Finite Impulse Response Model Research Articles

Development of a software sensor for phosphorus in municipal wastewater

AbstractDifferent multivariate techniques were applied to data from a wastewater treatment plant in order to develop a software sensor for phosphorus. The predictive power, measured as root mean square error of cross‐validation (RMSECV) and root mean square error of prediction (RMSEP), of partial least squares (PLS) models was found to be superior to that of multiple linear regression (MLR) and principal component regression (PCR) models. The result from using a static as well as a finite impulse response (FIR) model structure was also investigated. Good estimates of phosphorus were obtained for both kinds of model structure, but the FIR models were slightly better than the static ones. Out of the two different fractions of phosphorus that were modelled, i.e. total phosphorus and phosphate in solution, the best predictions were obtained for soluble phosphorus. Copyright © 2002 John Wiley & Sons, Ltd.

A new identification approach for FIR models

The identification of stochastic discrete systems disturbed with noise is discussed in this brief. The concept of general prediction error (GPE) criterion is introduced for the time-domain estimate with optimal frequency estimation (OFE) introduced for the frequency-domain estimate. The two estimation methods are combined to form a new identification algorithm, which is called the empirical frequency-domain optimal parameter (EFOP) estimate, for the finite impulse response (FIR) model interfered by noise. The algorithm theoretically provides the global optimum of the model frequency-domain estimate. Some simulation examples are given to illustrate the new identification method.

L2 Model reduction and variance reduction

In this contribution we examine certain variance properties of model reduction. The focus is on L 2 model reduction, but some general results are also presented. These general results can be used to analyze various other model reduction schemes. The models we study are finite impulse response (FIR) and output error (OE) models. We compare the variance of two estimated models. The first one is estimated directly from data and the other one is computed by reducing a high order model, by L 2 model reduction. In the FIR case we show that it is never better to estimate the model directly from data, compared to estimating it via L 2 model reduction of a high order FIR model. For OE models we show that the reduced model has the same variance as the directly estimated one if the reduced model class used contains the true system.

LEARNING OF FIR AND ARX NEURAL NETWORKS WITH EMPIRICAL RISK MINIMIZATION ALGORITHM

The probably approximately correct (PAC) learning theory was originally introduced to address static models where the input data were assumed to be i.i.d. In many real applications; however, datasets and systems to be modeled are often dynamic. This encourages the efforts to extend the conventional PAC learning theory to address typical dynamic models such as finite impulse response (FIR) and auto regressive exogenous (ARX) models. This paper presents such extensions for the PAC learning theory and uses the resulting theory to evaluate the learning properties of some families of FIR and ARX neural networks. For ARX models, besides the learning properties of the neural models, stochastic stability of the models are also evaluated.

Outliers in process modeling and identification

Model-based control strategies like model predictive control (MPC) require models of process dynamics accurate enough that the resulting controllers perform adequately in practice. Often, these models are obtained by fitting convenient model structures (e.g., linear finite impulse response (FIR) models, linear pole-zero models, nonlinear Hammerstein or Wiener models, etc.) to observed input-output data. Real measurement data records frequently contain "outliers" or "anomalous data points," which can badly degrade the results of an otherwise reasonable empirical model identification procedure. This paper considers some real datasets containing outliers, examines the influence of outliers on linear and nonlinear system identification, and discusses the problems of outlier detection and data cleaning. Although no single strategy is universally applicable, the Hampel filter described here is often extremely effective in practice.

REGRESSOR SELECTION WITH THE ANALYSIS OF VARIANCE METHOD

Identification of non-linear finite impulse response (N-FIR) models is studied. In particular the selection of model structure, i.e., to find the best regressors, is examined.In this paper it is shown that a statistical method, the analysis of variance, is a better alternative than exhaustive search among all possible regressors, in the identification of the structure of non-linear FIR-models. The method is evaluated for different conditions on the input signal to the system. The results will serve as a foundation for the extension of the ideas to non-linear autoregressive processes.

VARIANCE ASPECTS OF L2-MODEL REDUCTION WHEN UNDERMODELING – THE OUTPUT ERROR CASE

In this contribution, variance properties of L2 model reduction are studied. That is, given an estimated model of high order we study the resulting variance of an L2 reduced approximation. The main result of the paper is showing that estimating a low order output error (OE) model via L2 model reduction of a high order model gives a smaller variance compared to estimating a low order model directly from data in the case of undermodeling. This has previously been shown to hold for FIR (Finite Impulse Response) models, but is in this paper extended to general linear OE models.

Asymptotic performance of second-order algorithms

This paper re-examines the asymptotic performance analysis of second-order methods for parameter estimation in a general context. It provides a unifying framework to investigate the asymptotic performance of second-order methods under the stochastic model assumption in which both the waveforms and noise signals are possibly temporally correlated, possibly non-Gaussian, real, or complex (possibly noncircular) random processes. Thanks to a functional approach and a matrix-valued reformulated central limit theorem about the sample covariance matrix, the conditions under which the asymptotic covariance of a parameter estimator are dependent or independent of the distribution of the signal involved are specified. Finally, we demonstrate the application of our general results to direction of arrival (DOA) estimation, identification of finite impulse response models, sinusoidal frequency estimation for mixed spectra time series, and frequency estimation of sinusoidal signal with very lowpass envelope.

Identification of linear systems using polynomial kernels in the frequency domain

Abstract In prior work we presented an identification algorithm using polynomials in the time domain. In this article, we extend this algorithm to include polynomials in the frequency domain. A polynomial is used to represent the imaginary part of the Fourier transform of the impulse response. The Hilbert transform relationship is used to compute the real part of the frequency response and hence the complete process model. The polynomial parameters are computed based on the computationally efficient linear least square method. The order of the polynomial is estimated based on residue decrement. Simulated and experimental results show the effectiveness of this method, particularly for short input/output data sequence with high signal to noise ratio. The frequency domain polynomial model complements the time domain methods since it can provide a good estimate of the time to steady state for time domain FIR (finite impulse response) models. Confidence limits in time or frequency domain can be computed using this approach. Noise rejection properties of the algorithm are illustrated using data from both simulated and real processes.

Identification of the Tennessee Eastman challenge process with subspace methods

Abstract The Tennessee Eastman challenge process is a realistic simulation of a chemical process that has been widely used in process control studies. In this case study, several identification methods are examined and used to develop MIMO models that contain seven inputs and ten outputs. ARX and finite impulse response models are identified using reduced-rank regression techniques (PLS and CCR) and state-space models identified with prediction error methods and subspace algorithms. For a variety of reasons, the only successful models are the state-space models produced by two popular subspace algorithms, N4SID and canonical variate analysis (CVA). The CVA model is the most accurate. Important issues for identifying the Tennessee Eastman challenge process and comparisons between the subspace algorithms are also discussed.

Magnetic noise compensation using FIR model parameter estimation method

AbstractFor magnetic noise compensation in the field of detection (magnetic anomaly detection) of magnetic dipole targets (such as sunken ships) by magnetic sensors carried on an aircraft, a quadratic method of compensation of scalar magnetic sensors has been reported. However, in order to use a highly sensitive vector magnetic sensor such as a superconducting quantum interference device, it is necessary to obtain the scalar magnetic field (intensity of the magnetic field) accurately from the three‐axis vector field. Also, in quadratic compensation, a special flight is needed, imposing a significant burden on the platform crew members for the acquisition of data for quadratic compensation. In the present paper, an FIR (Finite Impulse Response) model parameter estimation method is proposed that allows magnetic noise compensation for a three‐axis vector magnetic sensor without a special flight. The experimental data confirm the effectiveness of the proposed FIR model parameter estimation method. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 85(3): 1–11, 2002

Local Linear Modeling for Control of Batch Processes

This paper contains of four contributions. An existing modeling framework for batch processes, which consists of a set of Finite Impulse Response (FIR) models, has been extended with the effect of initial conditions on batch evolution. It has been shown that an analogous modeling framework can be derived from a set of AutoRegressive models with eXogenous (ARX) inputs. The ARX models are superior to the FIR models with respect to parameterization and thus with respect to indentifiability as well as for capturing multivariable correlations. Based on the presented modeling framework, an existing Iterative Learning Control (ILC) algorithm has been extended with the effect of initial conditions and noisy measurements. The ILC algorithm is set up in a Model Predictive Control (MPC) framework. The presented tools and algorithms are demonstrated on simulated fed-batch yeast fermentations.

On learning of Sigmoid Neural Networks

AbstractThe Probably Approximately Correct (PAC) learning theory creates a framework to assess the learning properties of static models for which the data are assumed to be independently and identically distributed (i.i.d.). One important family of dynamic models to which the conventional PAC learning can not be applied is nonlinear Finite Impulse Response (FIR) models. The present article, using an extension of PAC learning that covers learning with m‐dependent data, the learning properties of FIR modeling with sigmoid neural networks are evaluated. These results include upper bounds on the size of the data set required to train FIR sigmoid neural networks, provided that the input data are uniformly distributed. © 2001 John Wiley & Sons, Inc.

Optimal Estimation and Sequential Channel Equalization Algorithms for Chaotic Communications Systems

Many previously proposed communications systems based on chaos disregard common channel distortions and fail to work under realistic channel conditions. In this paper, optimal estimation and sequential channel equalization algorithms are proposed for chaotic communications systems where information is encoded using symbolic dynamics representations. For the optimal estimate of the transmitted signal, the symbolic dynamics representation of chaotic systems is first exploited to represent the chaotic dynamics of the signal by an equivalent trellis diagram. Then, the Viterbi algorithm is used to achieve an optimal estimate of the noise corrupted chaotic sequence. For the sequential channel equalization algorithm, the dynamics-based trellis diagram is expanded to accommodate a finite impulse response (FIR) model of the channel. Once the initial estimate of the channel parameters is obtained through the training sequence, then the Viterbi algorithm is used to estimate the chaotic sequence. If necessary, channel parameters can then be updated through successive estimates of the chaotic sequence. The proposed algorithms are simulated for both time-invariant and time-varying channels.

Robust Stability Conditions for SISO Dynamic Matrix Control

AbstractThis paper presents the robust stability conditions for single‐input/single‐output (SISO) dynamic matrix control (DMC). Model uncertainty is described by using a range of possible plant impulse responses, and a new form of DMC algorithm based on a finite impulse response (FIR) model is discussed. Then robust stability conditions for the new DMC algorithm are derived by applying Jury's dominant coefficient lemma. These results provide theoretical foundations for analyzing and designing predictive control systems.

Turbo equalization for GMSK signaling over multipath channels based on the Gibbs sampler

We consider the problem of Bayesian data restoration for Gaussian minimum shift keying (GMSK) signals over unknown multipath channels. As an alternative to the linear approximation method employed in the conventional finite impulse response (FIR) model, we develop a nonlinear signal model for this system. A Bayesian equalizer based on the Gibbs sampler, a Markov chain Monte Carlo (MCMC) procedure, is developed for estimating the a posteriori symbol probability in the GMSK system without explicit channel estimation. The basic idea of this technique is to generate ergodic random samples from the joint posterior distribution of all unknowns, and then to average the appropriate samples to obtain the estimates of the unknown quantities. Being soft-input soft-output in nature, the proposed Bayesian equalization technique is well suited for iterative processing in a coded system, which allows the Bayesian equalizer to successively refine its processing based on the information from the decoding stage, and vice versa.

Robust Disturbance Rejection for FIR Systems with Bounded Parameters

Abstract A robust MPC algorithm is formulated for systems described by a finite impulse response (FIR) model with a constant output disturbance. Uncertainty in the system is parameterized by ellipsoidal bounds on the FIR parameters. Cost function constraints are used to provide off-set free control. The steady-state properties of the algorithm are analyzed and a simulation example is provided to illustrate advantages of the proposed approach.

Model Order Selection of N-FIR Models by the Analysis of Variance Method

Identification of nonlinear finite impulse response (N-FIR) models is studied. In particular the selection of model structure, Le., to find the contributing input time lags, is examined. A common method, exhaustive search among models with all possible combinations of the input time lags, has some undesired drawbacks, as a tendency that the minimization algorithm gets stuck in local minima and heavy computations. To avoid these drawbacks it is needed to know the model structure prior to identifying a model.In this contribution it is shown by experiment that a statistical method, the analysis of variance, is a good alternative to exhaustive search in the identification of the structure of nonlinear FIR-models.It is possible to reduce the risks of getting an erroneous model structure due to the non-convexity of the minimization problems, reduce the computation time needed and also get a good estimate of how far the fit of the desired model can be enhanced.

A comparison of white test signals used in active sound cancellation

Several different test signals with flat power spectrum, such as white noise, Schroeder-phased waveform, and Galois noise sequences were generated and used to adaptively model the error path in an active sound cancellation (ASC) controller. The standard filtered-X LMS (FXLMS) algorithm was used with a Finite Impulse Response (FIR) model of the error path and an FIR controller structure. Both adaptive FIR filters were operated during the active sound cancellation of 80 and 125 Hz tones. The residual modeling error for different test signal mean power spectral densities (PSD) was determined. It was discovered that the residual error decreased with an increase in the mean PSD, until a minimum residual error was achieved. When the mean PSD was increased beyond this value, no further decrease in residual error occurred. Each test signal was distinguished by the minimum mean PSD that achieved the minimum residual error. All three test signals achieved approximately the same residual error at approximately the same mean PSD for both the 80 and 125 Hz tone. Therefore, the best test signal was selected as the signal with the lowest peak factor, in this case the Schroeder-phased waveform. Given a low peak factor, power can be injected into the test waveform without significantly increasing the size of the time domain envelope.

Robust control of linear time-varying systems with constraints

In this paper, we generalize the robust MPC algorithm proposed by Campo and Morari for control of uncertain linear time-varying systems, represented by finite impulse response models, with constraints. A necessary and sufficient condition on the set of plants for guaranteeing robust asymptotic stability of the closed-loop system is stated. Although these results hold for any uncertainty description expressed in the time domain, the on-line computational complexity of the resulting optimization problem depends on the uncertainty description. For a class of uncertainty descriptions, we show that the optimization problem can be cast as a linear program of moderate size. The algorithm is demonstrated on a simple example. Copyright © 2000 John Wiley & Sons, Ltd.