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### Abstract

This Ph.D. thesis includes fundamental considerations about topologies, algorithms, implementations,
methods etc., that can enter in the next generation of active control (AC) systems.
Specifically, a new variant of feedforward control referred to as confined feedforward active control
(CFFAC) is proposed. This topology is constituted from a set of reference sensors that are
positioned on a surface that completely confines the desired zones of quite. A set of performance
sensors monitors the achieved noise reduction. This CFFAC topology in turn is embedded in a
multiple-input and multiple-output (MIMO) system that facilitates both feedforward and feedback
control. The general system is then referred to as hybrid MIMO confined-feedforward feedback
(HMIMOCFFFB) active noise reduction (ANR) system. The investigation of a multi-channel
ANR system with hybrid feedforward and feedback topologies is motivated by requirements of
high ANR attenuation in extreme noise environments as typically experienced onboard airborne
military platforms. Noise recordings acquired on such platforms reveal very high sound pressure
levels often exceeding 140 dB re. 20 μPa. Moreover, these noise signals exhibit large temporal
as well as spatial variations. Inherent limitations are related to the use of stand-alone feedback
AC implementation commonly applied in modern ANR headset. In such systems the anti-noise
signal is notoriously behind the primary disturbance in time. Accordingly, in demanding military
applications requirements on more advanced and effective ANR system designs prevail.
The achievable ANR performance in a feedforward system (FFS) is to a large extent determined
by the degree of coherence between the set of reference sensors and the set of error sensors (or
performance sensors). Accordingly, this thesis includes a number of coherence analysis that are
based on diffuse sound field measurements in a reverberant chamber and measurements conducted
onboard a CH-47D Chinook helicopter. From these coherence analysis it can be concluded
that the CFFAC system with 10 reference sensors applied to pilot helmets potentially provides
approximately 25 dB noise reduction at 100 Hz decreasing to approximately 10 dB attenuation
at 900 Hz. Moreover, there is no apparent sign of saturation of the noise reduction with an
increasing number of reference sensors. Accordingly, by using more reference sensors the spatial
sampling rate is increased which in turn most likely also will lead to an increased ANR bandwidth.
The hybrid system is also constituted from a continuous-time feedback system (FBS) and a
discrete-time FBS. The continuous-time FBS is primarily responsible for additional broadband
noise reduction, whereas the discrete-time FBS primarily is responsible for the attenuation of
periodic signals.
Owing to the requirement on causal operation of a physical AC system time delays will also to a
large extent determine the achievable performance in FFS design and in particular in FBS design.
A quantity referred to as the spatially-weighted-averaged acquisition lead time is introduced to
represent the averaged time-advance obtained by each reference sensor relative to each performance
sensor involved in the proposed CFFAC system. A problem exist when one attempts to
model a physical spatially distributed system with no obvious input and output channel definition
by a finite lumped-elements multi-channel system. Usually, no unique transfer function
x
exist as the system is not point-wise excited, but excited over an area as in the case of diffuse
sound field illumination.
A new method for acoustical signal processing that is referred to as joint-channel residual spectral
analysis (JCRSA) is developed. The JCRSA method is used for the extraction of joint signal
information from different observation positions in space. The idea is to separate each spectrum
in a coherent spectrum and a residual spectrum. The contents of the coherent spectrum can be
obtained from a linear superposition of the other signals, whereas the residual spectrum bears
information that is unique to each specific channel. In a specific example a system consisting of
10 reference sensors flush-mounted on a Gentex HGU-55/P helmet that in turn is mounted on a
head and torso simulator (HATS), is exposed to diffuse sound field illumination. By applying the
JCRSA method the spatially-weighted-averaged acquisition lead times provided by the reference
sensors relative to the performance sensors are estimated to be as much as 800-900μs.
The thesis also includes a detailed description of a new idea for a computational efficient implementation
of a multi-channel system in which the adaptive filters for adaptive control as well as
the adaptive filters used for plant modeling are allowing to take different lengths.
A new and more general variant of the affine projection algorithm has been developed. This
adaptive filter algorithm that is denoted by multiple-channel-αγΠ-affine projection algorithm
includes parameters for both weight-driven and control-effort-driven leakage, adaptive tap-weight
regularization as well as numerical regularization. A simplification of this algorithm leads to the
MC-αγΠ-NLMS algorithm that is an extended variant of the NLMS algorithm.
Off-line simultaneous system identification capabilities of a complex system involving a total 4
secondary paths, 20 feedback paths and 4 control-performance paths is demonstrated. Different
adaptive filters and parameterizations hereof are examined.
A novel and general multi-rate adaptive filter for adaptive AC has been developed. Specifically,
a system involving 3 different sampling rates has been implemented and the results hereof are
presented. In this multi-rate system conversion take place at highly oversampled rates in order to
reduce the delays in the secondary paths. The non-adaptive control is performed at a somewhat
lower rate. Hereby, a compromise between delays related to the generation of the anti-noise
signal and the computational load involved is ensured. Finally, the adaptive control that might
be computational intensive takes place at an even slower sampling rate hereby relaxing the
requirements on a high bandwidth. It is demonstrated that computational savings as high as
40% can be achieved in a 192, 24, 3 kHz triple-rate system as compared with a 24 kHz single-rate
system without sacrificing the ANR performance.
It is common engineering practice to apply an assumption of Gaussian distributed signals. However,
many phenomena encountered in daily life fall into a generalization of the normal distribution
that is referred to as α-stable distributions. Noise sources encountered in the domain of
AC are sometimes best fitted to the family of α-stable distributions. This thesis includes a brief
technical introduction to the stable distributions and description of the adaptive filter that can
be used for AC.
Large parts of the HMIMOCFFFB system including the developed methods and algorithms have
been implemented in a real-time environment (RTE) that includes a signal processor. Test on the
helmet system will continue and a dedicated reference test unit (RTU) for AC is currently being
designed.

Original language | English |
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Number of pages | 911 |
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ISBN (Print) | 978-87-911-8485-7 |

Publication status | Published - Nov 2008 |

## Projects

- 1 Finished

## Active Noise Concellation Headset

Elmkjær, T. H. L., Jacobsen, F., Sjøstrøm, S. O., Laugesen, S., Jensen, S. H. & Rafaely, B.

01/09/2001 → 24/11/2008

Project: PhD

## Cite this

Elmkjær, T. H. L. (2008).

*Foundations of Active Control - Active Noise Reduction Helmets*.