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lms algorithm for adaptive control of combustion oscillations

COMBUSTION SCIENCE AND TECHNOLOGY 2001年第1期164卷 65-93页

作者： Evesque, S Dowling, AP Univ Cambridge Dept Engn Cambridge CB2 1PZ England

Self-excited oscillations of a ducted flame, bunting in the wake of a bluff-body flame-holder, are considered. The non-linear kinematic model used here to describe these oscillations calculates the influence of the velocity fluctuations on the shape of the flame surface, and hence on the heat release rate. It is easy and quick to vary parameters in our model, and therefore a theoretical and numerical adaptive control strategy is developed, aiming at eliminating the flame instabilities. The control is based on an IIR filter, its coefficients being optimised by the lms algorithm Some system identification (SI) is necessary because the output of the adaptive filter does not interfere directly with the combustion oscillations, but only through a transfer function. Our control strategy, carried out with an on-line SI, gives very satisfactory results, and several new ideas are developed. Firstly it is shown that, in the lms algorithm running the controller, a term, usually neglected without mathematical justification, must be included in the gradient estimate in order to suppress the oscillations. Secondly, a new lms-based on-line SI procedure, using an additional random noise and global quantities available in an experiment, is described and tested successfully in our numerical simulation. Finally, an efficient method to overcome the IIR instability is implemented, and our controller proves successful at reducing the pressure oscillations both under varying operating conditions and in the presence of a background noise.

关键词： combustion control adaptive control combustion instabilities lms algorithm

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lms algorithm for unbiased parameter estimation of noisy autoregressive signals

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ELECTRONICS LETTERS 2001年第8期37卷 536-537页

作者： So, HC City Univ Hong Kong Dept Elect Engn Kowloon Hong Kong Peoples R China

A computationally simple algorithm is devised for unbiased autoregressive (AR) modelling in the presence of white noise, assuming that the power ratio of the AR driving source and the measurement noise is known. Convergence analysis of the proposed method is included and simulation results are presented to validate the theoretical derivations as M ell as to evaluate its estimation performance.

关键词： noisy autoregressive signals Simulation, modelling and identification unbiased parameter estimation white noise AR modelling estimation performance evaluation lms algorithm convergence analysis Interpolation and function approximation (numerical analysis) Signal processing and detection autoregressive processes parameter estimation Signal processing theory convergence of numerical methods least mean squares methods

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Non-Uniform Norm Constraint lms algorithm for Sparse System Identification

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IEEE COMMUNICATIONS LETTERS 2013年第2期17卷 385-388页

作者： Wu, F. Y. Tong, F. Xiamen Univ Key Lab Underwater Acoust Commun & Marine Informa Xiamen Peoples R China

Sparsity property has long been exploited to improve the performance of least mean square (lms) based identification of sparse systems, in the form of l0-norm or l1-norm constraint. However, there is a lack of theoretical investigations regarding the optimum norm constraint for specific system with different sparsity. This paper presents an approach by seeking the tradeoff between the sparsity exploitation effect of norm constraint and the estimation bias it produces, from which a novel algorithm is derived to modify the cost function of classic lms algorithm with a non-uniform norm (p-norm like) penalty. This modification is equivalent to impose a sequence of l0-norm or l1-norm zero attraction elements on the iteration according to the relative value of each filter coefficient among all the entries. The superiorities of the proposed method including improved convergence rate as well as better tolerance upon different sparsity are demonstrated by numerical simulations.

关键词： p-norm like non-uniform norm constraint lms algorithm sparsity exploitation

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On the properties of the reduction-by-composition lms algorithm

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-ANALOG AND DIGITAL SIGNAL PROCESSING 1999年第11期46卷 1440-1445页

作者： Chen, SG Kao, YA Chen, CY Natl Chiao Tung Univ Dept Elect Engn Hsinchu Taiwan Natl Chiao Tung Univ Inst Elect Hsinchu 30039 Taiwan

The recently proposed low-complexity reduction-by-composition least-mean-square (lms) algorithm (RClms) costs only half multiplications compared to that of the conventional direct-form lms algorithm (Dlms), This work intends to characterize its properties and conditions for mean and mean-square convergence. Closed-form mean-square error (MSE) as a function of the lms step-size mu and an extra compensation step-size alpha are derived, which are slightly larger than that of the Dlms algorithm. It is shown, when mu is small enough and alpha is properly chosen, the RClms algorithm has comparable performance to that of the Dlms algorithm. Simple working rules and ranges for alpha and mu to make such comparability are provided. For the algorithm to converge, a tight hound for alpha is also derived. The derived properties and conditions are verified by simulations.

关键词： adaptive signal processing convergence lms algorithm

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The Extended Feature lms algorithm: Exploiting Hidden Sparsity for Systems with Unknown Spectrum

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2021年第1期40卷 174-192页

作者： Yazdanpanah, Hamed Apolinario Jr, Jose A. Univ Sao Paulo Inst Math & Stat Dept Comp Sci BR-05508090 Sao Paulo SP Brazil Mil Inst Engn IME Program Def BR-22290270 Rio De Janeiro RJ Brazil Mil Inst Engn IME Program Elect Engn BR-22290270 Rio De Janeiro RJ Brazil

The feature least-mean-square (F-lms) algorithm has already been introduced to exploit hidden sparsity in lowpass and highpass systems. In this paper, by proposing the extended F-lms (EF-lms) algorithm, we boosted the F-lms algorithm to exploit hidden sparsity in more general systems, thosewhich are neither lowpass nor highpass. To this end, by means of the so-called feature matrix, we reveal the hidden sparsity in coefficients and utilize the l(1)-norm to exploit the exposed sparsity. As a result, the EF-lms algorithm will improve the convergence rate and the steady-state mean-squared error (MSE) as compared to the traditional least-mean-square algorithm. Moreover, in thiswork, we analyze the convergence behavior of the coefficient vector and the steady-state MSE performance of the EF-lms algorithm. Through synthetic and real-world experiments, it has been seen that the EF-lms algorithm can improve the convergence rate and the steady-state MSE whenever the hidden sparsity is revealed.

关键词： Adaptive filtering lms algorithm Feature Sparsity l(1)-norm Computational complexity

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OPTIMUM DESIGN OF THE lms algorithm USING 2 STEP SIZES FOR ADAPTIVE FIR FILTERING

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SIGNAL PROCESSING 1992年第2期26卷 197-204页

作者： WANG, CL CHEN, RY [a]Institute of Electrical Engineering National Tsing Hua University Hsinchu Taiwan 30043 ROC

In this paper, a two step-size lms algorithm, called dual lms (Dlms) algorithm, is proposed for adaptive FIR filtering. The new algorithm operates as if two lms algorithms are working in cooperation, where the transition threshold between the two lms algorithms and their step sizes are optimally chosen to yield the most rapid convergence under an initial and desired mean-square error. Over the range of interest in practical applications, it is shown via analysis and numerical evaluation that the worst-case initial mean-square error can be used to estimate the optimum switching instant from the first lms algorithm to the second one. As compared to the original lms algorithm, the Dlms algorithm gains a great improvement in convergence performance with little increase in hardware complexity. Computer simulation is employed to show the effectiveness of the algorithm.

关键词： ADAPTIVE FILTERING ECHO CANCELLATION lms algorithm

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Convergence behavior of the lms algorithm in subband adaptive filtering

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SIGNAL PROCESSING 2001年第5期81卷 1053-1059页

作者： Ohno, S Sakai, H Shimane Univ Dept Math & Comp Sci Matsue Shimane 6908504 Japan

Subband adaptive filtering with an lms-type algorithm has been considered as a possible alternative to the conventional fullband adaptive filtering. However, its convergence behavior has not yet been sufficiently analyzed. In this paper, an approximate expression for the convergence behavior of the cancellation error of the critically sampled subband adaptive digital filters (ADF) is presented. It is represented in the frequency domain and enables us to infer whether the subband ADF is efficient in terms of convergence speed. Computer simulations are presented to see the validity of the expression. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： adaptive filter subband adaptive filtering lms algorithm convergence behavior

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Stochastic analysis of the lms algorithm for cyclostationary colored Gaussian inputs

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SIGNAL PROCESSING 2019年 160卷 127-136页

作者： Bermudez, Jose C. M. Bershad, Neil J. Eweda, Eweda Univ Fed Santa Catarina Dept Elect & Elect Engn Florianopolis SC Brazil Univ Calif Irvine Dept Elect & Comp Engn Irvine CA 92717 USA C4 Adv Solut POB 43269 Abu Dhabi U Arab Emirates Univ Fed Santa Catarina Dept Engn Eletr BR-88040970 Florianopolis SC Brazil

This paper studies the stochastic behavior of the lms algorithm for a system identification framework when the input signal is a cyclostationary colored Gaussian process. The unknown system is modeled by the standard random walk model. Well-known results for the lms algorithm are extended to the cyclostationary case and used for predicting the mean-square weight deviation (MSD) and excess meansquare error (EMSE) behavior of the algorithm. Monte Carlo simulations provide strong support for the theory. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Adaptive filters Analysis lms algorithm Cyclostationary signals Stochastic algorithms

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On the convergence of the lms algorithm with a rank-deficient input autocorrelation matrix

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SIGNAL PROCESSING 2009年第11期89卷 2244-2250页

作者： McLernon, D. C. Lara, M. M. Orozco-Lugo, A. G. Univ Leeds Inst Integrated Informat Syst Sch Elect & Elect Engn Leeds LS2 9JT W Yorkshire England Ctr Res & Adv Studies IPN Commun Sect Mexico City 07360 DF Mexico

In all books and papers on adaptive filtering, the input autocorrelation matrix R-xx is always considered positive definite and hence the theoretical Wiener-Hopf normal equations (R(xx)h = r(xd)) have a unique solution h = h(opt) ("there is only a single global optimum", [B. Widrow, S. Stearns, Adaptive Signal Processing, Prentice-Hall, 1985, p. 21]) due to the invertibility of R-xx (i.e., it is full-rank). But what if R-xx is positive semi-definite and not full-rank? In this case the Wiener-Hopf normal equations are still consistent but with an infinite number of possible solutions. Now it is well known that the filter coefficients of the least mean square (lms), stochastic gradient algorithm, converge (in the mean) to the unique Wiener-Hopf solution (h(opt)) when R-xx is full-rank. In this paper, we will show that even when R-xx is not full-rank it is still possible to predict the (convergence) behaviour of the lms algorithm based upon knowledge of R-xx, r(xd) and the initial conditions of the filter coefficients. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Adaptive filtering lms algorithm Stochastic gradient Minimum-norm

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STOCHASTIC CONVERGENCE OF THE lms algorithm IN ADAPTIVE SYSTEMS

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SIGNAL PROCESSING 1987年第4期13卷 339-352页

作者： BOLAND, FM FOLEY, JB Department of Microelectronics and Electrical Engineering Trinity College University of Dublin Dublin 2 Ireland

This paper presents an analysis of lms-driven adaptive filters based on stochastic stability theory. Previous work in this area is critically reviewed, and the nature of convergence of sequences of random variables and of stochastic stability are discussed. In applying a theorem of Kushner to the lms adaptive filter, it is found that the system is initially exponentially stable with the excess mean square error tending to zero. However, eventually a point in the convergence process is reached beyond which further convergence cannot be guaranteed. With the system in a state of dynamic equilibrium, an expression is derived for an upper bound to the residual mean square error. The compromise involved in balancing the conflicting requirements of fast rate of convergence and low steady-state residual error is examined and the effect of inadequate filter length is considered. The theoretical assertions are supported by a set of computer simulation experiments. Dargestellt wird die Analyse eines adaptiven Filters, das nach dem Kriterium kleinster Fehlerleistung gesteuert wird, auf der Basis einer stochastichen Stabilitäts-Beschreibung. Ältere Arbeiten hierzu werden kritisch beleuchtet, und die Art der Konvergenz stochastischer Folgen und der stochastischen Stabilität werden diskutiert. Wenn man ein Theorem von Kushner auf das Filter anwendet, so läßt sich zeigen, daß das System zunächst ‘exponentiell stabil’ ist und daß der quadratische Fehler gegen Null strebt. Schließlich wird jedoch ein Punkt des Konvergenzvorgangs erreicht, nach dem eine weitere Konvergenz nicht garantiert werden kann: Das System befindet sich im Zustand eines dynamischen Gleichgewichts. Hier läßt sich eine obere Schranke für den verbleibenden quadratischen Fehler herleiten. Zwischen den widersprüchlichen Anforderungen einer raschen Konvergenz und eines kleinen Fehlers im eingeschwungenen Zustand ist ein Kompromiß zu treffen; es wird untersucht, und die Auswirkung eines nicht angepaßten Filters wird be

关键词： Stochastic stability adaptive filter lms algorithm

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