International Conference on Computing, Communication and Automation (ICCCA2015)
Noise reduction using FeedForward ANC System based on Online Secondary Path Modeling 1
Atul Pillania, 2 Manoj Kumar Sharma, 3 Naresh Kumar
University Institute of Engineering and Technology Panjab University, Chandigarh, India 1
[email protected],
[email protected],
[email protected]. Abstract— Destructive interference is the principle on which ANC (active noise control) system is based. In destructive interference an anti-noise signal is generated using adaptive filter and is superimposed upon noise signal, as a result the unwanted noise is reduced. The secondary path of ANC is assessed off-line prior to use of ANC system when no reference noise exists. But, in practical applications, reference noise exists and secondary path may be varying with time. This may lead to ANC system instability and adaptive filter may not be able to converge. In such cases, this time varying secondary path should be modeled online to make sure proper functioning of ANC system. In this paper, ANC system based on online modeling of secondary path is applied to ambulance siren noise. The simulations performed in MATLAB show that noise level is reduced by approximately 37 dB, which is a considerable reduction in noise level. Keywords—Active noise control; online secondary path modeling; FxLMS; acoustic noise.
I.
INTRODUCTION
Noise pollution becomes more intense as the use of industrial machines and home appliances is increasing in our daily routine. Noise has damaging effects on human hearing capability. The research has shown that the sustained exposure to the high noise put the humans at the risk of high blood pressure, headache, fatigue, stress, anxiety and loss of concentration which results in reduced productivity [1, 2]. For higher frequency (above 1.5 kHz) passive noise control methods provide reasonable noise reduction. Passive noise control techniques include barriers, enclosures, silencers and ear muff etc., but these methods are not effective for noise reduction at low frequency. Therefore, to provide noise reduction at lower frequency active noise control (ANC) method has been developed in last decades [3-5]. ANC system is based upon destructive superposition. In ANC, a signal called anti-noise signal, of equal amplitude and opposite phase of unwanted noise is generated. This anti-noise signal is superimposed on the noise signal which results in cancelation of unwanted noise. This method has been applied to many industrial applications such as air conditioning systems, industrial motors, exhaust fan, aircrafts, MRIs etc. ANC system is designed using adaptive filters which are based on Least Mean Square (LMS) algorithm. Secondary path model is used in design of ANC system, as it takes into account the
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time delay caused by electronic components used in ANC system. The realization of LMS algorithm with secondary path transfer function is called Filtered-x Least Mean Square algorithm (FxLMS) [6, 7], shown in Fig 1. The secondary path is estimated off-line prior to run of active noise control system. For practical applications the secondary path may vary with time and it is required to estimate the secondary path online when the ANC system is in use [5]. Reduction of ambulance siren noise for patient is an important application of ANC system. A siren is used on ambulance to inform other people on the road that the ambulance is approaching and to give a way. In this process ambulance siren generates loud noise. Siren sound is very irritating for the patient in the ambulance and it can further affect his health condition. This ambulance siren noise can be reduced and a zone of silence can be created near patient using active noise control system and result can further be improved by using online secondary path modeling. Paper outline In section II FxLMS based ANC system is discussed. Section III describes online secondary path modeling in ANC system. Simulation results using ambulance siren are given in section IV and conclusion is summarized in section V. II.
TRADITIONAL ANC SYSTEM
ANC system uses Filtered-x Least Mean Square (FxLMS) [6, 7]. It takes into consideration secondary path effects, i.e. input signal is filtered by estimate of secondary path filter of ANC system. It is shown in Fig 1. Primary path between reference microphone and error microphone is represented by P(z). W(z) represents the adaptive filter. Its weights are varying according to Least Mean Square algorithm and it takes filtered x input through estimate of secondary filter instead of simple reference noise input, for weights updation, it is called Filtered-x Least Mean Square (FxLMS) algorithm. Weights are varied in order to reduce error signal e(n) at error microphone.
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International Conference on Computing, Communication and Automation (ICCCA2015) x(n)
d(n)
P(z)
second approach is inferior to the first and the first one can be valid for whole frequency range. Two important methods of online modeling of secondary path based on first approach which uses additional random noise are given by Bao et al. [10] and Kuo et al. [11]. These two methods try to decrease the influence of modeling of secondary path on the weight updation of W(z) filter and vice versa. These two methods achieved some significant improvement in online secondary path modeling. However, the agitation problem caused by v(n) random noise and W(z) remain unaddressed [12].
e(n) +
+ y(n)
W(z)
S(z)
Sˆ ( z ) x′(n)
Zhang et al. [14] proposed cross-updated online secondary modeling, which takes into consideration the perturbation effect caused by v(n) and w(n).The Zhang’s methods for online modeling is shown in Fig 2.
LMS Fig. 1. FxLMS based ANC system.
S(z) is secondary path impulse response, it takes into consideration of the D/A converter, power amplifier, path followed by noise from the loudspeaker to error microphone, secondary loudspeaker, error microphone, preamplifier, antialiasing filter, smoothing filter, and A/D converter [12, 13]. Sˆ ( z ) is the estimate of secondary path. This estimate of secondary path varies with time in practical applications, so online model of secondary path is used to capture this time varying effect. x(n) is primary noise signal at reference microphone. e(n) is error signal obtained by e(n)= d(n)- y′(n) , where d(n)=p(n)*x(n); and y′(n) = s (n ) * y (n ) y(n)=w(n)*x(n). Weights, w(n), of adaptive filter are updated by using
w(n + 1) = w(n) + μ x′(n)e(n) where the step size of the w(n) filter is
(10)
μ
;
x ′( n ) = sˆ( n ) * x ( n ). III.
Fig. 2. ANC system with secondary path modeling (Zhang’s methods) [14].
ONLINE SECONDARY PATH MODELLING
The secondary path, S(z) is assessed before the run of ANC system when noise signal x(n) is not applied for reduction. But, x(n) is always present in real time applications and secondary path may be fluctuating with time. To take into consideration this time varying effect of secondary path, it should be modeled online to ensure that the adaptive filter converge properly for noise reduction. There are two important requirements for online modeling of secondary path [3], one of them is that the modeling of Sˆ ( z ) would not be depended on the updating of W(z). Second one is that adaptive filter W(z) operation should not be affected by estimation of S(z). But these requirements appeared to be contradictory. This contradiction was appeared in method given by Eriksson et al. [8], in which random noise is used for modeling of secondary path. The additional random noise introduced into ANC system which is used to model S(z), is one of two approaches used in online modeling. Second approach is to model the secondary path online using the output, y(n), of adaptive filter W(z). An evaluation of these two methods conducted by C. Bao et al. [9] show that the
In Zhang’s method shown in Fig 2 uses three adaptive filters: W(z) is controller adaptive filter of ANC; Sˆ ( z ) is used for estimation of secondary path online; H(z) is used for removing perturbation effect. The output of Sˆ ( z ) for random noise is uˆ ( n) = sˆ( n) * v(n ) , which is subtracted from the error signal e(n), to yield a new signal, e′(n) = e(n) − sˆ(n) * v(n) , this new error signal is used to update the weights of filter w(n). Error signal is, e(n)= d(n)- y′(n) +s(n)*v(n). In case modeling is ideal, i.e. S(z)= Sˆ ( z ) , then e′( n) = d ( n) − s (n) * y (n) . This shows that e′(n) becomes totally correlated with x(n) and the interference due to v(n) is totally disappeared. This e′(n) is also used as the desired signal for adaptive filter H(z). The weight updating equation of W(z) is given as
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w(n + 1) = w(n) + μ w x′(n)e′(n). The modernizing equation of H(z) is given as
(2)
International Conference on Computing, Communication and Automation (ICCCA2015)
h(n + 1) = h(n) + μ h x(n) * (e′(n) − z (n)).
error microphone is calculated. The SNR of the system is given by:
(3)
where μ h is the step size used for updating H(z) filter. The output of filter H(z) is z(n)=x(n)*h(n). This output is subtracted from e(n) to produce a new signal g(n)=e(n)-z(n), and g(n) is used in adaptive filter Sˆ ( z ) as the desired signal. So, updating equation for filter Sˆ ( z ) is
sˆ(n + 1) = sˆ(n) + μ s v(n) * ( g (n) − uˆ (n)).
⎛ ∑ e 2 (n)( ANC _ OFF ) ⎞ ⎟⎟ SNR = 10 log10 ⎜⎜ 2 ⎝ ∑ e (n)( ANC _ ON ) ⎠
(5)
The SNR is obtained 37 dB approximate that indicates ambulance noise is reduced significantly.
(4)
As a result of using e′(n) , the perturbation caused by v(n) greatly decreased. IV. SIMULATION RESULTS In this paper, feedforward ANC system based on online secondary path modeling is applied on ambulance siren noise recorded from the ambulance of Health Center of Panjab University, Chandigarh, India. Simulation for the same are performed using MATLAB 2011 software. Ambulance siren noise taken as reference noise signal is shown in Fig 3. This reference noise signal is applied to ANC system for noise reduction to create region of silence near patient. In the simulation, firstly primary path transfer function P(z) and secondary path transfer function S(z) are measured and weights of H(z) is taken zero. Primary path P(z), secondary path S(z) and H(z) have tap length of 128 long each. For updating coefficient of adaptive filters step size μ w =0 .05,
μh
=0.03 and
μ s =0.006 are used.
Fig. 4. The residual noise signal (ANC with online secondary path modeling is ON)
The Power spectral Density (PSD) describes the signal power distribution over the given frequency range. The Fig 5(a) represents the PSD of reference ambulance siren noise signal and Fig 5(b) represents PSD of residual noise signal after applying ANC. It indicates ANC with online secondary path modeling give better result.
Fig. 3. The Ambulance Siren Signal taken as reference noise signal (ANC OFF)
The Fig. 4. shows the residual noise signal after applying the active noise control with secondary path modeled online using cross updated filters. The result in Fig 3 and 4 shows that the ANC successfully reduced the ambulance siren noise, results in quieter and comfortable zone near patient. To observe the qualitative reduction in the noise, SNR (signal to noise ratio) of the reference noise and the residual noise at the
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Fig. 5(a). Power spectral Density for reference noise signal of the ambulance siren noise (ANC OFF)
International Conference on Computing, Communication and Automation (ICCCA2015) V.
Fig. 5(b). Power spectral Density for residual noise signal (ANC ON)
The ANC performance has been tried for the ambulance siren noise over the several trials by changing the weight updation parameter, μw. The performance over the several trials can be generalized using smoothened ensemble average square error (SEASE), ξ sd (n) [15]. This is calculated as per equations (6)-(8).
ξ sd (n) = 10 log10 (ξ S (n)) , ξ S (n) = λξ S (n − 1) + (1 − λ )ξ (n), 1 ξ ( n) = K
(6)
Noise pollution is increasing day by day; it is becoming important to restrain noise as much as possible. The loss of concentration and low productivity are two major consequences of noise at the workplace. However, ambulance siren noise is irritating for patient plus hinders necessary communication among medical team and patient. So, ANC can be used to reduce noise. In this paper, ANC with online secondary path modeling is used to reduce the noise of ambulance siren inside the ambulance so that patient does not feel uncomfortable. The simulations are performed on MATLAB. It shows that noise is reduced by 37 dB. Hence ANC with online secondary path modeling using FxLMS is effective method for noise reduction and can be utilized in many more applications. The power spectral density response of ANC OFF and ANC ON signifies that ambulance noise reduction is an important application of active noise control system from the health point of view of patient in ambulance. ACKNOWLEDGMENT This work is done under the Special Assistance Programme (SAP) of University Grants Commission (UGC), New Delhi, India. REFERENCES [1]
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