LMS Algorithm Step Size Adjustment for Fast Convergence

In the areas of acoustic research or applications that deal with not-precisely-known or variable condi- tions, a method of adaptation to the uncertainness or changes is usually necessary. When searching for an adaptation algorithm, it is hard to overlook the least mean squares (LMS) algorithm. Its simplicity, speed of computation, and robustness has won it a wide area of applications: from telecommunication, through acoustics and vibration, to seismology. The algorithm, however, still lacks a full theoretical analysis. This is probabely the cause of its main drawback: the need of a careful choice of the step size – which is the reason why so many variable step size flavors of the LMS algorithm has been developed. This paper contributes to both the above mentioned characteristics of the LMS algorithm. First, it shows a derivation of a new necessary condition for the LMS algorithm convergence. The condition, although weak, proved useful in developing a new variable step size LMS algorithm which appeared to be quite different from the algorithms known from the literature. Moreover, the algorithm proved to be effective in both simulations and laboratory experiments, covering two possible applications: adaptive line enhancement and active noise control

Stability Conditions for the Leaky LMS Algorithm Based on Control Theory Analysis

The Least Mean Square (LMS) algorithm and its variants are currently the most frequently used adaptation algorithms; therefore, it is desirable to understand them thoroughly from both theoretical and practical points of view. One of the main aspects studied in the literature is the influence of the step size on stability or convergence of LMS-based algorithms. Different publications provide different stability upper bounds, but a lower bound is always set to zero. However, they are mostly based on statistical analysis. In this paper we show, by means of control theoretic analysis confirmed by simulations, that for the leaky LMS algorithm, a small negative step size is allowed. Moreover, the control theoretic approach alows to minimize the number of assumptions necessary to prove the new condition. Thus, although a positive step size is fully justified for practical applications since it reduces the mean-square error, knowledge about an allowed small negative step size is important from a cognitive point of view

Numerical prediction of combustion induced vibro-acoustical instabilities in a gas turbine combustor

Introduction of lean premixed combustion to gas turbine technology reduced the emission of harmful exhaust gas species, but due to the high sensitivity of lean flames to acoustic perturbations, the average life time of gas turbine engines was decreased significantly. Very dangerous to the integrity of the gas turbine structure is the mutual interaction between combustion, acoustics and wall vibration. This phenomenon can lead to a closed loop feedback system, with as a result fatigue failure of the combustor liner and fatal damage to the gas turbine rotor. In this paper the use of numerical tools for CFD and CSD analysis is described to predict the hazardous frequencies at which the instabilities can occur. The two way interaction of the combustible compressible flow and structural walls is investigated with the application of the partitioning fluid-structure interaction approach. In this technique the fluid and structural model are considered as individual but coupled dynamic systems. Information of conditions at the fluid-structure interface is exchanged at given time steps through the interface connection created between the numerical domains. Therefore, the partitioned approach can take the full advantage of existing, well developed and tested codes for both, fluid and structure analysis. Next to the fluid-structure interaction analysis, acousto-elastic and modal models are applied to get insight into the acoustic and vibration pattern during the instability process. The calculations use elements devoted to the solution of the acoustic and structural fields. This approach has the advantage of high resolution of the acoustics, but takes into account only one way combustion dynamics (taken from the CFD results). All numerical solutions are compared to experimental results obtained on a laboratory test rig. The data is evaluated for both, pressure and velocity fields

The bluff body stabilized premixed flame in an acoustically resonating tube: combustion CFD and measured pressure field.

The resulting limit cycle amplitude and frequency spectrum of a flame placed in a combustor of rectangular cross section is investigated. The partially premixed flame is stabilized on a bluff body placed in the upstream half of the combustor. The bluff body is an equilateral triangular wedge with one of the edges pointing in upstream direction. Acoustically there is an open downstream end and theer are variable acoustic conditions at the upstream end. In order to assess the properties of the flame in this combustor, steady state flame simulations have been performed of the flame in the enclosure. These provided the fields of the mixing of gases, temperature and the velocity. A test rig was manufactured for this burner at the University of Twente. In a first set of experiments, gas temperature, pressure field and flame chemiluminescence in the combustor were measured as a function of power and acoustic inlet condition. It was observed that the combustor exhibited strong natural pressure oscillations. The measured pressure, temperature and chemiluminescence data are compared to the CFD simulations and to numerical calculations of the acoustics presented in a companion paper by M.Heckl