Finite Impulse Response Model Identification Research Articles

Quantification and Propagation of Uncertainties in Identification of Flame Impulse Response for Thermoacoustic Stability Analysis

The thermoacoustic behavior of a combustion system can be determined numerically via acoustic tools such as Helmholtz solvers or network models coupled with a model for the flame dynamic response. Within such a framework, the flame response to flow perturbations can be described by a finite impulse response (FIR) model, which can be derived from large eddy simulation (LES) time series via system identification. However, the estimated FIR model will inevitably contain uncertainties due to, e.g., the statistical nature of the identification process, low signal-to-noise ratio, or finite length of time series. Thus, a necessary step toward reliable thermoacoustic stability analysis is to quantify the impact of uncertainties in FIR model on the growth rate of thermoacoustic modes. There are two practical considerations involved in this topic. First, how to efficiently propagate uncertainties from the FIR model to the modal growth rate of the system, considering it is a high dimensional uncertainty quantification (UQ) problem? Second, since longer computational fluid dynamics (CFD) simulation time generally leads to less uncertain FIR model identification, how to determine the length of the CFD simulation required to obtain satisfactory confidence? To address the two issues, a dimensional reduction UQ methodology called “Active subspace approach (ASA)” is employed in the present study. For the first question, ASA is applied to exploit a low-dimensional approximation of the original system, which allows accelerated UQ analysis. Good agreement with Monte Carlo analysis demonstrates the accuracy of the method. For the second question, a procedure based on ASA is proposed, which can serve as an indicator for terminating CFD simulation. The effectiveness of the procedure is verified in the paper.

A robust global approach for LPV FIR model identification with time-varying time delays

Robust identification of the linear parameter varying (LPV) finite impulse response (FIR) model with time-varying time delays is considered in this paper. A robust observation model based on Laplace distribution is established to deal with the output data contaminated with the outliers, which are commonly existed in modern industries. A Markov chain model is utilized to model the correlation between the time delays as they do not simply change randomly in reality. A transition probability matrix and an initial probability distribution vector are used to govern the switching mechanism of the time delays. Since it is difficult to optimize the complex log likelihood function directly, the derivations of the proposed algorithm are performed under the framework of Expectation-Maximization (EM) algorithm. A numerical example and a chemical process are utilized to verify the effectiveness of the proposed approach.

Positive FIR System Identification using Maximum Entropy Prior

Bayesian nonparametric methods have been introduced in a linear system identification paradigm to avoid the model and order selection problem. In this framework, a finite impulse response (FIR) model is considered, and the impulse response is realized as a zero-mean Gaussian process. The identification results mainly depend on a prior covariance (kernel) which has to be estimated from data. But the Gaussian prior assumption is inappropriate when the impulse response is constrained on an interval. This paper considers the positive FIR model identification problem using non Gaussian prior where a positive model denotes a system with the nonnegative impulse response. A suitable prior is selected as the maximum entropy prior when the impulse response has interval constraints. A truncated multivariate normal prior is shown to be the maximal entropy prior for positive FIR model identification. Simulation results demonstrate that the proposed prior shows significantly better robustness.

Identification of FIR Models for LTI Multiscale Systems using Sparse Optimization Techniques

Finite impulse response (FIR) models are very popular in process industries because of their simple model structure, flexibility to explain arbitrary complex stable linear dynamics and finally their ease of implementation in on-line applications. In general, identification of FIR models requires large number of parameters to be estimated. In case of systems with multiple time scales, the length of FIR model structure under conventional uniform sampling becomes arbitrarily high due to simultaneous presence of fast and slow dynamics. This results in more variability in the estimated parameters when the conventional methods such as ordinary least squares are used. In this work, the FIR model estimation problem is formulated as a sparse optimization problem, where the sparse representation of impulse response coefficients for linear-time invariant multiscale systems in the time-frequency domain is exploited in order to explain the overall FIR model effectively with fewer number of coefficients and thereby incurring less variability in the estimated parameters. The effectiveness of proposed methodology is demonstrated by means of simulation case studies.

FIR model identification of multirate processes with random delays using EM algorithm

The motivation for this article comes from our development of soft sensors for chemical processes where several challenges are encountered. For example, quality variables in chemical processes are often measured off‐line through laboratory analysis. Collection of samples and subsequent analyses inevitably introduce uncertain time delays associated with the irregularly sampled quality variables, which add significant difficulty in identification of process with multirate (MR) data. Considering the MR system with random sampling delays described by a finite impulse response (FIR) model, an Expectation–Maximization (EM)‐based algorithm to estimate its parameters along with the time delays is developed. Based on the identified FIR model, two algorithms are proposed to recover the approximate output error (OE) or transfer function model. Two simulation examples as well as a pilot‐scale experiment are provided to illustrate the effectiveness of the proposed methods. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4124–4132, 2013

FIR model identification: Parsimony through kernel compression with wavelets

AbstractAlthough finite impulse response (FIR) models are nonparsimonious, they are frequently used in model predictive control systems because they can fit arbitrarily complex stable linear dynamics. However, identification of FIR models from experimental data may result in data overfitting and high modeling uncertainty. To overcome this, FIR models may be determined by regularization‐based least squares and indirectly after prior identification of other parametric models such as ARX. In both cases, some prior knowledge about the model is essentially assumed to be known. ARX models, although parsimonious in terms of the number of identified parameters, perform poorly for bad choices of model structure and order. A methodology for the direct identification of parsimonious FIR models is proposed. In this way, most advantages of the FIR structure are retained without its disadvantages. The idea relies on the effective use of some prior information about the model through wavelet‐based signal compression. The proposed methodology is compared with other FIR identification methodologies, on the basis of the closeness of the identified FIR to the true FIR, steady‐state gain estimation, and analysis of the prediction residuals on a cross‐validation set of fresh data. Simulation studies on a single‐input‐single‐output process show that this method performs very well in all tests considered. Certain industrial practices are shown to be special cases of the proposed formalism.

Normalized lattice algorithms for least-squares FIR system identification

Recently developed algorithms for least-squares identification of autoregressive models are extended in this paper so as to facilitate least-squares identification of finite impulse-response models. The algorithms belong to the class of square-root normalized lattice algorithms, hence they share the computational efficiency and good numerical behavior of the latter. Two versions are presented-one for identifying time-invariant models and the other for tracking time-varying parameters. New lattice-form realizations of the identified FIR models are given. The general framework is then specialized to the important cases of prediction and smoothing.