Integrated simulation of active noise cancellation using a computational fluid
dynamics approach
Arun CHERKKIL; Vinod NARAYANAN; Nithin V. GEORGE
Indian Institute of Technology Gandhinagar, India

Abstract
An attempt has been made in this paper to simulate active noise control (ANC) in a three dimensional space using
computational fluid dynamics and pressure acoustics. We have considered a rectangular box, with primary andsecondary sources at the two opposite sides of the box. A model of ANC has been developed, which considers
a cardboard surface and air as the fluid. A control algorithm, which interacts with the fluid dynamic model has
also been developed, which tries to achieve active noise control. The proposed approach can be used as an initial
feasibility study to predict acoustic pressure field inside the control space.
Keywords: Computational fluid dynamics, active noise control

1

INTRODUCTION

Noise control strategies may be broadly classified into passive noise control (PNC) and active noise control(ANC). ANC has been reported to be effective for low frequency noise mitigation when compared to PNC[1].
The basic principle of ANC is destructive interference of sound. In a feed-forward ANC system, a primary microphone is used to measure the reference signal, a loudspeaker is used to produce the necessary control soundand an error microphone is used to sense the residual noise. The loudspeaker is controlled by an adaptive controller, which is usually an adaptive filter. The most widely used controller is an adaptive finite impulse response(FIR) filter, the weights of which are updated using a filtered-x least mean square algorithm (FxLMS)[2].
The effectiveness of an FxLMS algorithm based ANC system is dependent on appropriate modeling of thesecondary path, which is the electro-acoustic path from the loudspeaker to the error microphone[3]. When ANC
is implemented in a 3D space, multiple loudspeakers and microphones are necessary, making the implementation
a multi-channel ANC[4], also requiring different algorithms to achieve the same[5],[6]. For implementing ANC
in a new environment, the first step is a modeling of the secondary paths, which is followed by appropriate
placement of the loudspeakers and microphones. A suitable algorithm is then implemented to achieve ANC[7].
In an endeavour to design a mechanism to visualize noise cancellation in an arbitrary space, before attempting
any physical implementation, this paper proposes a fluid dynamic modeling scheme. The arbitrary space inwhich the noise cancellation is envisioned is modeled by using a finite elements method. Further, the loudspeakers necessary for achieving ANC are introduced in this model as surface perturbations. The microphones
are considered as acoustic pressure probes. In addition, the control algorithm is implemented in a MATLAB
environment, with a real time interface achieved using MATLAB LivelinkT M . The proposed approach is also
envisioned to help in determining optimal positions of loudspeakers and microphones in a given ANC system
implementation. Other similar approaches include methods based on finite difference time domain approach [8],wave field synthesis [9] and finite element method [10].
A real time implementation of ANC in a rectangular cardboard box has also been carried out and the expected sound levels during the noise cancellation process has been visualized using the proposed fluid dynamicapproach. This method can serve as an initial feasibility study to predict acoustic pressure field inside the control space. The rest of the paper is organized as follows: The geometry, governing equations and the modelling
strategy followed in this paper is introduced in Section 2. The simulations results obtained through the proposed
method are also presented in this section. Section 3 deals with the experimental setup as well as a discussion
on the experimental results and the concluding remarks are drawn in Section 4.

39abFigure 1. a. The geometry b. Meshing

2GEOMETRY, GOVERNING EQUATIONS AND MODELINGAn attempt has been made to create a simulation mechanism to understand noise cancellation at various locations in an arbitrary three dimensional space. We have used COMSOL multiphysics to achieve this task. Thegeometry, which includes an air column inside a rectangular box, was developed in the software using COMSOL geometry interface. Two separate rectangular sub-geometry are made, to simulate the primary and controlspeakers, on opposite faces of the rectangular box. Meshing is another crucial step in the numerical simulation
wherein the geometry is subdivided into smaller cells and the equations of motion are solved. Here a finemeshing is performed using a free tetrahedral mesh with minimum element size of 0.01 m and a maximum of
0.1 m. The mesh size has been considered to be less than one-sixth of the minimum wavelength involved inthis exercise. As the maximum frequency used in this study is 200 Hz, we have used a maximum element sizeof 0.1 m, which is less than one sixth of the minimum wavelength λ = c/ f = 343/200, where c is the speedof sound in air and f is the frequency of interest. It may be noted that we have used uniform meshing in thisstudy. The geometry and the meshing used is shown in Figure 1. The medium has been assumed as stationary,with no flow into or out of the system. The Neumann boundary conditions has been taken for the surfaces of
the rectangular box, which is defined as∂ P0= 0,(1)∂nwhere P0 is the acoustic pressure at the boundary and n is the normal vector to the surface. In COMSOLenvironment, this boundary condition is also referred to as the sound hard boundary condition. A pressureboundary condition is applied to primary speaker. The pressure condition can replicate a speaker diaphragm
generating a time dependent harmonic pressure signal, which is explicitly defined using a field function. Thecontrol speaker is also given a pressure boundary condition wherein the pressure values are updated for eachtime step of the simulation through the LivelinkT M feature for MATLAB provided with COMSOL software.
In this study, we have assumed the air column within in the rectangular box to be stationary. Thus we use
a pressure acoustics physics model, which solves the 3D acoustic wave equation to analyze this system. The
sound produced by the primary or the secondary speakers can be considered as small perturbations. This allows
us to make a linear approximation approach also referred to as the classical acoustic approach. The 3D acoustic

40

Figure 2. The impulse response for the secondary path in simulation
wave equation which we have tried to implement in this study is given by∇2 P0 =1 ∂ 2 P0,
c2 ∂t 2(2)which has been obtained from the momentum equation, mass conservation equation and the state equation givenby∂u(3)− ∇ · P0 = ρ0 ,∂t
∂ ρ0= −ρ0 ∇ · u,
(4)
∂tanddPt= c2(5)dρtrespectively. In the above mentioned relations, P0 is the acoustic pressure, Pt = (P0 + P0 ) is the total pressure,c is the speed of sound, ρ0 is the fluid density, ρ 0 = (ρt − ρ0 ) is the change in density and bmu is the fluid
particle velocity. The acoustic wave model used in COMSOL Multiphysics also takes a similar form and isdefined as follows:1 ∂ 2 pt
1+ ∇ · − (∇pt − qd ) = Qm ,(6)ρc2 ∂t 2ρwhere pt is the acoustic pressure, ρ is the specific mass qd dipole source and Qm is the monopole source [11].
A multi-frontal massively parallel sparse parallel solver (MUMPS) has been used to solve the system of linear
equations in the simulation. A time dependent study has been performed to understand how sound propagatesin the medium with time. The pressure wavefront of the primary loudspeaker travels at a speed of 343 m/s(as the domain has been selected as air) and reaches the error microphone (which is placed at the geometriccentre point of the cardboard box model), which is at a distance of 0.375 m from the primary loudspeaker in
343(m/s)/0.375(m) = 0.00109(s). Thus to accurately capture the sound field at the error microphone, we haveused a time stepping of 0.001 s in this study.
The first step in the proposed integrated simulation task is a secondary path modeling. A band limited white
noise was generated in MATLAB and was used to drive the primary loudspeaker model. The response at theerror microphone for this input was captured in the COMSOL model. The input signal as well as the error
microphone response were used to estimate the secondary path model using an offline implementation of theLMS algorithm. The impulse response of the secondary path obtained is shown in Figure 2. This secondary41

a. 115 Hz, µ = 0.1

b. 115 Hzc. 150 Hz, µ = 0.1

d. 150 Hz

e. 200 Hz, µ = 0.01

f. 200 HzFigure 3. Control speaker signal (a, c, e) and corresponding error signals (b, d, f) for 115 Hz, 150 Hz and 200Hz
path impulse response was used in the FxLMS algorithm to control the sound field in the COMSOL model, bydriving the control loudspeaker using MATLAB LiveLinkT M . The three noise cancellation scenarios consideredin the experimental study were repeated using the proposed COMSOL model. The control signal applied forthe three cases and the corresponding error signals are shown in Figure 3. We can also observe a close match
between the noise cancellation results obtained using simulation as well as experimental study. Figure 4 shows
the pressure surface plots and iso-surfaces for the simulation run at 115 Hz. It shows how pressure levels
inside the domain varies with the control speaker. Thus the proposed approach acts as a good visualization
tool for understanding noise cancellation in 3D environment. This can also help in checking feasibility of noise
cancellation before attempting any real time implementation for any arbitrary sound column, which could bemodeled in a COMSOL platform.

42

a. Surface plot

b. Iso-surfacesc. Vertical slice plot

Figure 4. Simulation results (Using COMSOL 5.2a) for pressure fields at 115 Hz,µ = 0.1
With the modern day developments in computational fluid dynamics and computational acoustics, we will beable to easily predict the noise propagation in any space and also the noise generation patterns from various
types of flow phenomenon, by coupling the acoustic wave equations with the Navier-Stokes equation. With
increasing resources for computation and technology computational acoustics coupled with computational fluid
dynamics is expected to become a great product design and problem solving tool [12].

3EXPERIMENTAL SETUP AND RESULTS

The experimental setup considered in this paper consists of a rectangular corrugated cardboard box of size
175 × 65 × 75 cm, with the two smaller inner walls covered with polystyrene sheets of 100 mm thickness. Two
Presonus Eris E5 studio monitors are then placed at two sides of the larger surface of the box by cutting twoholes of size 32 × 15 cm, with the loudspeaker diaphragm facing the inside of the box. The first loudspeakeracts as the primary noise source and the second loudspeaker is the control loudspeaker. The setup described43Figure 5. Experimental setup showing the control speaker
above is shown in Figure 5. An attempt has been made to implement feedback ANC in the box, with an error microphone (Behringer C2 microphone) placed at the geometric centre of the box. A Behringer U-Phoria
UMC404HD audio interface has been used to connect the speakers and the microphone with the adaptive controller, which has been implemented on a Simulink platform in a 64 bit Windows 10 PC, with 2.2 GHz Intel
Core i7 processor with 6 GB RAM.
The first task in a feedback ANC implementation is the estimation of the secondary path transfer function. Aband-limited white noise in the band 10-500 Hz was played through the control speaker and was measured
using the error microphone. These signals were used to estimate the secondary path transfer function and wehave used LMS algorithm for this task. The impulse response of the estimated secondary path is shown inFigure 6. An FxLMS algorithm was implemented to achieve noise cancellation. We have considered three casesof single tone noise control, with the primary disturbances of 115 Hz, 150 Hz and 200 Hz. These frequencies
are so chosen so as not to exceed the cut on frequency for the box model. This avoids inclusion of multiple
modes inside the domain [13]. The error signal, measured at the error microphone for the three cases andthe convergence characteristics are shown in Figure 7. A significant noise reduction can be observed from theconvergence characteristics. The reduction is sound level in terms of sound pressure level was also measured
using a sound level meter. The sound levels for the three cases, before and after noise cancellation is shown inTable 1.

Figure 6. Impulse response of the secondary path in experiment44

a. 115 Hz

b. 150 Hz

c. 200 Hz

Figure 7. Measured Error Mic values from Experiment.
Table 1. Reduction in Sound Pressure level (dB)Frequency [Hz]
115
150
200

Without ANC (dB)
86.6
83.2
85.4

With ANC (dB)
71.2
68.6
73.4

The results obtained from the experiment and the simulation does follow the same trend, but the reduction insound pressure levels at the measured point is higher in the simulation than in the experimental setup. This may
be accounted to the fact that the default boundary conditions in COMSOL are for ideal cases. By implementing
an impedance boundary condition at domain surface and applying perfectly matching layers (PML) to simulate
infinite boundaries may offer comparable and physically accurate results.

4CONCLUSION

This paper develops a computational fluid dynamic scheme for analyzing ANC systems. This has been achievedby considering a stationary air column as the fluid and implementing loudspeakers as surface perturbations

45

where pressure values are updated using pressure field functions. In the control speaker, this pressure variationis governed by a FxLMS algorithm. The proposed approach acts as an effective visualization tool for noise
cancellation within an arbitrary space without the need for a physical implementation. The simulation study
was followed by an experimental study, wherein ANC was implemented in a 3D space of properties similar tothe one used in the simulation.

ACKNOWLEDGEMENT
This work is supported by the Department of Science and Technology, Government of India under the Core
Grant Scheme (CRG/2018/002919).

REFERENCES[1] P. A. Nelson and S. J. Elliott, Active control of sound.

Academic press, 1991.

[2] S. M. Kuo and D. Morgan, Active noise control systems: algorithms and DSP implementations. John Wiley& Sons, Inc., 1995.
[3] S. M. Kuo and D. Vijayan, “A secondary path modeling technique for active noise control systems,” IEEE
Transactions on Speech and Audio Processing, vol. 5, no. 4, pp. 374–377, 1997.
[4] S. J. Elliott, C. C. Boucher, and P. A. Nelson, “The behavior of a multiple channel active control system,”IEEE Transactions on Signal Processing, vol. 40, no. 5, pp. 1041–1052, 1992.
[5] S. Elliott, I. Stothers, and P. Nelson, “A multiple error lms algorithm and its application to the activecontrol of sound and vibration,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 35,no. 10, pp. 1423–1434, 1987.
[6] S. C. Douglas, “Fast implementations of the filtered-x lms and lms algorithms for multichannel active noisecontrol,” IEEE Transactions on Speech and Audio Processing, vol. 7, no. 4, pp. 454–465, 1999.
[7] N. V. George and G. Panda, “Advances in active noise control: A survey, with emphasis on recent nonlinear techniques,” Signal processing, vol. 93, no. 2, pp. 363–377, 2013.
[8] A. Szarvas and L. Sujbert, “Efficiency testing of active noise control by acoustic field modeling,” Periodica
Polytechnica Electrical Engineering and Computer Science, vol. 59, no. 4, pp. 147–159, 2015.
[9] A. Lapini, M. Biagini, F. Borchi, M. Carfagni, and F. Argenti, “Active noise control for pulse signals bywave field synthesis,” in Signal Processing Conference (EUSIPCO), 2016 24th European. IEEE, 2016, pp.
883–887.
[10] A. Ohadi and A. Emadi, “Active noise control simulation in a passenger car cabin using finite elementmodeling,” SAE Technical Paper, Tech. Rep., 2005.
[11] L. Koudela, J. Jansa, and P. Karban, “Numerical modeling of transient acoustic field using finite element
method,” Poznan University of Technology Academic Journals. Electrical Engineering, no. 73, pp. 155–160,
2013.
[12] H. K. Versteeg and W. Malalasekera, An introduction to computational fluid dynamics: the finite volume
method. Pearson education, 2007.
[13] M. L. Munjal, Acoustics of Ducts and Mufflers, 2nd Edition.

46Wiley, 2014.