A multiple error LMS algorithm and its application to the active control of sound and vibration

Abstract

An algorithm is presented to adapt the coefficients of an array of FIR filters, whose outputs are linearly coupled to another array of error detection points, so that the sum of all the mean square error signals is minimized. The algorithm uses the instantaneous gradient of the total error, and for a single filter and error reduces to the "filtered x LMS" algorithm. The application of this algorithm to active sound and vibration control is discussed, by which suitably driven secondary sources are used to reduce the levels of acoustic or vibrational fields by minimizing the sum of the squares of a number of error sensor signals. A practical implementation of the algorithm is presented for the active control of sound at a single frequency. The algorithm converges on a timescale comparable to the response time of the system to be controlled, and is found to be very robust. If the pure tone reference signal is synchronously sampled, it is found that the behavior of the adaptive system can be completely described by a matrix of linear, time invariant, transfer functions. This is used to explain the behavior observed in simulations of a simplified single input, single output adaptive system, which retains many of the properties of the multichannel algorithm.

Active noise control of a diesel generator in a luxury yacht

“…An active tonal noise control system can be efficiently implemented using a feedforward controller and the most commonly employed algorithm is the filtered reference, or filtered-x, Least Mean Squares (LMS) algorithm [5]. The multichannel formulation of this algorithm was originally presented in the late 1980s [18] and has since been used in a variety of applications. The block diagram in Figure 3 shows the general outline of the multichannel feedforward control system.…”

Behavior of adaptive algorithms in active noise control systems with moving noise sources.

“…The algorithms used in the simulations were filtered-x LMS, NLMS, and RLS algorithms. The weight update procedures for these algorithms are listed below: filtered-x LMS [3] uðn þ 1Þ ¼ uðnÞ À "rðnÞeðnÞ ð 4Þ…”

“…If we extend the system to multi-channel, there will be another practical problem, such as effect of the number of noise detecting sensors. Another simulations are thus performed with multiple error filtered-x LMS (MEFX-LMS) algorithm [3].…”

“…The authors have applied the active control technique to suppress diffracted sound by a noise barrier [1,2], in which the multiple error filtered-x LMS algorithm [3] was used to examine the effect of the control relative to a stationary noise source. However, if we try to extend our findings to traffic noise control, the assumption of a stationary environment is apparently insufficient due to significant changes of the primary paths.…”

Differential and finite-difference problems of active shielding

“…The first theoretical papers in this field by Jessel, Malyuzhinets and Fedoryuk appeared about 30 years ago [5,10,3], while the first publications related to some possible realistic implementation arose much later (see, e.g., [1,2]). The most comprehensive theoretical and practical reviews can be found in books [11,4,14].…”