Aeroacoustics: Introduction, Measurement, Computation and ... · Aeroacoustics: Introduction, Measurement, Computation and Control ... Numerical Validation ... Introduction, Measurement,

Aeroacoustics: Introduction, Measurement,Computation and Control

Xun Huang

Mechanics and Aerospace EngineeringPeking University

Lecture for China Aerodynamics Research Institute of Aeronautics,June 2010

[email protected] (Peking University) Aeroacoustics June 2010 1 / 46

Personal Track of Record

95-99 NWPU 99-02 THU 02-03 GE GRC 03-09 UoS 09-Present PKUBackground: Aeroacoustics, Signal Processing, and Control.


Some ANTC members


My Research Group at PKU

(a) Long Bai (b) Qingkai Wei (c) Jianchao Ji

(d) Chi Xu (e) Igor Vinogradov


PKUHyper

(f) Hypersonic vehicle (g) Rapid prototype controller


Outline for the Lecture of Aeroacoustics

1 Motivation

2 Beamforming

3 Observer

4 Validations

5 Summary


Motivation

The Research Objectives?

(h) Cruise noise? (i) Cabin noise reduction?

Carbin noise


Motivation

Magic of Human Technology

”I had the privilege to fly once in an Air France Concord. The mostnoteworthy thing was that it was not really any different from any otheraircraft. The cabin noise was quite normal.”Where the noise mainly from?


Motivation

Landing and Take-off Noise Problems


Motivation

CARDC 2020 Objectives


Motivation

Innovative Designs Emerging


Motivation

Strategy Problem for Our Country


Motivation

Aircraft Noise at Various Flight Stages

Take off noise Landing noise


Motivation

Aircraft Noise Certification

To solve the problem

Set overall noise reduction objective;

Identify noise sources;

Modify/improve design accordingly;

Check aerodynamics and noise performance.

Applicable methodologies

Theory (aeroacoustics), experiments (array) and computation (CAA).


Motivation

Certification

But provide little information for aeroacoustic design.


Motivation

Noise Measurements

Flow-induced noise study hence focuses on noise measurements.


Beamforming

Array Measurement Fundamentals


Beamforming

Array Measurement Directivity


Beamforming

Classical Beamforming Formulations

Noise source

Given x(t) ∈ R1 or X (jω) ∈ C

1

Array outputs

Time domain: y(t) = 14πr x(t − τ), τ = r

C .

Frequency domain: Y(jω) = 14πr X (jω)e−jωτ = G(r, jω)X (jω).

Classical beamforming

X (jω) = (G∗G)−1G∗Y(jω), following Moore-Penrose pseudoinverse.


Beamforming

Problems in Classical Beamforming

Background noise can at least be partially resolved by algorithmdevelopment.


Beamforming

Problems in Classical Beamforming (Cont’)

Background noise and solutions

Array outputs YB(jω) = G(r, jω)XB , and YBS(jω) = G(r, jω)XBS .

If XBS = XB + XS , sound satisfies superposition.

Define AB = YBY∗B, ABS = YBSY∗

BS , < AS >≈< ABS > − < AB >.

Open problem: cases with coherent sources, i.e. < XBX ∗S > 6= 0.


Beamforming



Beamforming


−0.4

−0.2

0

0.2

0.4

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

−0.5

0

0.5

1

1.5

Background noise

Mic array

Signal of interest

Z(m)

X(m)

Y(m)

Beam pattern

Plane of interest

Low resolution and solutionsAdvanced beamforming method: CLEAN, DAMAS, LORI,adaptive beamforming, robust beamforming, etc.

Increase array diameter (better resolution) with more microphones(less spatial aliasing), but its beamforming cost increases as well.

Open problem: real-time computation burden.


Beamforming



Beamforming



Beamforming

Anechoic Chamber Experiments


Beamforming

Wind Tunnel Experiments


Beamforming

Wind Tunnel Experiments


Observer

Observer IntroductionOpen problems remain : real-time computation burden.Can we develop a real-time algorithm that can identify coherent noisesources? Borrow idea from classical control theory.

Signal model

x(t) = Ax(t) + Bu(t), state equation, a new equation.y(t) = Gx(t), measurement equation.


Observer


Signal model


Observer˙x(t) = Ax(t) + Bu(t) + L(y − y).y(t) = Gx(t), where x is the estimation of x .


Observer


Signal model


Observer˙x(t) = Ax(t) + Bu(t) + L(y − y).y(t) = Gx(t), where x is the estimation of x .

Estimation error

e = x − ˙x = (A− LG)e, e approaches 0 as long as the eigenvalue(s) of(A − LG) is(are) less than 0, which is assured by accordingly setting L.


Observer

Observer in Frequency Domain

Time domain to frequency domain

y(t) =∑∞

m=−∞ Ymejmt , x(t) =∑∞

m=−∞ Xmejmt .

Signal model in frequency domain

Xm = AXm, Ym = GXm = 14πr Xme−jmτ .

Observer in frequency domain˙X = AX + L(Y − Y), Y = GX , whose discrete from is recursive oversampling blocks, in other words, the algorithm holds real-timecapability.


Observer

Observer In Wind Tunnel

(

YB

YBS

)

=

(

GGejφ G

)(

XB

XS

)

, (1)

where φ is the phase shift due to the time difference between the twomeasurements of YB and YBS .


Observer

Observer-Based Method

The linear state model of the sound propagation is:(

XB|k+1XS|k+1

)

=

(

A 00 A

)(

XB|kXS|k

)

, (2)

(

YB|kYBS |k

)

=

(

G 0Geiφ G

)(

XB|kXS|k

)

. (3)

The corresponding state observer are:(

XB|k+1

XS |k+1

)

=

(

A 00 A

)

(

XB|kXS|k

)

+ L

[

(

YB |kYBS |k

)

−

(

YB|kYBS |k

)]

,

(4)(

YB|kYBS |k

)

=

(

G 0Geiφ G

)

(

XB|kXS|k

)

. (5)


Observer

Remarks of Observer Algorithm

A =?Given a stationary and ergodic signal process (the assumptionadopted in beamforming), A is an identity matrix for scanned point(s).

Samples

AD

CV

olta

ge

100000 102000 104000 106000 108000 110000 112000 114000 1160002.2

2.3

2.4

2.5

2.6

2.7

2.8

Block k Block k+1 Block k+3Block k+2


Observer

Remarks of Observer Algorithm

A =?Given a stationary and ergodic signal process (the assumptionadopted in beamforming), A is an identity matrix for scanned point(s).

Samples

AD

CV

olta

ge

100000 102000 104000 106000 108000 110000 112000 114000 1160002.2

2.3

2.4

2.5

2.6

2.7

2.8

Block k Block k+1 Block k+3Block k+2

φ =? Assumed known in X. Huang, JAXA, 2009, but can be

φ|k+1 = φ|k + mH∗(Y|k − Y|k ), (6)

where H , ∂Y/∂φ.


Observer

Summary of the Algorithm

(

XB|k+1

XS|k+1

)

=

(

A 00 A

)

(

XB|kXS|k

)

+ L

[

(

YB|kYBS |k

)

−

(

YB |kYBS |k

)]

,

(7)(

YB |kYBS |k

)

=

(

G 0Geiφ|k G

)(

XB|kXS |k

)

, (8)

φ|k+1 = φ|k + mH∗(Y|k − Y|k ). (9)

Prepare A, G, initial guess φ and X , and compute L;

Collect one block of data Y and generate an sound image.

Conduct Eq. (9) to approximate φ.

Recursively repeat above two steps for each block.


Observer

Point Spread Function

(j) Beamforming. (k) Observer.

−0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25−30

−25

−20

−15

−10

−5

0

5

x

dB

beamformingobserver

(l)


Validations

Numerical ValidationTwo monopoles of 3 kHz are closely placed. Both are coherent with120 deg difference in φ. The bottom right one is regarded as abackground noise. An array consists of 56 microphones. Typicalbeamforming and observer-based method are tested to remove thecoherent background noise below.

x-axis (m)

y-ax

is(m

)

0.4 0.2 0 0.2 0.4

0.4

0.2

0

0.2

0.4

SPL12345678910

(m) Coherent noise sources.

−0.4

−0.2

0

0.2

0.4

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

−0.5

0

0.5

1

1.5

Background noise

Mic array

Signal of interest

Z(m)

X(m)

Y(m)

Beam pattern

Plane of interest

(n) Array [email protected] (Peking University) Aeroacoustics June 2010 36 / 46

Validations

Numerical Validation (Cont’)

x-axis (m)

y-ax

is(m

)

0.4 0.2 0 0.2 0.4

0.4

0.2

0

0.2

0.4

SPL12345678910

(o) Classical beamforming, aver-aged over 100 blocks.

x-axis (m)

y-ax

is(m

)0.4 0.2 0 0.2 0.4

0.4

0.2

0

0.2

0.4

SPL12345678910

(p) Observer result of the 500thblock.

Animation


Validations

Computational Costs

Beamforming cost

AB = YBY∗B, ABS = YBSY∗

BS , < AS >≈< ABS > − < AB >,|X (jω)| =

√

(G∗G)−1G∗ < AS > G(G∗G)−1.Cost O(N × N × b), N is array sensor number, and b sample blocks.

Observer cost

(

XB|k+1

XS|k+1

)

=

(

A 00 A

)

(

XB|kXS|k

)

+ L

[

(

YB|kYBS |k

)

−

(

YB |kYBS |k

)]

,

φ|k+1 = φ|k + mH∗(Y|k − Y|k ).

Cost O(N × N) for each sample block.


Validations

Convergence Rate

The convergence of the estimation error (φ − φ) of each sampling datablock, where φ is approximated for each scanned points.

Blocks

Est

imat

ion

erro

r(de

g)

0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30


Validations

Convergence Rate (Cont’)Approximate φ for a representative scanned point only. Adjust φ in theoriginal data (black line), the estimation φ can approach φ quickly in10 blocks, which last less than 1 s. However, an error of 5 deg betweenφ and φ appears.

Blocks

φ

0 100 200 300 400 500

50

100

150

200

Phase shiftPhase estimation

(deg

)


Validations

Experimental Setup of PKUArray


Validations

Experimental Setup (Cont’)


Validations

Experimental Results

x-axis (m)

y-ax

is(m

)

0.4 0.2 0 0.2 0.4

0.4

0.2

0

0.2

0.4

SPL12345678910

(q) Beamforming, BKG.

x-axis (m)

y-ax

is(m

)

0.4 0.2 0 0.2 0.4

0.4

0.2

0

0.2

0.4

SPL12345678910

(r) Beamforming, no BKG.

x-axis (m)

y-ax

is(m

)

0.4 0.2 0 0.2 0.4

0.4

0.2

0

0.2

0.4

SPL12345678910

(s) Observer, k=1.

x-axis (m)

y-ax

is(m

)

0.4 0.2 0 0.2 0.4

0.4

0.2

0

0.2

0.4

SPL12345678910

(t) Observer, [email protected] (Peking University) Aeroacoustics June 2010 43 / 46

Validations

Experimental Results (Cont’)

The estimation φ|k is insensitive to the chosen of φ|k=0.

Blocks

φ

0 20 40 60 80 100170

175

180

185

190

195

200

Initial estimation=180 degInitial estimation=172 degInitial estimation=196 deg

estim

atio

n(d

eg)


Summary

Summary

Summarise of the history of aeroacoustics;

Introduce classical beamforming and its aeroacoustic applications;

Propose a new algorithm holds real-time capability;

Provide various numerical and experimental results.


Summary

Thank You!Questions?


Aeroacoustics: Introduction, Measurement, Computation and ... · Aeroacoustics: Introduction, Measurement, Computation and Control ... Numerical Validation ... Introduction, Measurement,

Documents