Frequency domain identification with adaptive rational orthogonal system

A comparative study of the MAX and SUM machine-learning algorithms using virtual fuzzy sets

There are six main algorithms for real-time identification of FIR systems from binary measurements on the output. The objective of this paper is to propose a first short comparison of these methods based on the description of each method and on some numerical simulations. This comparison should help the user in choosing an algorithm if necessary.

This paper presents a new method to identify the model of a small-scale helicopter in frequency domain using harmony search (HS) algorithm. The dynamics of the small-scale helicopter are simplified to four single-input/single-output (SISO) linear subsystems near the hover point, and the HS optimisation algorithm is used to identify each subsystem's parameters. Time-domain verification is made to check the validity of the identified models. The verification results show that the identified models are accurate and effective enough to describe the dynamics of the helicopter. The identified models show that the dynamics of the roll, pitch and yaw channels are mainly dominated by the lightly damped second-order modes. Identification and verification results show that the application of HS algorithm in system identification is suitable and useful.

This study addresses the challenges of infinite impulse response (IIR) system identification by introducing an improved cooperation search algorithm (ICSA). Improved cooperation search algorithm enhances the original cooperation search algorithm (CSA) through the integration of a pattern search algorithm and opposition-based learning, aiming to improve both exploration and exploitation capabilities. The algorithm's performance was evaluated against diverse IIR plants of varying orders using convergence analysis, scatter plots, and statistical metrics. Results demonstrate ICSA's superiority over CSA, achieving significantly lower mean squared error (MSE) values across different system orders and model types. Notably, ICSA outperformed CSA by up to 27 orders of magnitude for matched-order models and up to 95.85% for reduced-order models. The algorithm also exhibited more consistent performance, with substantially lower standard deviations in many cases. Statistical validation through the Wilcoxon signed-rank test further confirmed ICSA's enhanced performance. This research highlights ICSA's efficacy in producing efficient IIR systems, demonstrating its potential for more accurate system identification compared to existing methods. Cite this article as: C. Ersalı and B. Hekimoğlu, "Improved cooperation search optimization algorithm for infinite impulse response system identification," Electrica, 24(3), 733-747, 2024.

This dissertation presents a new method for the statistical performance analysis of subspace system identification algorithms. A perturbation expansion of the singular value decomposition is used to approximate the effects of process and measurement noise on the identified system poles. Eigenvalue variance results are obtained that do not depend on asymptotic statistics and are therefore applicable for short data records. These performance measures are conditional upon the specific input and the parameters of the actual system being identified. This method is demonstrated on two variations of the Numerical Subspace State-Space System Identification (N4SID) algorithm. The accuracy of these theoretical performance measures is validated using simulation. Finally, this new method is applied to the first step of three well known subspace identification algorithms to determine the effects of row and column weighting on the variance of identified poles.

We propose a new algorithm for the adaptive identification of sparse systems. The algorithm is based on the minimization of the RLS cost function when regularized by adding a sparsity inducing ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm penalty. The resulting recursive update equations for the system impulse response estimate are in a similar form to the regular RLS. However, they include novel terms which account for the sparsity prior. The proposed, ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> relaxation based RLS algorithm emphasizes sparsity during the adaptive filtering process and allows for faster convergence when the system under consideration is sparse. Computer simulations comparing the performance of the proposed algorithm to conventional RLS and other adaptive algorithms are provided. Simulations demonstrate that the new algorithm exploits the inherent sparse structure effectively.

Adaptive filtering techniques have gained much popularity in the modeling of unknown system identification problem. These techniques can be classified as either iterative or direct. Iterative techniques include stochastic descent method and its improved versions in affine space. In this paper we present a comparative study of the least mean square (LMS) algorithm and some improved versions of LMS, more precisely the normalized LMS (NLMS), LMS-Newton, transform domain LMS (TDLMS) and affine projection algorithm (APA). The performance evaluation of these algorithms is carried out using adaptive system identification (ASI) model with random input signals, in which the unknown (measured) signal is assumed to be contaminated by output noise. Simulation results are recorded to compare the performance in terms of convergence speed, robustness, misalignment, and their sensitivity to the spectral properties of input signals. Main objective of this comparative study is to observe the effects of fast convergence rate of improved versions of LMS algorithms on their robustness and misalignment.

A class of adaptive algorithms for acoustic echo cancellation (AEC) and speech dereverberation have been developed and analyzed in this thesis. The starting point of this work is the affine projection (AP) based non-blind channel identification algorithms for AEC. The proposed. sparseness constrained improved proportionate AP algorithms (SC-IPAPA-I and SC-IPAPA-II) exploit the sparseness of the estimated channel and allocate different effective step sizes accordingly. The performance of these algorithms has been studied in the context of single-channel AEC and tracking capability. The performance of a blind channel identification algorithm with additive noise is studied by providing reasons for the degradation in perforrnance of the rnultichannel least-rnean-square (MCLMS) algorithm in the presence of additive noise. Subsequently, it is shown mathematically, through a cross-correlation based cost function, that minimizing the power of a filtered version of the received signals can suppress the noise effect. The performance of MCLMS and improved lVICLlVIS (LVICLMS) are evaluated using the normalized projection rnisalignment via lVlonte Carlo simulations. It is shown through simulations that the well-known normalized rnultichannel frequency-domain least-mean-square (NMCFLMS) algorithrn, originally developed for acoustic impulse response (AIR) identification in the frequency domain, also suffers from the noise robustness problem. A noise robust blind AIR estima.tion algorithm is then proposed. Inspired by the trivial solution achieved by NMCFLJVIS in the presence of noise, the proposed direct-path NMCFLMS algorithm with power constraint (DP-NMCFLMS-PC) jointly applies direct-path and power constraint to improve its robustness against noise. The DP-NMCLFMS-PC not only addresses the noise robustness issue but also achieves fast convergence compared to NMCFLMS. The adaptive multiple input/output inversion theorem (A-MINT) algorithm has been developed for channel equalization with application to speech dereverberation. In order to increase its convergence rate, the proposed algorithm suppresses any undesired non-zero coefficients in the estimated Kronecker delta function iteratively. This is achieved by applying the sparseness measure of the estimated Kronecker delta function and using it as an additional constraint to A-MINT. Unlike existing channel equalization systems, the proposed auto-relation aided MINT (A-RAM) algorithrn, which achieves good equalization performance, takes into account how the received signals are generated during its adaptation process. The differential output signals from two sub-systems are then utilized in the cost function during equalization. Sirnulation results have shown that the proposed A-RAM algorithm can achieve a higher rate of convergence leading to better dereverberated speech signal cornpared to existing MINT-based equalization algorithms.

The use of adaptive algorithms for blind system identification in speech dereverberation was proposed recently. This chapter reviews adaptive multichannel system identification using minimization of the cross-relation error. One of the algorithms that adopt this approach is the Normalized Multichannel Frequency Domain Least Mean Square (NMCFLMS) algorithm. We show that, in the presence of additive noise, the coefficients of the adaptive filter employing NMCFLMS converge initially toward the true acoustic impulse responses after which they then misconverge. We provide a technique to address this misconvergence problem in NMCFLMS. This is achieved by reformulating the minimization problem into one involving a constraint. As will be shown, this constrained minimization problem requires knowledge of the direct-path components of the acoustic impulse responses and one of the main contributions of this work is to illustrate how these direct-path components can be estimated under practical conditions.We will then illustrate how these estimates can be incorporated into the proposed extended NMCFLMS (ext-NMCFLMS) algorithm so as to address the problem of misconvergence. The simulation results presented showthe noise robustness of the proposed algorithm for both white Gaussian noise and speech inputs. In addition, we illustrate how errors due to the estimation of the direct-paths affect the performance of the proposed algorithm.

Modal parameter identification of a multiple-span post-tensioned concrete bridge using hybrid vibration testing data

The matrix inversion lemma gives an explicit formula of the inverse of a positive-definite matrix A added to a block of dyads (represented as BBH). It is well-known in the literature that this formula is very useful to develop a block-based recursive least-squares algorithm for the block-based recursive identification of linear systems or the design of adaptive filters. We already extended this result to the case when the matrix A is singular, and presented the matrix pseudo-inversion lemma. Such a singular case may occur in a situation where a given problem is overdetermined in the sense that it has more equations than unknowns. In this paper, based on these results, we propose a block-based adaptive multichannel super-exponential deflation algorithm. We present simulation results for the performance of the block-based algorithm in order to show the usefulness of the matrix pseudo-inversion lemma.

This work proposes an arctangent least mean square/fourth algorithm developed by incorporating the standard least mean square/fourth algorithm cost function with the arctangent framework for adaptive system identification. The performance of the proposed algorithm is verified through various simulations which shows that the proposed algorithm outperforms the conventional least mean square/fourth algorithm.

Fast ℓ1-recursive total least squares algorithm for sparse system identification

System identification deals with the problem of building the mathematical models of dynamical systems according to the input and output data. The open-loop system identification (Observer/Kalman Filter SystemIdentification, OKID) for stable systems without requiring feedback control is introduced first. For identifying marginally stable or unstable system, however, feedback control is required to ensure the overall system stability. The algorithm of closed-loop system identification (CLID) with known feedback dynamics is shown next.

Vector Fitting fractional system identification using particle swarm optimization