Time-varying Frequency Response Research Articles

A Novel Approach to Study the Time-Varying Additive Activity during the Electrorefining of Copper

Electrodeposition additives are key components to enhance the electrochemical deposition of metals, either in pure plating applications or during the electrorefining of metals. Many different additives, either organic or inorganic, are applied in industry, depending on the type of process. This work focusses on thiourea and chloride as common additives used for copper electrorefining. This electrochemical industrial process consumes an impure copper anode and produces a pure (99.995 %) copper cathode, while the anode impurities remain in the electrolyte. Additives assist the electroreduction process to produce smooth copper deposits, essential to avoid short circuits and the formation of unwanted cathode morphologies which can entrap impurities.Thiourea is a crucial but complex additive in copper refining. It is known to degenerate into formamidine disulfide (FDS) and both thiourea as FDS can undergo interactions with either copper ions in the solution or the cathode surface. Time dependent additive studies and fundamental knowledge of the effect of aged electrolyte on the cathodic part of the electrorefining process are scarce.The approach applied in this work enables the investigation of the time dependent effect of additives, in this case thiourea and chlorides, assisting the electroplating of copper. Fundamental knowledge of the assisted plating process is extended to create a corner stone for applied research, subsequently, semi-industrial circumstances are used to describe the additive behaviour in industrial relevant conditions. Operando Odd Random Phase Electrochemical Impedance Spectroscopy (ORP-EIS) is used to study the electrochemistry of the additive system [1,2]. Hereby, a multisine input signal is added to the DC current to perform the ORP-EIS experiment simultaneously with the plating process. This measurement technique allows an in situ monitoring of the electrochemical system for hour-long electrodeposition processes. The ORP-EIS technique enables a quantification of the nonlinearities and non-stationarities during the EIS experiment [3]. Additionally, the present non-stationarities are modelled and the nonlinearities are considered as nuisance factor to result in a best linear time-varying approximation [4,5]. An equivalent electrical circuit is used as model to extract the relevant physical parameters from the impedance data. The EIS study is complemented with an ex situ analysis of the thiourea concentration, through ion chromatography, as a function of plating time. Correlations could be made between electrochemical parameters and actual thiourea concentrations [2].[1] T. Collet, et al., An operando ORP-EIS study of the copper reduction reaction supported by thiourea and chlorides as electrorefining additives, Electrochimica Acta (2021) 138762. [2] T. Collet, et al., The time-varying effect of thiourea on the copper electroplating process with industrial copper concentrations, Electrochimica Acta (2022) 141412. [3] Van Gheem, et al., Electrochemical impedance spectroscopy in the presence of non-linear distortions and non-stationary behaviour part i: Theory and validation, Electrochimica Acta 49 (2004) 4753–4762. [4] N. Hallemans, et al., Detection, Classification, and Quantification of Nonlinear Distortions in Time-Varying Frequency Response Function Measurements, IEEE Transactions on Instrumentation and Measurement, 70 (2021) 6500814. [5] N. Hallemans, et al., Best Linear Time-Varying Approximation of a General Class of Nonlinear Time-Varying Systems, IEEE Transactions on Instrumentation and Measurement, 70 (2021) 6503814.

Photonic time-frequency filter based on the software-defined time-frequency prism.

We propose a microwave photonic 2D time-frequency filter based on a photonic time-frequency prism. A time-varying frequency response is realized by deviating the passband of a 1D ordinary frequency filter in the 2D time-frequency plane. The proposed time-frequency filter features highly reconfigurable frequency-sweeping speed and bandwidth, thanks to the software-defined photonic time-frequency prism. With the proposed technique, separation of multiple linear and nonlinear chirp signals with overlapped spectra is experimentally demonstrated.

In-process adaptive milling for large-scale assembly interfaces of a vertical tail driven by real-time vibration data

Assembly interfaces, the joint surfaces between the vertical tail and rear fuselage of a large aircraft, are thin-wall components. Their machining quality are seriously restricted by the machining vibration. To address this problem, an in-process adaptive milling method is proposed for the large-scale assembly interface driven by real-time machining vibration data. Within this context, the milling operation is first divided into several process steps, and the machining vibration data in each process step is separated into some data segments. Second, based on the real-time machining vibration data in each data segment, a finite-element-unit-force approach and an optimized space–time domain method are adopted to estimate the time-varying in-operation frequency response functions of the assembly interface. These FRFs are in turn employed to calculate stability lobe diagrams. Thus, the three-dimensional stability lobe diagram considering material removal is acquired via interpolation of all stability lobe diagrams. Third, to restrain milling chatter and resonance, the cutting parameters for next process step, e.g., spindle speed and axial cutting depth, are optimized by genetic algorithm. Finally, the proposed method is validated by a milling test of the assembly interface on a vertical tail, and the experimental results demonstrate that the proposed method can improve the machining quality and efficiency of the assembly interface, i.e., the surface roughness reduced from 3.2 μm to 1.6 μm and the machining efficiency improved by 33%.

Detection, Classification, and Quantification of Nonlinear Distortions in Time-Varying Frequency Response Function Measurements

The class of nonlinear time-varying (NLTV) systems includes all possible systems and, hence, is difficult to identify. Still, when the nonlinearities are not too strong then, depending on the application, a linear model might be sufficient for approximating the true response. To quantify the approximation error of the linear model, detecting and quantifying the nonlinear behavior are of key importance. In this article, we propose a fully automated procedure for detecting, classifying, and quantifying the nonlinear distortions in the response, possibly subject to a trend, of a specific class of NLTV systems to odd random phase multisine excitations. The result is a measurement of the time-varying frequency response function together with uncertainty bounds due to noise and nonlinear distortions. The user only has to specify four integer numbers: an upper bound on: 1) the degree on the time-domain polynomial modeling of the trend; 2) the degree of the frequency-domain polynomial basis function; 3) the number of frequency-domain hyperbolic-like basis functions, all used for modeling the output spectrum; and 4) a quality measure-called degrees of freedom (dof)-of the noise variance estimate. Guidelines are provided for obtaining reasonable values for these upper bounds.

Nonparametric Identification of Linear Time-Varying Systems using Gaussian Process Regression

Linear time-varying systems are a class of systems, the dynamics of which evolve in time. This results in a time-varying frequency response function where each frequency has a time-varying gain. In classical identification techniques, basis functions are employed to fit these time-varying gains. In this paper a new method based on Gaussian process regression is presented. The advantage of the proposed method is a more convenient model structure and model order selection.

Time-Variant Frequency Response Function Measurement in the Presence of Missing Data

Missing data are an important issue in large-scale low-cost wireless sensor networks. In these measurement applications, sensor failure, data transmission errors, and data removal for saving transmission power are the main causes for the missing data. This paper studies the impact of missing data on the measurement of the time-variant frequency response func- tion (TV-FRF) of linear time-variant systems. A nonparametric procedure for estimating the missing data and the TV-FRF is proposed. The theory is illustrated by simulations and experiments.

Hybrid Time-Variant Frequency Response Function Estimates Using Multiple Sets of Basis Functions

A new method for estimating the nonparametric time-variant frequency response function (TV-FRF) and its variance of a hybrid time-varying system is proposed. By parameterizing the hybrid time variation using Legendre polynomials and Haar multiresolution wavelets, the TV-FRF identification problem is reduced to a time-invariant FRF estimation problem. The stepwise regression method and Akaike information criterion are applied to select the significant basis functions without manual intervention. This method can achieve high estimation accuracy and small uncertainty without requiring prior knowledge of the time variation of system dynamics. Simulations and an experiment are included to illustrate the method.

Time-Variant Frequency Response Function Measurement of Multivariate Time-Variant Systems Operating in Feedback

The classical time-invariance assumption is often not (exactly) met in real-life applications. As a natural extension of the frequency response function (FRF), the time-variant FRF (TV-FRF) provides quick insight into the complex dynamics of time-variant systems. Recently, a procedure has been proposed to estimate nonparametrically the TV-FRF from known input, noisy output measurements of time-variant systems operating in open loop. However, in many applications, feedback is present either due to an explicit control action or due to the interaction between a nonideal actuator and the system under test. The extension of the open-loop approach to noisy input, noisy output measurements of time-variant systems operating in closed loop requires the deconvolution of the time-variant impulse response of the cascade of two time-variant systems. In this paper, this nontrivial problem is solved for a particular class of time-variant systems. The robustness of the approach with respect to the system assumption is demonstrated via simulations and measurements on an electronic circuit.

Nonparametric frequency response function estimates for switching piecewise linear systems

This paper proposes two algorithms (ATIRMM and ALPM) for estimating the time-varying behavior of single input single output (SISO) switching piecewise linear systems. Walsh basis functions are used to capture the non-smooth fast varying dynamics. The piecewise time-varying frequency response function (TV-FRF) is approximated by the sum of a series of LTI FRFs multiplied with a set of Walsh functions. The best linear time invariant approximation (BLTIA) of the TV-FRF is estimated with small uncertainty. Besides the BLTIA, the two methods are capable of estimating the noise power spectrum and the TV-FRF. The error analysis shows that ATIRMM delivers more accurate TV-FRF and BLTIA estimations, while ALPM has better performance in noise power spectrum estimation. The conclusions are illustrated by simulations.

Time-Variant Frequency Response Function Measurements on Weakly Nonlinear, Arbitrarily Time-Varying Systems Excited by Periodic Inputs

In quite some applications, the linear dynamics of the system under test evolve over time in a smooth nonperiodic manner. The dynamic behavior of such systems is uniquely described by the time-variant frequency response function (TV-FRF). However, since most real-life systems behave nonlinearly to some extent, it is important to detect and quantify the deviation between the ideal linear time-variant (LTV) framework and the true non-LTV dynamics. Therefore, in this paper, a nonparametric estimation procedure is developed for detecting and quantifying the noise level and the level of the nonlinear distortions in TV-FRF measurements using random-phase multisine excitations. As a result, the users can decide whether or not the LTV framework is accurate enough to describe the true dynamics in their particular application. The proposed measurement procedure is illustrated on a time-variant electronic circuit.

An RLS Tracking and Iterative Detection Engine for Mobile MIMO-OFDM Systems

This paper presents a tracking and detection engine for 2 $\times$ 2 spatial-multiplexing multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems under highly time-selective fading channels. A recursive least-squares (RLS) adaptive algorithm is adopted to track time-varying channel frequency response. Besides, iterative MIMO signal detection is used, including inter-carrier interference (ICI) cancellation, to enhance system performance. To avoid error propagation in the decision-directed RLS adaptation, ordered-selection mechanism and signal strength criteria are incorporated so that more reliable detection results can be selected for calculating channel statistics. The scheduling strategies and hardware reduction techniques are proposed for implementation of the computation-intensive RLS adaptive algorithm and ICI cancellation. This baseband processor has been fabricated in 90 nm CMOS technology and has 1023K gates. At the nominal operating frequency of 15.36 MHz, it provides throughput of 76.8 Mbps with 64-QAM up to 240 Km/hr. For constellation of 16-QAM and QPSK, the mobility of 360 Km/hr is supported. The power consumption is 11.8 mW at 0.7 V supply voltage. The operating frequency can be raised up to 103 MHz to offer 515 Mbps throughput with power consumption of 202 mW at 1.2V.

TIME-VARIANT FREQUENCY RESPONSE FUNCTION FOR ANALYSIS OF TIME-VARYING MECHANICAL SYSTEMS

System Identification is an important and often complex process in many areas of engineering. This process is not easy when parameters of the analysed system vary with time. In such cases classical methods fail to identify parameters properly. The work demonstrated in this paper deals with identification of natural frequencies of time-variant systems. The paper presents the application of the Time-Variant Frequency Response Function for this analysis. Calculation procedure requires division of output spectrum by input spectrum which often leads to division by close to zero values, and that leads to infinite (or undefined) values of resulting transfer function. Additional processing is required for interpretation. The major focus and challenge relate to ridge extraction of the above time-frequency characteristics. The methods presented in the paper are illustrated using experimental multi-degree-of-freedom system. The results show that the proposed method captures correctly the dynamics of the analysed time-variant systems.

Nonparametric time-variant frequency response function estimates using arbitrary excitations

The time-variant frequency response function (TV-FRF) uniquely characterises the dynamic behaviour of a linear time-variant (LTV) system. This paper proposes a method for estimating nonparametrically the dynamic part of the TV-FRF from known input, noisy output observations. The arbitrary time-variation of the TV-FRF is modelled by Legendre polynomials. In opposition to existing solutions, the proposed method is applicable to arbitrary inputs.

Wavelet-Based Frequency Response Function: Comparative Study of Input Excitation

Time-variant systems can be found in many areas of engineering. It is widely accepted that the classical Fourier-based methods are not suitable for the analysis and identification of such systems. The time-variant frequency response function—based on the continuous wavelet transform—is used in this paper for the analysis of time-variant systems. The focus is on the comparative study of various broadband input excitations. The performance of the method is tested using simulated data from a simple MDOF system and experimental data from a frame-like structure.

A Flexible and Scalable Structure to Compensate Frequency Response Mismatches in Time-Interleaved ADCs

In this paper, we present a flexible and scalable structure to compensate frequency response mismatches in time-interleaved analog-to-digital converters (TI-ADCs). The flexibility of the structure allows for designing compensation filters independent of the number of channels that can achieve any desired signal-to-noise ratio due to the scalability of the structure. Therefore, the compensation structure may be used to compensate time-varying frequency response mismatches in TI-ADCs, as well as to reconstruct uniform samples from nonuniformly sampled signals. We analyze the compensation structure, investigate its performance, and demonstrate application areas of the structure through numerous examples.

Robust OFDM Receivers for Dispersive Time-Varying Channels: Equalization and Channel Acquisition

In orthogonal frequency-division multiplexing, time variations of a multipath channel lead to a loss of orthogonality between the subcarriers, and thereby limit the achievable throughput. This paper proposes a general framework for a controlled removal of intercarrier interference (ICI) and channel acquisition. The core idea behind our method is to use a finite power series expansion for the time-varying frequency response, along with the known statistical properties of mobile radio channels. Channel acquisition and ICI removal are accomplished in the frequency domain and allow for any desired tradeoff between the residual ICI level, the required training for channel acquisition, and processing complexity. The proposed approach enables a high spectral efficiency (64-quadrature amplitude modulation mode) of digital video broadcasting-terrestrial in highly mobile environments.

A comparative study of iterative channel estimators for mobile ofdm systems

We investigate two iterative channel estimators for mobile orthogonal-frequency division multiplexing. The first estimator is based on iterative filtering and decoding whereas the second one uses an a posteriori probability (APP) algorithm. The first method consists of two cascaded one-dimensional Wiener filters, which interpolate the unknown time-varying two-dimensional frequency response in between the known pilot symbols. As shown, the performance can be increased by feeding back the likelihood values at the output of the APP-decoder to iteratively compute an improved estimate of the channel frequency response. The second method applies two APP estimators, one for the frequency and the other one for the time direction. The two estimators are embedded in an iterative loop similar to the turbo decoding principle. As shown in detail, this iterative estimator is superior and its performance is independent of whether the chosen time-frequency pilot grid satisfies the two-dimensional sampling theorem or not. The bit-error rate as a function of the signal-to-noise ratio is used as a performance measure. In addition, the convergence of the iterative decoding loop is studied with the extrinsic information transfer chart.

Rapid estimation of the range-doppler scattering function

Under wide sense stationary uncorrelated scattering (WSSUS) conditions, the signal spreading due to a random channel may be described by the scattering function (SF). In an active acoustic system, the received signal is modeled as the superposition of delayed and Doppler spread replicas of the transmitted waveform. The SF completely describes the second-order statistics of a WSSUS channel and can be considered a density function that characterizes the average spread in delay and Doppler experienced by an input signal as it passes through the channel. The SF and its measurement will be reviewed. An estimator is proposed based on a two-dimensional (2-D) autoregressive (AR) model for the scattering function. In order to implement this estimator, we derive the conditional minimum variance unbiased estimator of the time-varying frequency response of a linear channel. Unlike conventional Fourier methods, the AR approach does not suffer from the usual convolutional smoothing due to the signal ambiguity function. Simulation results are given.

Nonstationary Random Critical Excitation for Acceleration Response

The critical excitation method is promising as a robust method for accounting for inherent uncertainties in predicting forthcoming earthquake events and for constructing design earthquake ground motions in a reasonable way. Most of the proposed theories are based on deterministic approaches and deal with displacement responses. A stochastic acceleration response index is treated here as the objective function to be maximized. The power (area of power spectral density function) and the intensity (magnitude of power spectral density function) are fixed and the critical excitation is found under these restrictions. It is shown that the original idea for stationary random inputs can be utilized effectively in the procedure for finding a critical excitation for nonstationary acceleration responses of nonproportionally damped structural systems. Several numerical examples are presented to demonstrate the characteristics of generalized time-varying frequency response functions for models with various stiffness and damping distributions.

Time-domain wave-oriented data processing of scattering by nonuniform truncated gratings

In a companion paper [ J. Opt. Soc. Am. A11, 2675 ( 1994)] we investigated wave-oriented processing techniques that extract from frequency-domain (FD) scattering data for nonuniform truncated thin-wire or strip gratings the wave phenomenology that ties features in data to scattering mechanisms that are responsible for these features. The resulting observable-based parameterization (OBP) should be useful for construction of wave-based algorithms aimed, through forward and backward propagation routines, at design, classification, and imaging. The processing strategy projects the data, which are assembled on an elevated track at height z parallel to the grating-plane coordinate x, onto the (x, kx) phase-space subdomain by means of windowed Fourier transforms; here kx is the spatial spectral wave number corresponding to x. The (x, kx) phase-space distributions and their information content for various grating configurations are analyzed in detail and are related to previously derived analytic scattering models based on truncated local Floquet modes (FM’s) and on FM-modulated edge diffractions. We explore time-domain (TD) wave-oriented processing techniques for scattering by truncated gratings produced by a pulsed incident plane wave. By spatial–temporal resolution, the TD data base adds to the FD processing options. Time (t)–frequency (ω) phase-space distributions implemented through windowed transforms extract from TD data new TD phenomenology, TD-OBP, that differs fundamentally from that in the frequency domain: strongly dispersive TD-FM’s with prolonged time-varying frequency response ωm(t), where m is the FM index, and temporally well-resolved weakly dispersive impulselike edge diffractions. These phenomenologies extracted from the TD scattering data are interpreted in terms of, and shown to be in agreement with, previously developed analytic TD scattering models. The (t, ω) processing is applied to pulsed plane-wave scattering data produced for various grating configurations by previously calibrated numerical reference codes and reveals the changes in (t, ω) footprints that are attributable to departures from strict canonical truncated periodicity. Short-pulse TD excitation is found to resolve the element structure within each scattering cell directly, in contrast to (t, ω) processing, in which element-structure information is tied indirectly to the FM excitation strengths.