of power characterized inputs is obtained by decomposing the nonlinear system under analyzed based on Volterra series. Secondly, the correlations among the inputs of different orders are removed by utilizing CSA approach, obtaining an algorithm of identifying the nonlinear output frequency response functions (NOFRFs) and evaluating the contributions of different order nonlinearities to the output of the system. Two kinds of nonlinear systems were simulated numerically to verify the accuracy of the method. The results reached by the proposed method are very close to the numerical results obtained by the fourth order Runge–Kutta method. Finally, an experiment analysis was carried out, in which the vibration transmission properties of a bolt connection were tested when the bolt was fastened and loose respectively. The results of experiments reflected further the effectiveness of the method on distinguishing quantitatively the contributions of each order nonlinearities to the output of a nonlinear system. [ABSTRACT FROM AUTHOR]

Enhancing the dynamic properties of expansive soils using cementitious materials has attracted the attention of many researchers over the past few decades. Supplementary cementitious materials (SCMs) can be used as partial substitutes for cement owing to their pozzolanic activity that further improves the mechanical performance of cement-stabilized soils upon curing. In this study, the effect of cement and zeolite incorporation on the mechanical behavior of expansive clay was quantified using the pressure wave velocity (Vp) indicator obtained from ultrasonic pulse velocity tests performed at different curing times. Furthermore, a polynomial model was developed to establish the relationship between Vp and zeolite replacement levels at specific curing times and cement contents. The results show that a polynomial function captured the decreasing trend of Vp upon the increase in zeolite at curing times below 14 days. Additionally, the developed equation explained the upward trend of Vp owing to the pozzolanic activity of zeolite at later curing times with an accuracy of over 92%. The coefficients of the polynomial model also increased with the increment of the cement percentage which conformed to the consecutive rise in Vp. Ultimately, the polynomial coefficients were expressed in terms of cement content and curing time using the Volterra series. Using this model, the optimum percentage of cement replaced with zeolite (Zopt), the efficiency of using Zopt instead of cement, and the percentage of zeolite replacement to achieve equivalent Vp of cemented clay samples (ZC) were estimated. The findings of this study contribute to promoting geotechnical sustainability by replacing cement with zeolite that has a considerably lower environmental footprint. Clay is a type of soil that can be found in many construction projects. For instance, many roads and buildings' foundations are constructed on clay soils. To ensure the necessary strength of the clay under the main structure, the soil should often be stabilized using adhesive construction materials such as cement. Interestingly, a portion of the cement could be replaced with other minerals not only to improve engineering performance but also to promote sustainability by lowering cement consumption. In this study, the effect of zeolite as a partial replacement for cement on the strength of clay soils was experimentally evaluated. The effect of various design parameters, such as cement replacement level and curing time, on the stability of clays was investigated using an advanced technique called the ultrasonic pulse velocity (UPV) test. Furthermore, a simple mathematical model was proposed based on the experimental results to help engineers design the stabilization plan and timely decide about the next steps of the construction process. [ABSTRACT FROM AUTHOR]

Copyright of Study on Optical Communications / Guangtongxin Yanjiu is the property of Study on Optical Communications Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this article, two numerical methods (collocation method and Taylor method) are introduced to solve Volterra integral equation system. In the collocation method, using Bessel polynomials and collocation points, we convert the device into a matrix form and solve the device using the matrix form and obtain an approximate solution for the device. This answer is such that the larger the N becomes, the approximate answer is closer to the exact answer of the device. In Taylor method, With the use of the Taylor series, the system of integral equations is transformed into a matrix equation, and by integrating the output of this new system, a system of algebraic equations is created. By working through this device, we can obtain a rough solution for the Integral Equations device. Using these two methods when the answers are polynomial, we can get real answers. [ABSTRACT FROM AUTHOR]

In this paper a new method to find the parametric faults in weakly nonlinear analog circuit is proposed. Frequency domain volterra kernels are derived to calculate the test parameters i.e., nonlinear distortions and the cross spectral density. Volterra kernels are sensitive to device parameter and the components used to build the circuit. Device parameter and each component value are varied within the tolerance limit using Monte Carlo simulation. For the fault free circuit maximum and minimum values of the 3rd order harmonic, intermodulation distortion and the cross spectral density are measured. During testing, single and multiple faults are injected and the test parameters are measured. If any one or more test parameters are outside the predetermined bounds the circuit is declared to be faulty. This proposed method offers high fault coverage capability. To validate this method CMOS differential amplifier circuit is taken under consideration. [ABSTRACT FROM AUTHOR]

Uninterrupted monitoring of fetal cardiac health is essential for the timely diagnosis of congenital diseases. The maternal Electrocardiogram (mECG), which has the most significant impact, always tampers with the signals collected from the pregnant woman's abdomen. So, an efficient nonlinear filtering network based on artificial neural network (ANN) is required to eliminate the maternal part from the abdominal Electrocardiogram (aECG) that is traveled from the thoracic of the mother to the abdomen following nonlinear dynamics. In this work, we have presented an adaptive noise canceler (ANC) using 3-layer perceptron architecture where the inputs are expanded by the functional link expansion using the second-order Volterra series, and the weights are updated using backpropagation. The adaptive filter approximates the nonlinear mapping between the thoracic Electrocardiogram (tECG) and the maternal component present in the aECG. Here the thoracic signal is the reference signal, and the abdominal signal is the desired signal to the adaptive filter. The proposed methodology uses the advantages of both multilayer perceptron (MLP) as well as functional link neural network (FLNN) in mapping the nonlinearity and effectively determining the fetal Electrocardiogram (fECG) from the aECG. For the detailed analysis, we have used the real Daisy database, the Non-invasive Fetal ECG database, and the fetal ECG synthetic database from Physionet. The results show that the nonlinear functional link MLP using the Volterra series gives a high-level performance compared to other classical adaptive filtering techniques, as all the evaluation metrics are above 90%. [ABSTRACT FROM AUTHOR]

【Objective】Optical fiber dispersion, nonlinear impairments, and bandwidth limitation in high-speed passive optical access networks result in significant power budget loss with traditional intensity modulation and direct detection schemes, failing to meet the requirements of high-speed passive optical access networks.【Methods】In order to enhance the rate and performance of the intensity modulation and direct detection optical access system, this study explores the channel equalization method of VDFE-RLS based on Recursive Least Squares (RLS) algorithm, building upon the Volterra Decision Feedback Equalizer (VDFE), This equalizer uses RLS algorithm to update its tap coefficients. It includes a three-order Volterra series, allowing it to compensate for both linear and nonlinear impairments. VDFE-RLS is applied to the downlink optical access system with a single wavelength of 200 Gbit/s based on O-band intensity modulation and direct detection scheme after 20 km transmission.【Results】The experimental results show that the RLS outperforms the conventional Least Mean Square (LMS) algorithm in the equalization process. Moreover, VDFE-RLS achieves a power budget greater than 29 dB. When the length of the equalizer is the same, VDFE-RLS can increase the power budget by 2.2 dB compared with the conventional Volterra Feed Forward Equalization (VFFE)-RLS equalizer. When the length of VDFE-RLS equalizer is half that of VFFE-RLS, the VDFE-RLS can increase the power budget by 0.5 dB compared with the VFFE-RLS equalizer.【Conclusion】Compared with other traditional methods, the proposed method can shorten the length of the equalizer and increase the power budget of the system, ultimately restoring signals with better performance.

The Volterra integral-functional series is the classic approach for nonlinear black box dynamical system modeling. It is widely employed in many domains including radiophysics, aerodynamics, electronic and electrical engineering and many others. Identifying the time-varying functional parameters, also known as Volterra kernels, poses a difficulty due to the curse of dimensionality. This refers to the exponential growth in the number of model parameters as the complexity of the input-output response increases. The least squares method (LSM) is widely acknowledged as the standard approach for tackling the issue of identifying parameters. Unfortunately, the LSM suffers with many drawbacks such as the sensitivity to outliers causing biased estimation, multicollinearity, overfitting and inefficiency with large datasets. This paper presents an alternative approach based on direct estimation of the Volterra kernels using the collocation method. Two model examples are studied. It is found that the collocation method presents a promising alternative for optimization, surpassing the traditional least squares method when it comes to the Volterra kernels identification including the case when input and output signals suffer from considerable measurement errors. [ABSTRACT FROM AUTHOR]

Purpose: Online question-and-answer (Q&A) communities serve as important channels for knowledge diffusion. The purpose of this study is to investigate the dynamic development process of online knowledge systems and explore the final or progressive state of system development. By measuring the nonlinear characteristics of knowledge systems from the perspective of complexity science, the authors aim to enrich the perspective and method of the research on the dynamics of knowledge systems, and to deeply understand the behavior rules of knowledge systems. Design/methodology/approach: The authors collected data from the programming-related Q&A site Stack Overflow for a ten-year period (2008–2017) and included 48,373 tags in the analyses. The number of tags is taken as the time series, the correlation dimension and the maximum Lyapunov index are used to examine the chaos of the system and the Volterra series multistep forecast method is used to predict the system state. Findings: There are strange attractors in the system, the whole system is complex but bounded and its evolution is bound to approach a relatively stable range. Empirical analyses indicate that chaos exists in the process of knowledge sharing in this social labeling system, and the period of change over time is about one week. Originality/value: This study contributes to revealing the evolutionary cycle of knowledge stock in online knowledge systems and further indicates how this dynamic evolution can help in the setting of platform mechanics and resource inputs. [ABSTRACT FROM AUTHOR]

Due to increase in number of users and demand for higher data rates, the development of transmission systems which meets these requirements is of concern. Radio over Fiber (RoF) has emerged as such kind of technology which not only caters these requirements but also has the advantage of low system complexity, power consumption maintenance costs and low attenuation. But RoF systems suffer from nonlinear distortion caused by the presence of nonlinear system components. This nonlinear distortion results in intermodulation distortion and hence degrades system performance. For mitigating nonlinear distortion, a linearizer is required. A linearizer has inverse characteristics to that of RoF link. For design of the linearizer, accurate modelling of RoF link is required. So, in this paper, we have presented the modelling of a nonlinear RoF ink using cross term memory polynomial. [ABSTRACT FROM AUTHOR]

This study is concerned by the Collocation method for solving Volterra integral equations form of the Lane-Emden type numerically through the so-called Touchard polynomials, which are essentially binomial polynomials. Where the system of miniature linear equations is solved numerically using the MATALEB program. Then some examples are presented to verify the reliability and effectiveness of the method in addition to the speed of its convergence. [ABSTRACT FROM AUTHOR]

Background. Digital signal processing involves sampling continuous signals. Unlike linear systems, performing this operation in nonlinear systems has a number of features associated with expanding the spectrum of the output signal. The purpose of this research is to study the sampling of signals in nonlinear systems when solving problems of modeling the dynamics of the system and restoring the output signal. Materials and methods. A class of nonlinear systems defined by the Volterra expansion is considered. Discrete nonlinear filters are used to digitally simulate system behavior. The spectral representation of nonlinear systems through multidimensional characteristics (kernels) in the frequency domain is used. Results and conclusions. The choice of sampling frequency in nonlinear systems is determined by the type of problem being solved. At the same time, the tasks of identifying the dynamic characteristics of the system and restoring the output signal of the system are highlighted. For the linear case, these problems are identical and their solution is achieved by choosing the sampling frequency of the input signal in accordance with Kotelnikov’s theorem. It is shown that the effect of expanding the spectrum of the output signal imposes different requirements on the choice of sampling frequency when solving problems of identifying and restoring the output signal in nonlinear systems.

Optimal allocation of ward beds is crucial given the respiratory nature of COVID-19, which necessitates urgent hospitalization for certain patients. Several governments have leveraged technology to mitigate the pandemic's adverse impacts. Based on clinical and demographic variables assessed upon admission, this study predicts the length of stay (LOS) for COVID-19 patients in hospitals. The Kolmogorov–Gabor polynomial (a.k.a., Volterra functional series) was trained using regularized least squares and validated on a dataset of 1600 COVID-19 patients admitted to Khorshid Hospital in the central province of Iran, and the five-fold internal cross-validated results were presented. The Volterra method provides flexibility, interactions among variables, and robustness. The most important features of the LOS prediction system were inflammatory markers, bicarbonate (HCO3), and fever—the adj. R2 and Concordance Correlation Coefficients were 0.81 [95% CI: 0.79–0.84] and 0.94 [0.93–0.95], respectively. The estimation bias was not statistically significant (p-value = 0.777; paired-sample t-test). The system was further analyzed to predict "normal" LOS ≤ 7 days versus "prolonged" LOS > 7 days groups. It showed excellent balanced diagnostic accuracy and agreement rate. However, temporal and spatial validation must be considered to generalize the model. This contribution is hoped to pave the way for hospitals and healthcare providers to manage their resources better. [ABSTRACT FROM AUTHOR]

The multipath effect error (MEE) is typically not taken into account by the RTKLIB localization method, and this may lead to poor positioning accuracy. This paper proposes an expectation maximization (EM) algorithm for GPS positioning based on Volterra series, and the pseudoranges contaminated by MEE are considered as missing data. Firstly, the Volterra series is introduced to linearize the pseudorange equation. Then, the EM algorithm is used to iteratively update the user location and missing data. Compared with the RTKLIB method, the proposed algorithm has more accurate positioning accuracy. The simulation example shows the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Computational Mechanics / Jisuan Lixue Xuebao is the property of Chinese Journal of Computational Mechanics Editorial Office, Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The nonlinear Volterra equalizer has been proved to be able to solve the problem of nonlinear distortion, but it has high computational complexity and is difficult to implement. In this paper, a simplified second-order Volterra nonlinear equalizer designed for intensity modulation/direct detection systems based on direct modulated laser is proposed and demonstrated, taking into account the characteristics of the system. It has been proved that the received signal of direct modulation laser/direct detection system can be expressed in Volterra series form, but its form is too complex, and the device parameters should also be considered. We re-derived it and obtained a more concise form. At the same time, we proposed a method to simplify the second-order Volterra nonlinear equalizer without relying on device parameters. The performance of the proposed Volterra nonlinear equalizer is evaluated experimentally on a 56 Gb/s 4-ary pulse amplitude modulation link implemented by using a 1.55 µm direct modulation laser. The results show that, compared with the traditional Volterra nonlinear equalizer, the receiver sensitivity of the equalizer is only reduced by 0.2 dB at most, but the complexity can be reduced by 50%; compared with diagonally pruned Volterra nonlinear equalizers, the complexity of the equalizer is the same, but the reception sensitivity can be improved by 0.5 dB. [ABSTRACT FROM AUTHOR]

In recent years, Internet of Things (IoT) technologies have been increasingly utilized to collect enormous volumes of performance data for intelligent analysis and modeling of aero-engines. This has aided in the development of numerous data-driven solutions so that a strong knowledge of the intricate operations within the equipment is no longer needed. To characterize the dynamic nonlinear transient behavior of turbofan engines, fast response changes have the possibility of being captured accurately through high-order, long-memory-length Volterra series. However, exponentially increasing coefficients are still challenging to be handled properly. For fast and reliable modeling of turbofan engines, an Optimal Sparse Volterra (OSV) model is developed in this paper by reconstructing sparse nonzero coefficients after a global selection through particle swarm optimization. The OSV model focuses on the optimal sparsity of the Volterra kernels while being insensitive to the signal length. Besides, noise reduction and the correlation analysis method are specifically designed for sensor measurements of low-bypass ratio turbofan engines. The OSV model, as well as retaining the powerful descriptive capability of the Volterra series for nonlinear characteristics, finds the most relevant sets of variables and the set of model parameters automatically under the minimum computing workload. According to the experimental results, when real test data are used for turbofan transient maneuvers, the OSV model ensures that the mean absolute error is less than 5 × 1 0 − 4 for high-pressure rotor speed, thrust and exhaust temperature. Moreover, the nonzero identification coefficients produced by the OSV model in the experiments are less than 6% of the total coefficients. At the same time, the average running time required by the OSV model is less than 35% of that of traditional identification algorithms. [ABSTRACT FROM AUTHOR]

A rolling bearing fault diagnosis method based on the Volterra series and kernel principal component analysis (KPCA) is proposed. In the proposed method, first, the improved genetic algorithm (IGA) is used to identify the Volterra series model of the bearing in four states: normal, rolling element fault, inner ring fault, and outer ring fault. The Volterra time-domain kernel is used as the feature vector for kernel principal component analysis to classify and identify the faults. The feasibility of the fault diagnosis method of the Volterra level and kernel principal component analysis is verified by the experimental results. [ABSTRACT FROM AUTHOR]

In this article, three novel low-power and voltage Ku/K-band low noise amplifiers (LNAs) are proposed and designed. These three LNAs have an identical structure. The excellent simultaneous noise and input impedance matching are prevailed by employing a high-pass filter in front of the input port. This high-pass filter has two resonance frequencies under RLC load addressing simultaneous noise and input impedance matching. A capacitive shunt-shunt feedback and the inductive source degeneration as well as the common-source amplifier are applied to design the filter. The proposed LNAs consist of two stages and each stage takes advantage of the current-reused configuration. By shunt and series peaking technique, broadband, high and flat gains are achieved. The first, second, and third LNAs are adapted for functioning in Ku-band (12–18 GHz), K-band (18–26.5 GHz), and Ku/K-band (11–28 GHz), respectively. Because of excellent power linearity and low-power design, a low supply voltage of 1.2 V is chosen for LNAs by Volterra series analysis. The proposed LNAs have S11 and S22 parameters lower than − 10 dB, noise figures better than 2.5 dB, and S21 parameters greater than 9 dB. The power consumption of the first, second and third LNA are only 8.2, 13.8, and 11 mW; respectively. The excellent IIP3 of the Ku/K-band LNA is − 5 dBm. By applying group delay analysis, perfect group delay variations of the LNAs are better than ± 15 ps. [ABSTRACT FROM AUTHOR]

The nonlinear effects exhibited by structures under the action of wind loads have gradually stepped into the vision of wind-resistant researchers. By summarizing the prominent wind-induced nonlinear problems of four types of wind-sensitive structures, namely tall buildings, high-rise structures, flexible bridges, and transmission lines, the occurrence mechanism of their nonlinear effects is revealed, providing cutting-edge research progress in theoretical studies, experimental methods and vibration control. Aerodynamic admittance provides insights into the aerodynamic nonlinearity (AN) between the wind pressure spectrum and wind speed spectrum of tall building surfaces. The equivalent nonlinear equation method is used to solve nonlinear vibration equations with generalized van-der-Pol-type aerodynamic damping terms. The elastic–plastic finite element method and multiscale modeling method are widely employed to analyze the effects of geometric nonlinearity (GN) and material nonlinearity (MN) at local nodes on the wind-induced response of latticed tall structures. The AN in blunt sections of bridges arises from the amplitude dependence of the aerodynamic derivative and the higher-order term of the self-excited force. Volterra series aerodynamic models are more suitable for the nonlinear aerodynamic modeling of bridges than the polynomial models studied more in the past. The improved Lindstedt–Poincare perturbation method, which considers the strong GN in the response of ice-covered transmission lines, offers high accuracy. The complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects continue to consume significant computational resources and time, especially for complex wind field conditions and flexible and variable structural forms. It is necessary to further develop analytical, modeling and identification tools to facilitate the modeling of nonlinear features in the future. [ABSTRACT FROM AUTHOR]

Summary: The nonlinear power amplifier and the analogue output channel filter with nonconstant group delay add nonlinear and linear distortions to the satellite transmitted signal, respectively. Recently, there has been growing interest in using Wiener predistorters, consisting of separate nonlinear and linear components, to compensate for these distortions in the satellite downlinks. The Wiener predistorter has been shown to effectively deal with signal distortions and has lower complexity compared to other state‐of‐the‐art methods. In this paper, we argue that fully compensating the nonconstant group‐delay distortion degrades the overall performance of the Wiener predistortion systems. This is primarily due to the increased peak‐to‐average power ratio of the signal at the output of the linear predistorter. We show that the overall performance of the Wiener predistorter can be improved by undercompensating the group‐delay distortion. We propose two optimizations to address the PAPR growth problem and show using simulations that our approach leads to significant improvement in predistortion performance. Using our Wiener predistorter, the total degradation gap to the ideal limiter channel can be reduced to merely 0.34 dB for 64‐APSK modulated signals. [ABSTRACT FROM AUTHOR]

This study aims to focus on using the Volterra series and machine learning for forecasting random and chaotic wind speed regimes, since calm weather is mostly noticed at the local site, making dataset selection difficult. A novel method is proposed to predict Volterra kernels up to the third order, using a forward–back propagation neural network with 12-month measurements at Fujairah site (United Arab Emirates). Both daily and monthly wind speed datasets are investigated for forecasting. The three dominant hourly and daily kernels are extracted for each day and each month. Predicted future Volterra kernels are estimated from past values using both statistical analysis and individual neuro networks for each of the Volterra kernel coefficients. Using the evolved Volterra kernels, the hourly and daily wind speeds are forecasted with similar patterns of the measured values. Due to the random nature of wind speed at the local site, a two-layer with four neurons per layer neuro network is used to locate the most variable and intense speed during 8 h in the day. Forecasted wind speed is determined with errors arising from different sources, such as the utilization of only third-order Volterra kernels and the difficulty of machine training of the employed shallow network. Nevertheless, this work depicts a useful algorithm to forecast chaotic and random wind speed regimes. Computational time is a trade of the complexity of Volterra mathematical analysis. [ABSTRACT FROM AUTHOR]

A narrowband cascode inductive degeneration CMOS low-noise amplifier (LNA) with post-distortion (PD) linearization technique is designed by TSMC CMOS 180 nm technology for biosensor applications. A mathematical formulation for linearity analysis is drafted using the Volterra series method. This paper presents a new combination of an intermodulation (IMD) technique using a PMOS IMD sinker with a broadband pie-matching network in the drain of the main transistor. The main NMOS transistor and the auxiliary PMOS transistor operated in the saturation region improve the second-order intercept point (IIP2) and third-order intercept point (IIP3). The cascode linearized LNA demonstrates the improvement of the third-order intercept point + 13 dBm using the linearization technique in the2.4 GHz ISM band frequency range. The effect of the linearization technique on the design constraints of the LNA, such as power gain, noise figures, stability, and maximum gain, is also investigated. The simulation results show that the LNA achieves a minimum noise figure (NF) of 1.803 dB, a maximum power gain (S21) of 16.663 dB, and a low reflection coefficient (S11) of − 32 dB with a good stability factor in the frequency range of 2.4 GHz. [ABSTRACT FROM AUTHOR]

SensorCraft is an intelligence, surveillance, and reconnaissance (ISR) system that integrates unmanned flight platforms and airborne antenna arrays. Under gust loads, the high–aspect–ratio, light–wing structure of SensorCraft has considerable bending and torsion deformation, affecting the flight performance of unmanned flight platforms and leading to the loss of antenna arrays' electromagnetic performance. Taking SensorCraft as the background, a wing conformal antenna array was designed, an aircraft model with a passive wingtip device was established, a control law was developed by the LQG/LTR method, and a gust alleviation active–passive combined control method of a "LQG/LTR active controller + passive wingtip device" was proposed. By constructing an unsteady aerodynamic reduced–order model (ROM) based on the Volterra series and a conformal array pattern fast method based on the modal form, the effectiveness of the gust alleviation active–passive combined control method on the aircraft platform and antenna array was analyzed. The results show that structural deformation of the wing conformal antenna leads to changes in the main lobe gain, beam direction, and sidelobe level. The active–passive gust alleviation method has obvious advantages. Compared with the LQG/LTR active gust alleviation method, the peak value of wingtip displacement is reduced by 15.6%, and the peak value of the gain loss is reduced by 0.72 dB, which is conducive to better performance of the airborne conformal antenna array. [ABSTRACT FROM AUTHOR]

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 Tr-Volterra 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.

Abstract Graph-based learning and estimation are fundamental problems in various applications involving power, social, and brain networks, to name a few. While learning pair-wise interactions in network data is a well-studied problem, discovering higher-order interactions among subsets of nodes is still not yet fully explored. To this end, encompassing and leveraging (non)linear structural equation models as well as vector autoregressions, this paper proposes autoregressive graph Volterra models (AGVMs) that can capture not only the connectivity between nodes but also higher-order interactions presented in the networked data. The proposed overarching model inherits the identifiability and expressibility of the Volterra series. Furthermore, two tailored algorithms based on the proposed AGVM are put forth for topology identification and link prediction in distribution grids and social networks, respectively. Real-data experiments on different real-world collaboration networks highlight the impact of higher-order interactions in our approach, yielding discernible differences relative to existing methods.

The study solves the problem of filtering nonlinear systems based on the minimax adaptive algorithm of nonlinear systems by Volterra series of the second order, provided that the autocorrelation functions of the useful signal and interference are known with some errors according to the criterion of the maximum standard error of filtering. The author analyses the stationary performance of a minimax adaptive Volterra filter of the second order with the least mean square (LMS) with a constant step size of µ with a time-varying setting. A quantitative assessment of the steadystate excess root-mean-square error (RMSE) has been established, in which the contribution of incorrect gradient adjustment and tracking error is well characterized. Then the optimal step size is set for a time-varying secondorder minimax Volterra filter. Thus, we can study the correlation between the excess MSE and the optimal step size, on the one hand, and the parameters of a time-varying nonlinear system, on the other hand. A simple solution with minimal root-mean-square error for the minimax Volterra filter is obtained, based on the assumption that the input signal of the filter is Gaussian. In addition, we propose an iterative factorization method for developing a subclass of minimax Volterra filters, which can greatly simplify filtering operations. In addition, an adaptive algorithm for the Volterra filter is investigated, as well as its average convergence and asymptotic excess root-mean-square error. Finally, the usefulness of the Volterra filter is demonstrated by its use in studies of nonlinear drift oscillations of moored vessels exposed to random sea waves.

This article proposes a kernel‐based regularization least squares algorithm for nonlinear time‐delayed systems with unknown structure. Since the structure and the time‐delay of the model are unknown, a model pool constituted of several Volterra series is constructed with the aim of approximating the nonlinear model which has different time‐delays. Then, a self‐organizing maps method and a kernel‐based regularization method are interactively used to update the time‐delay and parameters. Compared with the traditional algorithms, the proposed algorithm has no limitation on the nonlinear model, and can describe the dynamics of the nonlinear model with a simple structure. Finally, simulation examples are given to show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the Volterra series and the pseudo-excitation method (PEM) are combined to establish a frequency domain method for the power spectral density (PSD) analysis of random vibration of nonlinear systems. The explicit expression of the multi-dimensional power spectral density (MPSD) of the random vibration response is derived analytically. Furthermore, a fast calculation strategy from MPSD to physical PSD is given. The PSD characteristics analysis of the random vibration response of nonlinear systems is effectively achieved. First, within the framework of Volterra series theory, an improved PEM is established for MPSD analysis of nonlinear systems. As a generalized PEM for nonlinear random vibration analysis, the Volterra-PEM is used to analyse the response MPSD, which also has a very concise expression. Second, in the case of computation difficulties with multi-dimensional integration from MPSD to PSD, the computational efficiency is improved by converting the multi-dimensional integral into a matrix operation. Finally, as numerical examples, the Volterra-PEM is used to estimate the response PSD for stationary random vibration of a nonlinear spring-damped oscillator and a non-ideal boundary beam with geometrical nonlinearity. Compared with Monte Carlo simulation, the results show that by constructing generalized pseudo-excitation and matrix operation methods, Volterra-PEM can be used for input PSD with arbitrary energy distribution, not only restricted to broadband white noise excitation, and accurately predict the secondary resonance phenomenon of the random vibration response of nonlinear systems in the frequency domain. [ABSTRACT FROM AUTHOR]

This paper develops a kernel regularization based Adam algorithm for nonlinear systems with unknown structure and time-delay by using self-organized maps. Based on the redundant rule method, a model pool constituted of several Volterra series is constructed which contains the true time-delayed model. Then, the Adam algorithm combining a self-organized maps technique is applied to iteratively estimate the time-delay and parameters. Furthermore, a kernel regularization method is introduced to deal with the curse of dimensionality, and by which a more simple Volterra model can be obtained. Experimental results show the effectiveness of proposed algorithm in estimating time-delay and parameters. [ABSTRACT FROM AUTHOR]

In order to improve the modeling performance of Volterra sequence for nonlinear neural activity, in this paper, a new optimization algorithm is proposed to identify Volterra sequence parameters. Algorithm combines the advantages of particle swarm optimization (PSO) and genetic algorithm (GA) improve the performance of the identification of nonlinear model parameters from rapidity and accuracy. In the modeling experiments of neural signal data generated by the neural computing model and clinical neural data set in this paper, the proposed algorithm shows its excellent potential in nonlinear neural activity modeling. Compared with PSO and GA, the algorithm can achieve less identification error, and better balance the convergence speed and identification error. Further, we explore the influence of algorithm parameters on identification efficiency, which provides possible guiding significance for parameter setting in practical application of the algorithm. [ABSTRACT FROM AUTHOR]

Featured Application: This paper provides a valuable theoretical basis for the post-flutter response calculation that considers the vertical–torsional coupling. The aeroelastic analysis method proposed in this paper, based on the Volterra ROM and Newmark-β method, simplifies the process of flutter critical wind speed predictions; it requires engineers to only identify four Volterra first-order kernels. This method could be used to effectively solve flutter problems in long-span bridges. This study proposes a novel reduced-order model (ROM), based on the Volterra series, for the aerodynamic force of the bridge deck section. Moreover, the ROM of the aerodynamic force of the streamlined box girder section of the Great Belt East Bridge (GBEB) is identified with computational fluid dynamic (CFD) simulations. Furthermore, an analysis method combining ROM aerodynamic force and Newmark-β integration is established to simulate the aeroelastic responses of the bridge deck section. Finally, the wind-induced vibration responses of the GBEB section are calculated near the flutter critical wind speed based on the Volterra series-based aeroelastic analysis and the fluid–structure interaction (FSI) numerical simulations in ANSYS Fluent, respectively. Moreover, to verify the applicability of the proposed method, the aeroelastic responses of the main deck section with the crash barriers of Lingdingyang Bridge (LDYB) are also simulated via the Volterra model and Newmark-β integration near the flutter critical wind speed. The results show that the first-order truncated Volterra model established in this study can accurately capture the aerodynamic response of the main girder, and the results are in good agreement with those of the CFD numerical simulation under forced vibration. Furthermore, the proposed method combined with ROM aerodynamic force and Newmark-β integration can effectively calculate the FSI of the bridge girder. The numerical results of the flutter critical wind speed and flutter frequency of GBEB and LDYB are consistent with the numerical results by the FSI method based on ANSYS Fluent and the existing numerical and experimental results, respectively. [ABSTRACT FROM AUTHOR]