Multichannel Active Noise Control with Spatial Derivative - - PowerPoint PPT Presentation

Introduction Proposed method Simulation result

School of Electrical and Electronic Engineering

Nanyang Technological University, Singapore. Site web : eeewebc.ntu.edu.sg E-mail : DSHI003@e.ntu.edu.sg Paper ID : 4068

Multichannel Active Noise Control with Spatial Derivative Constraints to Enlarge the quiet zone

Dongyuan Shi, Bhan Lam, Shulin Wen, and Woon-Seng Gan Digital Signal Processing Laboratory

Dongyuan Shi Derivative contraints active noise control 17 avril 2020 1 / 18

Introduction Proposed method Simulation result

Agenda

1

Introduction Active noise control Current solution

2

Proposed method Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints

3

Simulation result

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Introduction Proposed method Simulation result Active noise control Current solution

Section Plan

1

Introduction Active noise control Current solution

2

Proposed method

3

Simulation result

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Introduction Proposed method Simulation result Active noise control Current solution

Active noise control : It relies on an actuator generating the anti-noise wave, which has a 180o phase difference with the noise, to mitigate the unwanted acoustic noise at the error microphone. This technique has been widely applied in many areas, such as the ventilation ducts, vehicles, headphones, and apertures. Current issue : However, most of the active noise control algorithms aim to control the signal of the error sensor leading to local noise attenuation only around the error microphones.

Dongyuan Shi Derivative contraints active noise control 17 avril 2020 4 / 18

Introduction Proposed method Simulation result Active noise control Current solution

Current method : (1. Wave filed synthesis and boundary surface control. (2. Sound filed control based on wavenumber domain. (3. Spatial ANC based on spherical harmonic expansion. (4. ··· These methods can effectively gain a satisfactory noise control zone in the desired position. Disadvantage : However, these methods usually focus on the noise cancelation in an enclosed region and require many secondary sources and sensors.

Dongyuan Shi Derivative contraints active noise control 17 avril 2020 5 / 18

Introduction Proposed method Simulation result Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints

Section Plan

1

Introduction

2

Proposed method Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints

3

Simulation result

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Introduction Proposed method Simulation result Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints

Figure – 1. Block diagram of a K-L-M multichannel ANC system

When taking the Cartesian coordinates (x,y,z) into account , the control task

• f the generalized model shown in Fig. 1 can be written as

C(ω,x,y,z)W(ω) = H(ω,x,y,z) ∈ CM×K (1) where C(ω) ∈ CM×L and W(ω) ∈ CL×K denotes the secondary path and control filter maxtix, and H(ω,x) is the primary path.

Dongyuan Shi Derivative contraints active noise control 17 avril 2020 7 / 18

Introduction Proposed method Simulation result Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints

Figure – 2. The sound field of the mth error microphone

Since (1) does not specify the sound field at points other than the control points (positions of error microphones), the solution of (1) results in control filters that accurately fulfill the control task only at the positions of the error microphones. Spatial derivative constraints are applied by adding new control equations into (1), each of which constrains the derivative of the sound field (N vicinity points) near the error microphone to be zero.

Dongyuan Shi Derivative contraints active noise control 17 avril 2020 8 / 18

Introduction Proposed method Simulation result Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints

The corresponding first-order spatial derivative constrained control equation with respect the direction rim (i = 1,2,··· ,N, and N → ∞) is given by

L

• l=1

∂Cml(ω,xm,ym,zm) ∂rim Wlk(ω) = 0. (2) We replace (2) with the spatial difference constraint

L

• l=1

Cml,i(ω,xm,ym,zm) − Cml(ω,xm,ym,zm) t Wlk(ω) = 0. (3) where t denotes the distance between the error microphone and the vicinity point. The transfer function from the lth speaker to the ith vicinity point near the mth microphone is given by Cml,i(ω,xm,ym,zm) = Cml(ω,xm + t cosαi,ym + t cosβi,zm + t cosγi) (4)

Dongyuan Shi Derivative contraints active noise control 17 avril 2020 9 / 18

Introduction Proposed method Simulation result Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints

Combing the control equations and the spatial constraints, the control equations for the whole system becomes

• C(ω,x,y,z)W(ω) =

H(ω,x,y,z) (5) where C(ω,x,y,z) and H(ω,x,y,z) are given by

• C =

                                            C11(ω,x1,y1,z1) ··· C1L(ω,x1,y1,z1) . . . ··· . . . C11,i(ω,x1,y1,z1) ··· C1L,i(ω,x1,y1,z1) . . . ... . . . CM1(ω,xM,yM,zM) ··· CML(ω,xM,yM,zM) . . . ··· . . . CM1,i(ω,xM,yM,zM) ··· CML,i(ω,xM,yM,zM) . . . ··· . . . CM1,N(ω,xM,yM,zM) ··· CML,N(ω,xM,yM,zM)                                            

Dongyuan Shi Derivative contraints active noise control 17 avril 2020 10 / 18

Introduction Proposed method Simulation result Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints

and

• H =

                                            H11(ω,x1,y1,z1) ··· H1K(ω,x1,y1,z1) . . . ··· . . . H11(ω,x1,y1,z1) ··· H1L(ω,x1,y1,z1) . . . ... . . . HMK(ω,xM,yM,zM) ··· HMK(ω,xM,yM,zM) . . . ··· . . . HM1(ω,xM,yM,zM) ··· HMK(ω,xM,yM,zM) . . . ··· . . . HM1(ω,xM,yM,zM) ··· HMK(ω,xM,yM,zM)                                            

Dongyuan Shi Derivative contraints active noise control 17 avril 2020 11 / 18

Introduction Proposed method Simulation result Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints

By considering the spatial derivative constraints, the new error signal vector is

• btained as
• E(ω) =

D(ω) − C(ω,x,y,z)W(ω)X(ω). (6) The new disturbance vector is defined as

• D(ω) =

H(ω,x,y,z)X(ω). (7) The objective function is defined as J = E

• EH(ω)

E(ω)

• = E
• tr
• E(ω)

EH(ω)

• (8)

By using the negative gradient of (8) to update the coefficient, the recursive equation of the control filter matrix at the sample index n is obtained as Wn+1(ω) = Wn(ω) + µE

• CH(ω)

E(ω)XH(ω)

• (9)

Dongyuan Shi Derivative contraints active noise control 17 avril 2020 12 / 18

Introduction Proposed method Simulation result Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints

Taking the inverse discrete Fourier transform (IDFT) of (9) yields the equivalent time domain of (9) as wlk(n + 1) = wlk(n) + µE M

• m=1

x′

klm(n)em(n) + M

• m=1

N

• i=1

x′

klm,i(n)emi(n)

• (10)

Replacing the mean value of (10) with the instantaneous value yields

MCFxLMS

• wlk(n + 1) = wlk(n) + µ

M

• m=1

x′

klm(n)em(n)+µ M

• m=1

N

• i=1

x′

klm,i(n)emi(n)

• Derivative constraints

(11)

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Introduction Proposed method Simulation result

Section Plan

1

Introduction

2

Proposed method

3

Simulation result

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Introduction Proposed method Simulation result

Figure – 3. The 2D view of the simulation platform based on K-wave.

we carried out the ANC simulation in 2D with a noise chamber whose size was 2 m by 1.5 m, as shown in Fig.3. The primary source was placed in the back of the chamber, and the front facade of the chamber has a 60 cm wide slit. The two secondary sources were located on each side of the slit. The two error microphones were placed 40 cm away from the front side of the chamber, and the distance between them is set as 30 cm.

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Introduction Proposed method Simulation result

Figure – 4. Sound pressure level distribution

• f noise propagating from the noise chamber

into free field, where ’·’ represents the error microphone.

The frequency of the primary noise was set at 700 Hz.

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Introduction Proposed method Simulation result

Figure – 5. The contours of noise reduction level (dB) distribution in the free field

• utside the noise chamber.

The proposed algorithm can enlarge the quiet zone by using the less error microphones than the conventional MCFxLMS algorithm.

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Introduction Proposed method Simulation result

Thank you for your listening !!

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