Impulse Response Coefficients Research Articles

Residence time density (RTd) identification through deconvolution of finite time horizon input output data and its Application to a novel analytical dispersion process RTd model

This work presents first an approach to the identification of Residence Time density (RTd) and Residence Time Distribution (RTD) functions, through deconvolution of finite time horizon, input/output data generated by a zero-order hold input, using the novel concept of zero-order hold, average, impulse response coefficients. Subsequently, a novel RTd analytical expression is derived for an open-open axial dispersion process with a finite experimental section in a tube of infinite length, and an explanation is provided for this RTd model’s differences from the literature. This new RTd expression is then employed in two case studies to demonstrate the effectiveness of the proposed identification through a deconvolution conceptual framework in identifying RTd model parameters, and in assisting in the selection of RTd models which are compatible with experimental data.

Dispersed-sparsity-aware LMS algorithm for scattering-sparse system identification

We develop a least-mean-squares (LMS) algorithm to identify scattering-sparse systems, where the few significantly large coefficients of the unknown impulse response are dispersed along the full length, instead of grouped into clusters. Many wireless communication channels such as the underwater acoustic channels, cellular communication channels and aviation channels are typical scattering-sparse systems. In the proposed strategy, the difference between the ℓ1-norm and ℓ∞,1-norm of the uniformly-divided tap-weight vector of the adaptive filter is utilized as a penalty and is introduced into the mean-square-error cost function, where the ℓ∞,1-norm of the tap-weight vector is used to locate the unknown large coefficients in view of the characteristics of dispersed sparsity. A dispersed-sparsity-aware LMS (DS-LMS) algorithm is then proposed by following the stochastic subgradient method. We study the mean and mean-square behaviors of the proposed algorithm. We also provide theoretical guidelines for the parameter settings that ensure that the proposed DS-LMS algorithm converges to a lower mean-square-deviation (MSD) level than the traditional LMS algorithm. Simulation results verify the effectiveness of the proposed DS-LMS algorithm, and correctness of the theoretical findings.

Consistency of averaged impulse response estimators in vector autoregressive models

We show root‐T consistency of the smoothed AIC and smoothed BIC model averaging estimators (sAIC, sBIC) of impulse response coefficients in stationary vector autoregressive models of finite lag order. We also show that there is not one unique way to define the sAIC and sBIC estimators, but that instead there is a whole class of each of these defined by a weight scaling factor that allows the averaging estimator to become more similar to either its model selection counterpart or the equal weights averaging estimator. We also show asymptotic validity of a bootstrap method for estimating the averaging estimators' distributions. Simulations illustrate the benefits of using sAIC instead of AIC estimators.

Optimized FIR Filter Using Genetic Algorithms: A Case Study of ECG Signals Filter Optimization

The advancement in technology and the availability of specialized digital signal processing chips have made digital filter design and implementation more feasible in a variety of fields, including biomedical engineering. This paper makes two key contributions. First, it uses a genetic algorithm to optimize the coefficients of finite impulse response (FIR) filters. Second, it conducts a case study on using genetic algorithms to optimize FIR filters for electrocardiogram (ECG) biomedical signal noise removal. The goal of the proposed filter design approach is to achieve the desired signal bandwidth while minimizing the side lobe level and eliminating unwanted signals using a genetic algorithm. The results of a comprehensive analysis show that the genetic algorithm-based filter is more effective than conventional filter designs in terms of noise removal efficiency.

Localization and Estimation of Unknown Forced Inputs: A Group LASSO Approach

This paper studies the problem of locating the sparse set of sources of forcing inputs driving linear systems from noisy measurements when the initial state is unknown. This problem is particularly relevant to detecting forced oscillations in electric power networks. We express measurements as an additive model comprising the initial state and inputs grouped over time, both expanded in terms of the basis functions (i.e., impulse response coefficients). Using this model, with probabilistic guarantees, we recover the locations and simultaneously estimate the initial state and forcing inputs using a variant of the group LASSO (linear absolute shrinkage and selection operator) method. Specifically, we provide upper bounds on: (i) the probability that the group LASSO estimator incorrectly identifies the locations and (ii) the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2}$</tex-math></inline-formula> -norm of the estimation error. Our bounds depend on the number of measurements, inputs, and sensors; the sensor noise variance; and the minimum singular value of the observability and impulse response matrices. Our theoretical analysis is one of the first to provide a complete treatment for the group LASSO estimator for the left invertible linear systems with delay. Finally, we validate the performance of the estimator on synthetic models and the IEEE 68-bus, 16-machine power system.

Robust Design of a Fractional-Delay Repetitive Controller for Uncertain Feedback Control Systems and Its Validation on a Magnetic Bearing Test Rig

This article presents a robust design of a fractional-delay repetitive controller in the frequency domain. The control goal is to accurately suppress the control error caused by a disturbance whose period may be a non-integer multiple of the sampling period. Coefficients of the repetitive controller finite impulse response (FIR) filters are calculated by solving a convex optimization problem that includes constraints limiting both the sensitivity function and the control sensitivity function. The proposed new design algorithm is verified by experiments on a test rig to efficiently damp shaft vibrations of an active magnetic bearing (AMB).

Model order reduction based on low-rank decomposition of the cross Gramian

This paper considers model order reduction based on low-rank decomposition of the cross Gramian for linear systems. The proposed approach uses the low-rank factors of the cross Gramian to generate approximate balanced model for the large-scale system. Then, the reduced-order model is obtained by truncating the states corresponding to the small approximate Hankel singular values. The low-rank factors are directly constructed from the expansion coefficients of impulse responses in the space spanned by Legendre polynomials by solving block tridiagonal linear systems. In contrast to balanced truncation related approaches which require to solve Sylvester equation to compute the full cross Gramian, the proposed method needs to solve sparse linear equations, and only one singular value decomposition is applied to a low-dimensional matrix. The stability preservation of the reduced model is briefly discussed. And in combination with the dominant subspace projection method, the reduction procedure is modified to alleviate the shortcoming, which may unexpectedly lead to unstable systems even though the original one is stable. Finally, numerical experiments are given to demonstrate the effectiveness of the proposed methods.

Adaptive Infinite Impulse Response System Identification Using Elitist Teaching-Learning- Based Optimization Algorithm

Infinite Impulse Response (IIR) systems identification is complicated by traditional learning approaches. When reduced-order adaptive models are utilised for such identification, the performance suffers dramatically. The IIR system is identified as an optimization issue in this study. For system identification challenges, a novel population-based technique known as Elitist teacher learner-based optimization (ETLBO) is used to calculate the best coefficients of unknown infinite impulse response (IIR) systems. The MSE function is minimised and the optimal coefficients of an unknown IIR system are found in the system identification problem. The MSE is the difference between an adaptive IIR system's outputs and an unknown IIR system's outputs. For the unknown system coefficients of the same order and decreased order cases, exhaustive simulations have been performed. In terms of mean square error, convergence speed, and coefficient estimation, the results of actual and reduced-order identification for the standard system using the novel method outperform state-of-the-art techniques. For approximating the same-order and reduced-order IIR systems, four benchmark functions are examined utilizing GA, PSO, CSO, and BA. To demonstrate the improvements, the approach is evaluated on three conventional IIR systems of 2nd, 3rd, and 4th order models. On the basis of computing the mean square error (MSE) and fitness function, the suggested ETLBO approach for system identification is proven to be the best among others. Furthermore, it is confirmed that the suggested ETLBO method outperforms some of the other known system identification strategies. Finally, the efficiency of the dynamic nature of the control parameters of DE, TLBO, and BA in finding near parameter values of unknown systems is demonstrated through comparison data. The simulation results show that the suggested system identification approach outperforms the current methods for system identification.

Identification of MISO Hammerstein system using sparse multiple kernel-based hierarchical mixture prior and variational Bayesian inference

The Hammerstein model is a cascade composition of a static memoryless nonlinear function followed by a linear time-invariant dynamical subsystem, which is capable of modeling a wide range of nonlinear dynamical systems. Model structural parameter selection (including the model order and the nonlinearity order) and sparse representation of the static nonlinear function are two issues that receive increasing interests in Hammerstein system identification. In this paper, a novel Bayesian sparse multiple kernel-based identification method (BSMKM) for multiple-input single-output (MISO) Hammerstein system is proposed to handle those issues, where the basis-function model and the finite impulse response model are used to represent the nonlinear part and the linear part respectively. Firstly, in order to jointly realize the model parameter estimation, the sparse representation of static nonlinear function (the nonlinearity order selection can also be realized indirectly) and the model order selection of linear dynamical system, a hierarchical prior distribution is constructed based on Gaussian scale mixture model and sparse multiple kernel, which can characterize both inter-group sparsity and intra-group correlation structure. Then, a full Bayesian method based on variational Bayesian inference is proposed to estimate all unknown model parameters, including finite impulse response coefficients, hyperparameters and noise variance. Finally, the performance of the proposed BSMKM identification method is evaluated by numerical experiments using both simulation and real data.

Evaluating Satellite-Observed Ecosystem Function Changes and the Interaction with Drought in Songnen Plain, Northeast China

Drought is considered one of the devastating natural disasters worldwide. In the context of global climate change, the frequency and intensity of drought have increased, thereby affecting terrestrial ecosystems. To date, the interactions between ecosystem change and drought, especially their mutual lag and cumulative effects is unclear. The Songnen Plain in northeastern China is one of the three major black soil areas in the world and is highly sensitive to global change. Herein, to quantify the interaction between drought and ecosystem function changes in the Songnen Plain, integrating with time-series moderate resolution imaging spectroradiometer (MODIS), leaf area Index (LAI), evapotranspiration (ET), and gross primary productivity (GPP) data, we calculated the standardized precipitation and evapotranspiration index (SPEI) based on the meteorological data, diagnosed the causal relationship between SPEI and the ecosystem function indicators i.e., LAI, ET, and GPP, and analyzed the time-lag and cumulative effects between the degree of drought and three ecosystem function indicators using impulse response analysis. The results showed that the trend of SPEI (2000–2020) was positive in the Songnen Plain, indicating that the drought extent had eased towards wetness. LAI showed insignificant changes (taking up 88.34% of the total area), except for the decrease in LAI found in some forestland and grassland, accounting for 9.43%. The pixels showing a positive trend of ET and GPP occupied 24.86% and 54.94%, respectively. The numbers of pixels with Granger causality between LAI and SPEI (32.31%), SPEI and GPP (52.8%) were greater at the significance 0.05 level. Impulse responses between each variable pair were stronger mainly between the 6th and 8th months, but differed significantly between vegetation types. Grassland and cropland were more susceptible to drought than forest. The cumulative impulse response coefficients values indicated that the mutual impacts between all variables were mainly positive. The increased wetness positively contributed to ecosystem function, and in turn enhanced ecosystem function improved regional drought conditions to some extent. However, in the northeastern forest areas, the SPEI showed a significant negative response to increased ET and GPP, suggesting that the improved physiological functions of forest might lead to regional drought. There were regional differences in the interaction between drought conditions and ecosystem function in the Songnen Plain over the past 21 years.

Sparse estimation in linear dynamic networks using the stable spline horseshoe prior

Identification of the so-called dynamic networks is one of the most challenging problems appeared recently in control literature. Such systems consist of large-scale interconnected systems, also called modules. To recover full networks dynamics the two crucial steps are topology detection, where one has to infer from data which connections are active, and modules estimation. Since a small percentage of connections are effective in many real systems, the problem finds also fundamental connections with group-sparse estimation. In particular, in the linear setting modules correspond to unknown impulse responses expected to have null norm but in a small fraction of samples. This paper introduces a new Bayesian approach for linear dynamic networks identification where impulse responses are described through the combination of two particular prior distributions. The first one is a block version of the horseshoe prior, a model possessing important global–local shrinkage features. The second one is the stable spline prior, that encodes information on smooth-exponential decay of the modules. The resulting model is called stable spline horseshoe (SSH) prior. It implements aggressive shrinkage of small impulse responses while larger impulse responses are conveniently subject to stable spline regularization. Inference is performed by a Markov Chain Monte Carlo scheme, tailored to the dynamic context and able to efficiently return the posterior of the modules in sampled form. Numerical studies show that the new approach can accurately reconstruct “line by line” networks dynamics without assuming any knowledge on the topology also when thousands of unknown impulse response coefficients must be inferred from data sets of relatively small size.

Deterministic and Stochastic Modeling Approaches for Saturation Nonlinearity

Being different from the most traditional methods of nonlinearity modelling, non-parametric modelling approaches viz. deterministic and stochastic approaches for saturation nonlinearity are proposed in the sense of system impulse response. Based on deterministic approach, the closed-loop system involved saturation nonlinearity can be modelled as the response of the closed-loop system that is subject to impulse stimulation. Alternatively, the closed-loop system involved saturation nonlinearity can be modelled in stochastic manner, in which the impulse response coefficients are estimated by the FCOR algorithm. Moreover, it shows some linear relationship of the impulse response coefficients between different saturation ratios in both the deterministic and stochastic models. This is illustrated by three different numerical examples.

Moth Flame Optimization Algorithm for Optimal FIR Filter Design

This paper presents the application of Moth Flame optimization (MFO) algorithm to determine the best impulse response coefficients of FIR low pass, high pass, band pass and band stop filters. MFO was inspired by observing the navigation strategy of moths in nature called transverse orientation composed of three mathematical sub-models. The performance of the proposed technique was compared to those of other well-known high performing optimization techniques like techniques like Particle Swarm Optimization (PSO), Novel Particle Swarm Optimization (NPSO), Improved Novel Particle Swarm Optimization (INPSO), Genetic Algorithm (GA), Parks and McClellan (PM) Algorithm. The performances of the MFO based designed optimized FIR filters have proved to be superior as compared to those obtained by PSO, NPSO, INPSO, GA, and PM Algorithm. Simulation results indicated that the maximum stop band ripples 0.057326, transition width 0.079 and fitness value 1.3682 obtained by MFO is better than that of PSO, NPSO, INPSO, GA, and PM Algorithms. The value of stop band ripples indicated the ripples or fluctuations obtained at the range which signals are attenuated is very low. The reduced value of transition width is the rate at which a signal changes from either stop band to pass band of a filter or vice versa is very good. Also, small fitness value in an indication that the values of the control variable of MFO are very near to its optimum solutions. The proposed design technique in this work generates excellent solution with high computational efficiency. This shows that MFO algorithm is an outstanding technique for FIR filter design.

Laguerre-Gramian-based structure-preserving model order reduction for second-order form systems

A new structure-preserving model order reduction technique based on Laguerre-Gramian for second-order form systems is presented in this article. The main task of the proposed approach is to use the Laguerre polynomial expansion of the matrix exponential function to obtain the approximate low-rank decomposition of the Gramians for the equivalent first-order representation of the original second-order form system. The approximate balanced system is generated by a balancing transformation which is directly computed from the expansion coefficients of impulse responses in the space spanned by Laguerre polynomials, without computing the full Gramians for the first-order representation. Then, the reduced second-order model is constructed by truncating the states with small approximate Hankel singular values (HSVs). The above method has a disadvantage that it may unexpectedly result in unstable systems although the original one is stable. Therefore, modified reduction procedure combined with the dominant subspace projection method is presented to alleviate the limitation. Finally, two numerical experiments are provided to demonstrate the effectiveness of the algorithms.

Model-plant mismatch detection for cross-directional processes

This paper presents a two-component framework to detect model-plant mismatch (MPM) in cross-directional (CD) processes on paper machines under model-predictive control. First, routine operating data is used for system identification in closed loop; second, a one-class support vector machine (SVM) is trained to predict MPM. The iterative identification method alternates between identifying the finite impulse response coefficients of the spatial and temporal models. It converges, and the parameter estimates are asymptotically consistent. Coefficient estimates drawn from normal operation are used to train a one-class SVM, which then detects model-plant mismatch in subsequent routine operation. This approach applies to routine operating data without requiring external excitations. It can also distinguish mismatches in the process model from changes in the noise model. Examples of CD processes on paper machines are provided to verify the effectiveness of both components.

Inference in Structural Vector Autoregressions identified with an external instrument

This paper studies Structural Vector Autoregressions in which a structural shock of interest (e.g., an oil supply shock) is identified using an external instrument. The external instrument is taken to be correlated with the target shock (the instrument is relevant) and to be uncorrelated with other shocks of the model (the instrument is exogenous). The potential weak correlation between the external instrument and the target structural shock compromises the large-sample validity of standard inference. We suggest a confidence set for impulse response coefficients that is not affected by the instrument strength (i.e., is weak-instrument robust) and asymptotically coincides with the standard confidence set when the instrument is strong.

Nonlinear Kalman Filter-Based Robust Channel Estimation for High Mobility OFDM Systems

High-speed train (HST) and vehicle-to-vehicle (V2V), as typical scenes of 5G communication, have attracted extensive attention from academia and industry in recent years. Aiming at the channel characteristics of frequency-selective fading, fast time-varying and time-domain non-stationary in high mobility scenarios, a nonlinear Kalman filter-based high-speed channel estimation algorithm for orthogonal frequency-division multiplexing (OFDM) systems is proposed. We adopt basis expansion model (BEM) to eliminate the inter-subcarrier interference (ICI) caused by the fast time-varying characteristics. For the non-stationary characteristics of high mobility channel, a channel interpolation algorithm based on extended Kalman filter (EKF) is introduced to jointly estimate the channel impulse response (CIR) and time correlation coefficients. However, the EKF channel estimation uses structure of decision feedback to construct the observation matrix, which would lead to error propagation. This paper analyzes the generation of error propagation through theoretical derivation. Furthermore, for the error propagation of EKF, we introduce unscented Kalman filter (UKF) algorithm to perform Gaussian approximation of non-Gaussian observing system, and eliminate the influence by Kalman filter (KF). Simulation results demonstrate that the channel estimation accuracy of BEM-UKF is further improved compared with BEM-EKF, and the influence of pilot distance (PD) is smaller, which further improves the robustness of the algorithm.

Assessing the relationship between vegetation greenness and surface temperature through Granger causality and Impulse-Response coefficients: a case study in Mexico

ABSTRACTThe existence of a consistent inverse relationship between vegetation greenness and surface temperature has been the premise of many environmental studies. However, some authors have found that the nature of this relationship varies depending on the spatial and temporal scales of analysis as well as vegetation type. Therefore, this research aims to contribute to the understanding of this matter by evaluating the annual and intra-seasonal relationship between Leaf Area Index (LAI) and Land Surface Temperature (LST) in Central Mexico using monthly anomalies of Moderate Resolution Imaging Spectroradiometer (MODIS) data collected from 2002 to 2017. LAI is proposed as an alternative index to overcome the shortcomings of other widely used indicators of vegetation greenness (e.g. Normalized Difference Vegetation Index and Enhanced Vegetation Index). The presence/absence of any relationship is investigated through the notion of Granger causality, while the sign and strength of the relationship is estimated by means of an Impulse-Response (IR) function. Unlike traditional regression and correlation analysis, the Granger causality approach enables the examination of lagged effects of one variable over the other based on past values of both variables. IR coefficients, which have been rarely used in the related literature, help to model the over-time response of a variable with the change of another variable. The overall results indicate that, at any temporal scale, Granger causality from LST to LAI occurs more consistently than causality in the opposite direction. At the annual scale, the nature of the relationship is primarily inverse in both directions and usually weaker from LAI to LST. At the seasonal scale, the occurrence of LST to LAI causality is higher in spring (it occurs in about 40% of the evaluated pixels) and lower in winter (10%) among all forest types. The effect of LST on LAI is predominantly inverse (median coefficient 1 month after impulse −0.043) and particularly strong in deciduous broadleaf forest during summer. On the other hand, the effect of LAI on LST is mainly direct in autumn and inverse in the remaining seasons, except for evergreen needleleaf forest where the effect is inverse only in summer. The highest presence (23%) and strength (−0.039) of LAI to LST causality occur in spring over deciduous broadleaf forest. Based on these results, caution has to be exercised when assuming a consistent strong inverse relationship between vegetation greenness and surface temperature, which seems to be the general consensus in much of the literature that makes use of these two variables to study an environmental phenomenon.

A Novel Methodology for the Determination of Impulse Response Coefficients Applied to Transmission Line Protection Relays

Impulse Response Coefficients (IRC) of digital filters is an imperative step in the development of transmission line protection relay algorithms. Traditionally, Fourier-based filters are used in real applications, where IRC are fixed values of sine and cosine functions with a data window of one or more cycles. Based on state-of-the-art, Mother Wavelet coefficients used in Multiresolution Analysis, and Structuring Element coefficients used in Mathematical Morphology are usually proposed to develop protection algorithms. However, the proper choice of these coefficients is based on empirical process of trial and error. This paper proposes a novel methodology for optimally determining coefficients that depend on the waveform structure analyzed, which is determined using variance as the metric. Assessment of methodology for three case studies considering requirements of relay manufactures (response time, design, harmonic attenuation and other) is presented. The first assessment is to extract coefficients useful for distinguishing among non-fault conditions, harmonics, and arcing faults. The second one is to extract coefficients to filter harmonic components. The assessment is carried out considering different data windows and sampling rates. Test results highlight the efficiency of the model to determine specific coefficients for each case study analyzed. Interestingly, results also showed that the discovered coefficients can be used in another filtering technique. Thus, the third case study involves developing two fault classifiers, which are developed using mathematical morphology where the structuring elements used correspond to the coefficient vectors determined through the proposed methodology. There is a notable paucity of scientific literature focusing on this topic. Therefore, there are several important areas where this study makes an original contribution regarding protection relays.

Robust Analytical Design of Optimal Equiripple Lowpass FIR Filters

For the first time, an analytical design of optimal equiripple lowpass finite impulse response filters is presented. An analytical filter design, which is based on formulas, stands in contrast to the Parks-McClellan approach which is based on a numerical optimization. An advantage of evaluating impulse response coefficients using formulas over a numerical optimization is the robustness of the analytical design. Equiripple filters are optimal in terms of a minimal filter length for an arbitrary filter specification. The novel design is based on an equiripple approximating polynomial which approximates two constants in two disjoint intervals in optimal equiripple sense. A recursive formula for evaluating the impulse response of the filter is also introduced. The algorithm provides not only robust formulas for evaluating the impulse response, but also an analytical view on its coefficients. An example demonstrates the efficiency of the design. Its superiority in terms of robustness over the Parks-McClellan approach is emphasized.