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Vesa Välimäki & Seppo Uosukainen 1998 1

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Adaptive Design of a Unidirectional Adaptive Design of a Unidirectional Source in a Duct Source in a Duct

Vesa Välimäki1 and Seppo Uosukainen2

1Helsinki University of Technology

Laboratory of Acoustics and Audio Signal Processing (Espoo, Finland)

2VTT Building Technology, Acoustics

(Espoo, Finland)

ISMA23 - International Conference on Noise and Vibration Engineering

• Sept. 16-18, 1998, Leuven, Belgium

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Outline

➤ Introduction ➤ Principal unidirectional two-element constructions ➤ Adaptive design of a unidirectional two-element source ➤ Simulation examples ➤ Conclusions and future work

Adaptive Design of a Unidirectional Adaptive Design of a Unidirectional Source in a Duct Source in a Duct

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A unidirectional acoustic source in a narrow duct

➤ multiple actuators (see Refs. [1-7] of the paper) ➤ the input of each actuator must be processed (filtered)

Motivation

➤ to be used in feedforward broadband ANC systems ➤ anti-noise must to radiate downstream but not upstream

In this paper, we present structures and an adaptive design method for unidirectional two-element sources

Introduction Introduction

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➤ the acoustic feedback is eliminated ➤ feedback neutralization filter is not needed ➤ SPL does not increase in the upstream direction due to the

secondary source

➤ the sound pressure level may be attenuated in the

upstream direction, since further reflections from duct terminations are eliminated

Advantages of unidirectional sources Advantages of unidirectional sources

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➤ limited frequency band of about 2 to 4 octaves:

not unidirectional at low frequencies (close to 0 Hz) and above an upper frequency limit

➤ need for several actuators ➤ in practice, both disadvantages are tolerable ➤ also other ANC systems also suffer from these defects

Dis Disadvantages of unidirectional sources advantages of unidirectional sources

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➤ deviations in the actuator responses degrade the obtainable

attenuation of unidirectional ANC systems – mutual difference

➤ also, measurement error in the distance between the

actuator elements causes degradation

➤ to automatically overcome both problems, we propose an

adaptive design method that learns how to equalize the loudspeakers and account for the propagation delay between them

➤ related earlier work: Elliott, 1993

Why adaptive design? Why adaptive design?

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➤ 4 different unidirectional two-element structures have been

proposed:

– two-element Swinbanks source (Swinbanks, 1973) – three versions of the JMC-based two-element source

(Uosukainen & Välimäki, 1998)

➤ these will be reviewed in the following

Principal unidirectional Principal unidirectional 2-element constructions 2-element constructions

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Two-element Swinbanks source Two-element Swinbanks source

q1 q2 1/2 A c0/d ∫dt

τ

• 1

τL -τ/2

qL

➤ ideal 2-element unidirectional source by Swinbanks: – delay the 1st actuator by delay between the sources, τ – feed the actuators in oppposite phases ➤ the amplification factor is A = kd / sin(kd)

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JMC-based solutions JMC-based solutions

➤ the JMC method (Jessel, Mangiante & Canévet) is suitable

for formulating the ANC problem with the general system theory

➤ three types of secondary sources are needed: monopoles,

dipoles, and quadripoles

➤ in the case of plane waves (such as in a narrow duct),

quadripoles vanish

➤ ideal JMC actuators in a duct consist of monopole and

dipole sources only

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JMC-based two-element sources JMC-based two-element sources

➤ inter-channel delay can be optimized in 3 different ways

• 1. downstream
• 2. upstream
• 3. no delay at all

➤ the control structures for the 3 cases are illustrated next

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1/2

• 1/2

b a c0 /d ∫dt q1 q2 Σ Σ + + + _

τ/2 τ τL - τ/2

qL

Inter-channel delay optimized Inter-channel delay optimized downstream downstream

➤ filters a and b are given in Table 1

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Inter-channel delay optimized Inter-channel delay optimized upstream upstream

1/2

• 1/2

b a c0 /d ∫dt q1 q2 Σ Σ + + + _

τ/2 τ τL - τ/2

qL

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No Inter-channel delay No Inter-channel delay

1/2

• 1/2

b a c0 /d ∫dt q1 q2 Σ Σ + + + _

τL

qL ➤ in the non-adaptive case, the delayless version has been

found to be easiest to design (Uosukainen & Välimäki, 1998)

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S12(z)

Ventilation system Open end

H1(z) H2(z) S22(z) S21(z) S11(z)

Mic 1 Mic 1 Mic 2 Mic 2 Act 1 Act 1 Act 2 Act 2

⊕

M-LMS

– +

z-∆ NOISE ym1(n) ym2(n) y2(n) y1(n) e2(n)

• e1(n)
• Ref. signal
• Ref. signal

Delay Delay

Adaptive design of a unidirectional Adaptive design of a unidirectional two-element source two-element source

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Different phases of the adaptive design Different phases of the adaptive design

➤ adaptive design contains 3 phases

• 1. calibrate transfer functions Sij(z) from both actuators to

both microphones

• 2. calibrate the unidirectionality (using the above system)
• 3. calibrate the error path from the unidirectional source to

the error detector

➤ after these phases, the ANC operation may start using a

single-channel adaptive system (one more adaptive filter!)

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Adaptive Swinbanks configuration Adaptive Swinbanks configuration

➤ the proposed adaptive structure can in principle design any

• f the four unidirectional two-element structures

➤ here we show examples of designing the Swinbanks source ➤ the adaptive structures for the JMC-based structures are

shown in our paper

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Example 1 Example 1

➤ the delay between the two actuators has been chosen to be

T = 1/fs, that is, one sampling interval

5 10 15 20 −0.5 0.5 Sample index 5 10 15 20 −0.5 0.5 Sample index

➤ the impulse responses of

filters H1(z) and H2(z) are shown here (20 coefficients)

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0.1 0.2 0.3 0.4 0.5 −40 −20 Magnitude (dB) Normalized frequency 0.1 0.2 0.3 0.4 0.5 −8 −6 −4 −2 2 Magnitude (dB) Normalized frequency

➤ magnitude responses upstream (upper) and downstream

(lower) in Example 1

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➤ back-to-front ratio (La Fontaine & Shepherd, 1985)

0.1 0.2 0.3 0.4 0.5 0.5 1 Back−to−front ratio Normalized frequency

➤ obtainable sound radiation downstream (w/ideal anti-noise)

0.1 0.2 0.3 0.4 0.5 −40 −20 Magnitude (dB) Normalized frequency

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➤ magnitude responses upstream (upper) and downstream

(lower) in Example 2 (delay between actuators = 2 samples)

0.1 0.2 0.3 0.4 0.5 −40 −20 Magnitude (dB) Normalized frequency 0.1 0.2 0.3 0.4 0.5 −8 −6 −4 −2 2 Magnitude (dB) Normalized frequency

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Conclusions and future work Conclusions and future work

➤ automatic design of a unidirectional two-element system

was described

➤ further work is needed to implement and evaluate the

adaptive design of JMC-based unidirectional structures

➤ a more advanced adaptive system could be designed that

adapts all transfer functions online: H1(z), H2(z), Sij(z), and the error path model

➤ finally, adaptive unidirectional systems should be tested in

actual real-time situations