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 : DSHI 003 @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 Introduction 1 Active noise control Current solution Proposed method 2 Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints Simulation result 3 Dongyuan Shi Derivative contraints active noise control 17 avril 2020 2 / 18

Introduction Proposed method Simulation result Active noise control Current solution Section Plan Introduction 1 Active noise control Current solution Proposed method 2 3 Simulation result Dongyuan Shi Derivative contraints active noise control 17 avril 2020 3 / 18

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 180 o 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 Introduction 1 Proposed method 2 Spatial derivative constraints Adaptive Algorithm Implementing Spatial Derivative Constraints 3 Simulation result Dongyuan Shi Derivative contraints active noise control 17 avril 2020 6 / 18

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 of the generalized model shown in Fig. 1 can be written as C ( ω,x,y,z ) W ( ω ) = H ( ω,x,y,z ) ∈ C M × K ( 1 ) where C ( ω ) ∈ C M × L and W ( ω ) ∈ C L × 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 m th 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 r im ( i = 1 , 2 , ··· ,N, and N → ∞ ) is given by L � ∂C ml ( ω,x m ,y m ,z m ) W lk ( ω ) = 0 . ( 2 ) ∂r im l=1 We replace ( 2 ) with the spatial difference constraint � L C ml , i ( ω,x m ,y m ,z m ) − C ml ( ω,x m ,y m ,z m ) W lk ( ω ) = 0 . ( 3 ) t l=1 where t denotes the distance between the error microphone and the vicinity point. The transfer function from the l th speaker to the i th vicinity point near the m th microphone is given by C ml , i ( ω,x m ,y m ,z m ) = C ml ( ω,x m + t cos α i ,y m + t cos β i ,z m + t cos γ i ) ( 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 11 ( ω,x 1 ,y 1 ,z 1 ) C 1L ( ω,x 1 ,y 1 ,z 1 )  ···       . .    . .    . .   ···        C 11 ,i ( ω,x 1 ,y 1 ,z 1 ) C 1L , i ( ω,x 1 ,y 1 ,z 1 )   ···       . . ...   . .     . .       �   C = C M1 ( ω,x M ,y M ,z M ) C ML ( ω,x M ,y M ,z M )   ···       . .    . .    . .   ···        C M1 , i ( ω,x M ,y M ,z M ) C ML , i ( ω,x M ,y M ,z M )  ···       . .    . .    . .   ···     C M1 , N ( ω,x M ,y M ,z M ) C ML , N ( ω,x M ,y M ,z M ) ··· 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 11 ( ω,x 1 ,y 1 ,z 1 ) H 1K ( ω,x 1 ,y 1 ,z 1 )  ···       . .    . .    . .  ···         H 11 ( ω,x 1 ,y 1 ,z 1 ) H 1L ( ω,x 1 ,y 1 ,z 1 )  ···        . . ...    . .    . .       �   H = H MK ( ω,x M ,y M ,z M ) H MK ( ω,x M ,y M ,z M )   ···       . .    . .    . .   ···       H M1 ( ω,x M ,y M ,z M ) H MK ( ω,x M ,y M ,z M )   ···       . .     . .   . .   ···     H M1 ( ω,x M ,y M ,z M ) H MK ( ω,x M ,y M ,z M ) ··· 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 obtained 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 �� � � �� �� E H ( ω ) � E ( ω ) � E H ( ω ) J = E E ( ω ) = E tr ( 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 �� � W n+1 ( ω ) = W n ( ω ) + µ E C H ( ω ) � E ( ω ) X H ( 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 � M � � M � N � w lk ( n + 1) = w lk ( n ) + µ E x ′ klm ( n ) e m ( n ) + x ′ klm,i ( n ) e mi ( n ) ( 10 ) m=1 m=1 i=1 Replacing the mean value of ( 10 ) with the instantaneous value yields MCFxLMS � ���������������������������������������������� �� ���������������������������������������������� � M M N � � � x ′ x ′ w lk ( n + 1) = w lk ( n ) + µ klm ( n ) e m ( n )+ µ klm,i ( n ) e mi ( n ) ( 11 ) m=1 m=1 i=1 � ������������������������ �� ������������������������ � Derivative constraints Dongyuan Shi Derivative contraints active noise control 17 avril 2020 13 / 18

Introduction Proposed method Simulation result Section Plan Introduction 1 Proposed method 2 3 Simulation result Dongyuan Shi Derivative contraints active noise control 17 avril 2020 14 / 18