Excitation Signal Research Articles

Design and Analysis of Microstrip Patch Antenna Array and Electronic Beam Steering Linear Phased Antenna Array with High Directivity for Space Applications.

This study proposes an E-shaped microstrip patch antenna array (MSPAA). The substrate is RT/Duroid5880. Its 2.2 dielectric constant gives it a larger bandwidth than substrate materials with higher dielectric constants. The periphery dimension of a single E patch is 50 × 41 mm2. The areas of 2 × 2 and 3 × 3 MSPAAs are 120 × 96 and 180 × 144 mm2, respectively. Array members are 10 and 7 mm apart horizontally and vertically, respectively. MTM technology builds the projected MSPAA. This work looks at the effects of gain, reflection coefficient (return loss), directivity, bandwidth, and VSWR on proposed 2 × 2 and 3 × 3 MSPAAs with different patch lengths of 30, 40, and 60 mm, patch widths of 40, 50, and 60 mm, and substrate thicknesses of 0.8 and 1.6 mm. Also, this study compares the performance of existing E-shaped MSPAAs with proposed 2 × 2 and 3 × 3 MSPAAs. The suggested MSPAA performs better than the existing E-shaped MSPAA. The series network analyzer measures the prototype MSPAA's experimental outcomes. The polynomial is recommended for estimating the antenna array area with odd and even rows and columns. CST Studio Suite software analyzes and designs antenna arrays, and simulation findings are compared with hardware results. The main benefit of the proposed 2 × 2 MSPAA is that it reduces sidelobes. It has a gain of 8.9 dBi, a directivity of 8.95 dBi, a VSWR of 1.02, a return loss of -32.91 dB, and a bandwidth of 0.1 GHz at both 1.6 and 0.8 mm substrate material thicknesses. Across its operating range of 3.8-4.2 GHz, the recommended array antenna has a radiation gain of 7.01-7.81 dB and an efficiency of 68.51-71.11%. At 4 GHz, this study looks at how electronic steering affects the phase angle of the excitation signal, the number of elements, and the distance between elements in the beam steering linear phased antenna array (BSLPAA) using MATLAB.

Envelope correction for shear-longitudinal collinear wave mixing to extract absolute nonlinear acoustic parameters

This paper addresses the effect of the excitation envelope on the generated nonlinear resonant signal (NRS) for collinear wave mixing of shear and longitudinal waves. The aim is to explore how the absolute material nonlinearity can be extracted accurately for any enveloped sinusoidal excitation signal. A finite difference time domain (FDTD) model was built to simulate the effect of input waveforms on the NRS. A change in the measured nonlinearity was seen as the input waveforms were changed from rectangular to Hanning windowed tone burst. The required waveform correction was derived theoretically and validated against the FDTD simulation. Experimental measurements were carried out for different waveforms at several input amplitudes, demonstrating its influence over the NRS. The theoretically derived correction factor, which is required to map the small NRS to the rectangular tone burst resonant amplitude, was validated experimentally. The correction was then used to extract one the fundamental Murnaghan constant (m). Comparatively, Hanning tone burst inputs showed lower variance in the extracted material property due to better control of the frequency bandwidth, relative to that of the transducers. This opens the opportunity to using Hanning windowed tone burst inputs reliably for the measurement of the absolute nonlinearity parameter and m through collinear shear-longitudinal wave mixing.

Lock-In Thermography with Cooling for the Inspection of Composite Materials.

This paper presents the development of the lock-in thermography system with an additional cooling system. System feasibility is tested by investigating a square-shaped glass fiber-reinforced polymer (GFRP) with artificially made outer flaws. The influence of heating mode and sinusoidal excitation period on the defect detectability is considered. Thus, the experiment is split into two modes: the sample is solely heated in the first mode or simultaneously heated and cooled in the second. In each mode, the temperature measurement is performed first with a shorter excitation signal period and second with a longer one. The signal-to-noise ratio (SNR) is used to assess defect detection quantitatively. The comparative analysis shows that employing a mixed heating-cooling mode improves the SNR compared to the conventional heating mode. The further enhancement of the SNR is obtained by extending the excitation period. The combination of simultaneous heating and cooling with longer periods of the excitation signal allows for the best SNR values for the most detected defects.

Elastic Wave Mechanics in Damaged Metallic Plates

Human health monitoring (HHM) is essential for continued daily task execution, as is structural health monitoring (SHM) for structures to ensure the continual performance of their designed tasks with optimal efficiency. The existence of damage in a structure affects its optimal use through stiffness deterioration. Damage of different forms could occur in a structure but have the singular objective of material degradation, leading to its underuse for a task. Guided wave ultrasonics has shown strength in detecting sundry damage in structures, but most of the damage monitored and detected is unfilled with substances. However, some damage could trap and accumulate substances that could hasten material degradation through corrosion activities under favorable conditions, especially in the oil and gas industry. This study used the ultrasonic-guided waves’ pitch–catch inspection technique to identify damage filled with different materials. The assessment was based on the RMSD of the dominant Lamb wave mode’s average maximum amplitude and the response signals’ transmission coefficient (TC). A five-cycle tone burst of excitation signals of different frequencies was created to generate propagating Lamb waves in the structure. The fundamental antisymmetric mode was found to be more sensitive than the fundamental symmetric mode when detecting damage filled with various substances. At 80 kHz, the deviation of the current response signals from the baseline response signals due to different filled substances in the damage was distinct and decreased with increased fluid viscosity. Given that structures in the oil and gas sector are particularly susceptible to substance-induced damage, the outcomes of this study are paramount.

Electric-Force Conversion Performance of Si-Based LiNbO3 Devices Based on Four Cantilever Beams.

In micron or nano smart sensing systems, piezoelectric cantilever beams are distributed as major components in microsensors, actuators, and energy harvesters. This paper investigates the performance of four cantilever beam devices with "electric-force" conversion based on the inverse piezoelectric effect of lithium niobate (LiNbO3, LN) single-crystal materials. A new compact piezoelectric smart device model is proposed, designed as a single mass block connected by four beams, where devices exhibit smaller lateral errors (0.39-0.41%). The relationship between the displacement characteristics of cantilever beams and driving voltage was researched by applying excitation signals. The results show that the device has the maximum displacement at a first-order intrinsic frequency (fosc = 11.338 kHz), while the displacement shows a good linear relationship (R2 = 0.998) with driving voltage. The square wave signals of the same amplitude have greater "electrical-force" conversion efficiency. The output displacement can reach 12 nm, which is much higher than the output displacement with sinusoidal excitation. In addition, the relative displacement deviation of devices can be maintained within ±1% under multiple cycles of electrical signal loading. The small size, high reliability, and ultra-stability of Si-LN ferroelectric single-crystal cantilever beam devices with lower vibration amplitudes are promising for nanopositioning techniques in microscopy, diagnostics, and high-precision manufacturing applications.

Lamb wave phased array imaging based on phase-amplitude compounding algorithm

Aimed at improving the imaging performance of Lamb wave phased array based on Delay-and-Sum (DAS) of signal amplitude, a compounding imaging algorithm integrating amplitude and phase information of signal is proposed in this paper. By applying back propagation dispersion compensation, the pulse echoes caused by defects will be in-phase with the excitation signal, implementing signal focusing. In the proposed imaging algorithm, the amplitude imaging index is calculated by classical total focusing method (TFM) and the phase imaging index is calculated by phase coherence factor (PCF), which establishes the nonlinear mapping between imaging index and phase difference by sigmoid function with variable gradient. The final imaging results are the compound of two imaging indexes. The experimental validation is carried out on plates of different materials and dimensions with multiple types of defects based on uniform linear array. Compared with the imaging results of conventional TFM, the proposed imaging algorithm can effectively improve the signal-to-noise ratio (SNR) of the images and suppress artifacts, implementing threshold-free imaging.

The mutual influence of exciting and induced currents in the circular solenoid – massive conductor system

Problem. The flow of currents in the conductive elements of electrical systems is accompanied by the excitation of electromagnetic fields and the occurrence of induced currents. The excitation of the induced signals, in turn, leads to a change in the parameters of the actual exciting currents. The purpose of the work is to obtain analytical expressions for the quantitative analysis of the results of the mutual influence of the exciting and induced currents and to calculate their ratio depending on the geometric characteristics of the inductor systems. Methodology. The analysis of the processes of mutual influence is carried out on the example of a widespread inductor system, where a flat circular solenoid is placed above the surface of a massive conductor. Analytical expressions for eddy currents excited in a massive conductor and numerical estimates of the effect of induced currents on exciting currents in a solenoid are obtained. Results. It is shown that the influence of the induced current on the current in the solenoid is very significant at small distances between the solenoid and the surface of the massive solenoid. It has been found that an increase in the width of the solenoid winding leads to a significant increase in the influence of the induced current on the excitation current in the solenoid. It is shown that the inductance of the «circular solenoid - massive conductor» system drops with a decrease in the distance between the solenoid and the massive conductor and an increase in the radial dimensions of the solenoid, which requires an increase in the amplitude of the exciting current to maintain a given value of the magnetic flux in the system. Originality. The scientific novelty of this work lies in the proposal of an analytical approach and obtaining numerical estimates of the mutual influence of conductors with exciting and induced currents. Practical value. Estimates of the mutual influence of conductors with currents are of interest for the practice of designing structures of electrical systems for various purposes. Very promising in the direction further research is seen as carrying out experiments with measurements of the quantitative characteristics of the mutual influence of exciting and induced currents in various designs of electrical systems.

Disturbance Rejection-Based Optimal PID Controllers for New 6ISO AVR Systems

In the literature, different approaches that are employed in designing automatic voltage regulators (AVRs) usually model the AVR as a single-input-single-output system, where the input is the generator reference voltage, and the output is the generator voltage. Alternately, it could be thought of as a double-input, single-output system, with the excitation voltage change serving as the additional input. In this paper, unlike in the existing literature, we designed the AVR system as a sextuple-input single-output (6ISO) system. The inputs in the model include the generator reference voltage, regulator signal change, exciter signal change, amplifier signal change, generator output signal change, and the sensor signal change. We also compared the generator voltage responses for various structural configurations and regulator parameter choices reported in the literature. The effectiveness of numerous controllers is investigated; the proportional, integral and differential (PID) controller, the PID with second-order derivative (PIDD2) controller, and the fractional order PID (FOPID) controller are the most prevalent types of controllers. The findings reveal that the regulator signal change and the generator output signal change significantly impact the generator voltage. Based on these findings, we propose a new approach to design the regulator parameter to enhance the response to generator reference voltage changes. This approach takes into consideration changes in the generator reference voltage as well as the regulator signal. We calculate the regulator settings using a cutting-edge hybrid technique called the Particle Swarm Optimization African Vultures Optimization algorithm (PSO–AVOA). The effectiveness of the regulator design technique and the proposed optimization algorithm are demonstrated.

Dynamic Simulation and Test Verification of Hydraulic Automatic Tensioner for an Engine Timing Chain Drive System

As a fundamental component of an automobile engine's timing chain drive system, the hydraulic automatic tensioner significantly enhances fuel economy while minimizing system vibrations and noise. However, there is a noticeable lack of research on automatic hydraulic tensioners. This study presents a comprehensive calculation approach for the principal parameters of a hydraulic automatic tensioner. An effective method, grounded in hydraulics and multibody dynamics, was introduced for estimating the dynamic response of such a tensioner. The simulation model developed for the hydraulic tensioner is characterized by its rapid dynamic response, consistent operation, and high accuracy. The dynamic behavior of the tensioner was analyzed under varying boundary conditions, using sinusoidal signal excitation. It was observed that the maximum damping force increases with a decreasing leakage gap. Conversely, an increase in oil temperature or air content leads to a decrease in the maximum damping force. The reaction forces derived from these calculations align well with experimental results. This calculation and simulation approach offers considerable value for the design of innovative hydraulic tensioners. It not only streamlines the design phase, minimizes the number of trials, and reduces product costs, but also provides robust insights for evaluating the performance of hydraulic tensioners.

Automatic reinforcement for robust model‐free neurocontrol of robots without persistent excitation

SummaryModel‐based adaptive control suffers over parametrization from the many adaptive parameters compared to the order of system dynamics, leading to sluggish tracking with a poor adaptation transient without robustness. Likewise, adaptive model‐free neurocontrol that relies on the Stone–Weierstrass theorem also suffers from similar problems in addition to over‐fitting to approximate inverse dynamics. This article proposes a novel reinforced adaptive mechanism to guarantee a transient and robustness for the model‐free adaptive control of nonlinear Lagrangian systems. Inspired by the symbiosis of Actor‐Critic (AC) architecture and integral sliding modes, the reinforced stage neural network, analogous to the critic, injects excitation signals to reinforce the parametric learning of the adaptive stage neural network, analogous to the actor to improve the approximation of inverse dynamics. The underlying integral sliding surface error drives improved learning onto a low‐dimensional invariant manifold to guarantee local exponential convergence of tracking errors. Lyapunov stability substantiates the robustness with an improved transient response. Our proposal stands for a hybrid approach between AC and neurocontrol, where the reinforced stage does not require a value function nor reward to provide automatic reinforcement to the adaptive stage parametric adaptation. Dynamic simulations are presented for a nonlinear robot manipulator under different conditions.

Multi-Order Mode Excitation and Separation of Ultrasonic Guided Waves in Rod Structures Using 2D-FFT.

The ultrasonic guided wave technique is extensively used for nondestructive structural testing, and one of the key steps is to extract a single mode with certain purity from multi-order mixed modes. In this paper, the propagation of ultrasonic guided waves in the cylindrical rod is simulated first; the appropriate broadband excitation signal is selected to excite the multi-order modes in a specific frequency range; and the time-space signal containing multi-order modes is converted to the frequency-wavenumber domain signal by two-dimensional Fourier transform. In the frequency-wavenumber domain, the frequency-wavenumber ridge is extracted from the multi-mode frequency-wavenumber domain based on the dynamic programming method, and then the time-domain signal corresponding to a single mode can be reconstructed. By comparing the excited multi-order mode and the separated single mode with the theoretical results, it is observed that the two results are consistent. Thus, the employed mode-excitation method can accurately excite the multi-order modes in rod structures. Furthermore, the proposed method enables the separation of a single-mode wave with high purity, providing a foundation for future utilization of isolated modes.

Nonlinear-Control-Oriented Modeling of the Multi-Variable Underground Coal Gasification Process for UCG Project Thar: A Machine Learning Perspective

The Underground Coal Gasification (UCG) process is a complex and multi-physics phenomenon, thus making it difficult to develop a mathematical model that encapsulates all dynamical aspects. In this regard, data-driven modeling techniques offer a reliable alternative for prediction, control, and optimization of dynamical systems, but their application in UCG is still in the early stages. This work aims to bridge this gap by implementing three cutting-edge nonlinear identification structures: Non-linear Autoregressive with Exogenous Inputs (NARX), Hammerstein–Wiener (HW), and State-Space Neural Networks (SSNN) on the UCG process to obtain a multivariable control-oriented model. The contributions include synthesizing an excitation signal for data acquisition, outlining the non-linear system identification procedure, and comparing predictive capabilities using statistical tools. The simulation results demonstrate a rigorous comparison of various techniques for the heating value and flowrate of the syngas, which are the outputs of the UCG process. The results of the analysis show that NARX outperforms other structures in statistical metrics, with MAE, RMSE, and Best fit values of 1.51,1.9, and 0.9, respectively, for the heating value; and 0.25,0.31, and 0.94, respectively, for the flowrate. Consequently, the outputs of the NARX model are compared with the experimental data obtained from the UCG project Thar, which show a good match for both outputs.

Structural Health Monitoring of Chemical Storage Tanks with Application of PZT Sensors.

Chemical pressure storage tanks are containers designed to store fluids at high pressures, i.e., their internal pressure is higher than the atmospheric pressure. They can come in various shapes and sizes, and may be fabricated from a variety of materials. As aggressive chemical agents stored under elevated pressures can cause significant damage to both people and the environment, it is essential to develop systems for the early damage detection and the monitoring of structural integrity of such vessels. The development of early damage detection and condition monitoring systems could also help to reduce the maintenance costs associated with periodic inspections of the structure and unforeseen operational breaks due to unmonitored damage development. It could also reduce the related environmental burden. In this paper, we consider a hybrid material composed of glass-fiber-reinforced polymers (GFRPs) and a polyethylene (PE) layer that is suitable for pressurized chemical storage tank manufacturing. GFRPs are used for the outer layer of the tank structure and provides the dominant part of the construction stiffness, while the PE layer is used for protection against the stored chemical medium. The considered damage scenarios include simulated cracks and an erosion of the inner PE layer, as these can be early signs of structural damage leading to the leakage of hazardous liquids, which could compromise safety and, possibly, harm the environment. For damage detection, PZT sensors were selected due to their widely recognized applicability for the purpose of structural health monitoring. For sensor installation, it was assumed that only the outer GFRP layer was available as otherwise sensors could be affected by the stored chemical agent. The main focus of this paper is to verify whether elastic waves excited by PZT sensors, which are installed on the outer GFRP layer, can penetrate the GFRP and PE interface and can be used to detect damage occurring in the inner PE layer. The efficiency of different signal characteristics used for structure evaluation is compared for various frequencies and durations of the excitation signal as well as feasibility of PZT sensor application for passive acquisition of acoustic emission signals is verified.

Detection and elimination of insignificant interacting subsystems in MIMO closed-loop systems using the least mean square-based partial correlation algorithm

Closed-loop identification of multi-input multi-output (MIMO) systems in large-scale plants has significant difficulties due to subsystem interactions. This complexity is attributed to several input‒output variables, interactions such as recycling to improve or save material and energy, and disturbances such as heating or cooling within the plant. One of the fundamental problems in closed-loop identification is the input perturbation of the interacting subsystems to capture the dynamics of the system for producing an informative dataset and consequently obtaining an accurate model. However, perturbing all the interacting subsystems in the plant increases the applied excitation signals, which makes the identification a nontrivial task. Thus, a precise and quantitative procedure to evaluate the significance and contribution of such interacting subsystems before applying these excitation signals is required to simplify the identification task. Conventional partial correlation analysis is one of the implemented techniques to measure the significance of these interacting subsystems. However, this technique is based on least square estimation. Thus, incorrect estimation of the model errors is produced due to the correlations amongst the process inputs and unmeasured disturbances. Accordingly, this paper describes the implementation of a developed least mean square-based partial correlation algorithm for detecting and eliminating insignificant interacting subsystems of MIMO closed-loop systems. The developed algorithm can discriminate the interacting subsystems that substantially influence the plant interaction from those that do not by minimizing the model regression errors produced due to the process input correlation, unmeasured disturbances, and colored noise. The effectiveness of the proposed method is demonstrated through a case study.

Bubble detection in liquid metal by perturbation of eddy currents: Model and experiments

A model has been developed to predict the response of an eddy current flow meter (ECFM) to the passage of a non-conductive inclusion moving in a cylindrical tube filled with a liquid metal. The model can be solved analytically for small inclusion diameters and moderate AC frequencies of the excitation signal. This condition is expressed as vbSω≪1, where vb is the dimensionless inclusion volume and Sω is a function of the ratio between the characteristic length of the system and the penetration depth of the magnetic field. The magnetic induction equation for this problem has also been solved numerically. A very good agreement between the analytical model and numerical solutions has been found for vbSω≪1. Two experimental setups have been designed. First, the ECFM model has been validated by comparing the response due to the passage of traveling beads of known diameters in a low melting point alloy. In a second experiment, the diameters of ascending argon bubbles have been estimated with the ECFM model. The numerical model predicts the gas volume with very good accuracy in the range of bubble diameters studied, between 1.5 and 6 mm, while the analytical model only deviates significantly from the experimental data when vbSω≳0.1. Moreover, we establish that the ECFM can also measure the radial deviation of the bubble trajectory, and the results are consistent with the theoretical limit for isolated bubbles between the regimes of oscillating/zigzag motion of ellipsoidal bubbles and non-oscillating motion of spherical bubbles. Another observation is that the dependence of the ECFM response on the shape of the bubble is negligible; indeed, the ECFM response is well approximated by a linear relation with the bubble volume as is assumed in the analytical model. Finally, an estimation of the terminal rising velocity of bubbles was also carried out.

Application of Machine Learning Techniques in Phased Array Antenna Synthesis: A Comprehensive Mini Review

With the rapid development of modern communication systems, phased array antennas (PAAs) are widely used in many applications such as radars and 5G networks. In a PAA composed of multiple elements (antennas), beamforming or beam steering can be achieved by adjusting the phase difference in the excitation signals that feed each element of the array, eliminating the need for mechanical antenna movement. The performance quality of the communication systems heavily relies on the precise synthesis of the PAAs. PAA synthesis entails determining the geometric or physical shape of an antenna based on knowledge of its electrical parameters. Conventional methods for PAA synthesis use conventional electromagnetic models embedded in antenna design software’s. However, these models often pose challenges due to resource-intensive computations, lengthy simulation times, and potential high error rates. Machine learning (ML) techniques can be employed to optimize solutions in various telecommunication systems, including PAAs synthesis. In this article, we review and investigate the application of ML techniques in the synthesis of PAAs. The results of this study show that utilizing ML techniques can expedite the design process by threefold, while simultaneously reducing errors and increasing accuracy up to 99%.

Auto-balancing bridge based wide impedance spectrum measurement with consideration of Op-Amp input impedance.

In an auto-balancing bridge for high impedance measurements, an operational amplifier (Op-Amp) is used to follow the intermediate potential. However, the input impedance of the Op-Amp introduces significant effects in high impedance measurements. This paper proposes a two-step excitation method (TSEM) and an incremental iterative method (IIM). The TSEM determines the magnitude of the Op-Amp input impedance and the initial value of the device under test. The IIM utilizes the TSEM results as initial conditions to quickly bring the bridge to equilibrium. To overcome the distortion issues associated with small amplitude excitation signals generated by the DAC under low resolution conditions, a programmable gain amplifier is designed. Additionally, a half-cycle difference algorithm is developed prior to the three-parameter sine fit to mitigate low-frequency direct-current drift caused by power frequency, thus improving measurement accuracy. Experimental results demonstrate that when the reference impedance is set to 1 MΩ, impedance measurements ranging from 1 kΩ to 100 MΩ can be achieved within the frequency range of 1 to 100kHz. The precision evaluation reveals a relative standard deviation (RSD) of the modulus better than 0.384% and a standard deviation (SD) of the phase angle better than 3.49 mrad; especially for the impedance under test of 1 MΩ, the RSDis better than 0.006% and the SDis better than 0.1 mrad.

Measuring excess attenuation in littoral environments: Evolution of a measurement system

Atmospheric sound propagation measurements over long distances are generally lacking in the literature. This work presents the evolution of the system deployed to collect high spatial and temporal resolution synchronized acoustic and meteorological data. Specifically, the mature configuration includes: a long-range acoustic device capable of source levels up to 140 dB; up to four 7-channel acoustic arrays; two 7-m temperature profiling masts; and a scanning Doppler LIDAR system for volumetric wind profiling at ranges up to several kilometers. This work presents lessons learned over the various iterations of the system such as the design and evolution of the excitation signal used; physical configuration of the components of the system; logistics and planning concerns; post-processing challenges; and quality control considerations.

Optimal Design of Electromagnetic Tomography Flaw Detection System for Train Wheel Based on FPGA

Electromagnetic tomography (EMT) is a new type of nondestructive testing technology that can be used for metal flaw detection. The implementation of the signal demodulation and filtering algorithm of the current electromagnetic tomography flaw detection system relies on the microprocessor MCU, and the reliability is low in real time. To improve the reliability and system integration of signal processing and transmission of the electromagnetic tomography flaw detection system, this paper uses the field programmable gate array chip to integrate the excitation signal generation module and the digital demodulation module based on the EMT train wheel flaw detection system. A digital filter is designed, and the filter parameters are adjusted to achieve a signal-to-noise ratio of 15 dB. UDP communication protocol is utilized to realize Ethernet communication between FPGA and upper computer. Using three algorithms on the host computer for image reconstruction, the train wheel defect information is visualized. The experimental results show that the FPGA chip improves the immunity of the train wheel flaw detection system, realizes the high integration of the system, and achieves the purpose of train wheel defect detection.

Identification of the parametric array loudspeaker system using differential Volterra filter

The self-demodulation property of a parametric array loudspeaker (PAL) system can peel off audible sound modulated on ultrasonic wave and deliver it with high directivity, but also introduces nonlinear distortion. The PAL system can be modeled by the Volterra series expansion in any acoustic field region. However, measurements of Volterra kernel using simple frequency sweep excitation signals may not provide adequate information about the nonlinear system, and the use of wideband signals such as speech signals makes convergence difficult. Based on the Westervelt model, we propose a PAL system identification method utilizing the differential Volterra kernel. The results demonstrate superior fitting performance for real swept frequency output data and speech signal output data compared to the existing one-dimensional Volterra filter (ODVF). Additionally, the proposed method exhibits fewer parameters and faster convergence speed than the traditional volterra kernel.