Decoupling feedforward and feedback structures in hybrid active noise control systems for uncorrelated narrowband disturbances

Journal of Sound and Vibration 350 (2015) 1–10

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Decoupling feedforward and feedback structures in hybrid active noise control systems for uncorrelated narrowband disturbances Lifu Wu a,b,n, Xiaojun Qiu b, Ian S. Burnett b, Yecai Guo a a Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, School of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China b School of Electrical and Computer Engineering, Royal Melbourne Institute of Technology, Australia

a r t i c l e i n f o

abstract

Article history: Received 2 October 2014 Received in revised form 13 April 2015 Accepted 16 April 2015 Handling Editor: K. Shin Available online 5 May 2015

Hybrid feedforward and feedback structures are useful for active noise control (ANC) applications where the noise can only be partially obtained with reference sensors. The traditional method uses the secondary signals of both the feedforward and feedback structures to synthesize a reference signal for the feedback structure in the hybrid structure. However, this approach introduces coupling between the feedforward and feedback structures and parameter changes in one structure affect the other during adaptation such that the feedforward and feedback structures must be optimized simultaneously in practical ANC system design. Two methods are investigated in this paper to remove such coupling effects. One is a simplified method, which uses the error signal directly as the reference signal in the feedback structure, and the second method generates the reference signal for the feedback structure by using only the secondary signal from the feedback structure and utilizes the generated reference signal as the error signal of the feedforward structure. Because the two decoupling methods can optimize the feedforward and feedback structures separately, they provide more flexibility in the design and optimization of the adaptive filters in practical ANC applications. & 2015 Elsevier Ltd. All rights reserved.

1. Introduction Active noise control (ANC) has attracted considerable interests in the literature [1,2], as well as has been utilized in practical applications ranging from communication headsets [3,4] and helmets [5] to ventilation ducts [6,7]. Feedforward structures using the filtered-x least mean square (FxLMS) algorithm are widely used in ANC systems when a reliable reference signal is obtainable. They attenuate both broadband and narrowband noise by using reference sensors to obtain the reference signal and error sensors to monitor the performance. To achieve effective control, the reference signal needs to provide time-advanced information (i.e., the causality requirement) and to be highly correlated (i.e., the correlation requirement) with the primary noise [2]. However, if there is no appropriate location for the reference sensor, these two requirements may not be satisfied in some frequency bands with the result that the noise components in these frequency

n Corresponding author at: Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing University of Information Science and Technology, Nanjing 210044, China. E-mail address: [email protected] (L. Wu).

http://dx.doi.org/10.1016/j.jsv.2015.04.018 0022-460X/& 2015 Elsevier Ltd. All rights reserved.

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bands cannot be controlled by the feedforward structure. These noise components can be treated as the disturbance which is observed by the error sensor but uncorrelated with the reference signal. There are also some situations where an uncorrelated disturbance is only present at the error sensor, such as the noise generated by passing vehicles in electronic mufflers for automobiles [8]. Feedback structures differ from feedforward structures in that they do not require reference sensors to give a timeadvanced reference signal for the primary noise. A combination of feedforward and feedback structures is referred to as a hybrid feedforward and feedback structure (hereinafter, called a hybrid structure in short) and the secondary signal is generated on the basis of the output summation of both feedforward and feedback structures [8–13]. A hybrid structure uses the feedforward part to attenuate the primary noise correlated with the reference signal and uses the feedback part to cancel narrowband components “unobserved” by the reference sensor, so it is capable of controlling both noise and uncorrelated narrowband disturbances [9]. The computational complexity of the hybrid structure might be reduced when a lower order FIR filter is used to achieve the same performance as that using the feedforward or feedback ANC structure alone [1]. The hybrid structure also offers good performance in terms of narrowband and broadband noise control as well as high flexibility in ANC system design. For instance, a hybrid ANC structure was proposed by Akhtar et al. to control correlated and uncorrelated noise appearing at the error sensor and their proposed method was shown to have higher noise reduction than either the feedforward or the feedback structure due to the introduction of a third adaptive filter to generate appropriate signals for the feedforward and feedback structures [8]. In [12], a hybrid ANC architecture was presented and validated for a circumaural earcup and a communication earplug. The results show that the gain stability margins over a single feedforward structure are improved by orders of magnitude at certain frequencies when a source-independent feedback structure and a Lyapunov-tuned leaky LMS feedforward structure are combined and adjusted with individual gain factors. A multi-channel hybrid structure ANC system for infant incubators was introduced in [13] and it is reported that hybrid ANC structures are effective in canceling noise from infant incubators in real environments since the feedforward structure can cancel noise generated from sources outside the incubator while the feedback structure reduces the predictable noise inside the incubator. In common hybrid structures that combine the feedforward and feedback structures, the secondary signals of both structures are used to generate the reference signal for the feedback structure [1,2]. On the other hand, the error signal also depends on the secondary signals of both structures, so coupling is introduced between the two structures. The convergence speed and noise reduction performance of these hybrid structures deteriorate because the coupling causes the parameter changes in one structure to affect the other during adaptation and both feedforward and feedback structures must be optimized simultaneously in practical ANC system design. To the best of the authors' knowledge, this coupling effect has not been paid sufficient attention to in the literature and hence will be investigated in this paper. After analyzing the mechanism of the coupling effect, the paper introduces two methods for hybrid ANC structures which can alleviate the coupling effect between the feedforward and feedback structures. One is the simplified method which excludes the secondary signals from the synthesis of the reference signal in the feedback structure and uses the error signal directly, and the feedback structure in the simplified method is the same as the one in a recent publication [14]. The other method synthesizes the reference signal in the feedback structure with its own secondary signal and uses the generated reference signal as the error signal for the feedforward structure. Compared with Ref. [14], the new contribution of this paper is the coupling effect in the commonly used hybrid system which is analyzed and two alternate methods are presented to construct the decoupled hybrid systems. The advantage of the two methods is that the feedforward and feedback structures can be designed individually thanks to their decoupled form. 2. The decoupled hybrid ANC systems 2.1. The traditional combination method based system Fig. 1 shows the block diagram of a traditional combination method based hybrid system (tHybrid) which is commonly used in ANC applications. The feedforward structure is composed of one reference sensor to pick up the reference noise x(k), one error sensor to measure the residual noise e(k), one secondary sound source to generate the canceling signal yf(k) for attenuation of the primary noise d(k) and an uncorrelated narrowband disturbance denoted by v(k). Here the reference ^ signal x(k) is filtered through SðzÞ, the so-called estimation of the secondary path S(z), and the control filter Wf(z) is represented as a tap weight vector of length L, i.e., wf ðkÞ ¼ ½w0f ðkÞ; w1f ðkÞ…wLf  1 ðkÞT . The feedback structure consists of the control filter Wb(z) and the reference signal xb(k) which is synthesized on the basis of e(k) and the secondary signal y(k) ^ filtered by SðzÞ. By using the Z transforms of the signals in Fig. 1, the error signal in the tHybrid ANC system can be written as EðzÞ ¼ DðzÞ þ V ðzÞ þ SðzÞY ðzÞ

(1)

where Y(z) is the output summation of the feedforward and feedback structures Y ðzÞ ¼ Y f ðzÞ þ Y b ðzÞ:

(2)

Yf(z) and Yb(z) are the secondary signals of the feedforward and feedback structures, respectively Y f ðzÞ ¼ X ðzÞW f ðzÞ

(3)

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Fig. 1. Block diagram of the single channel hybrid ANC system based on the traditional combination method (the feedforward structure is shaded gray).

Y b ðzÞ ¼ X b ðzÞW b ðzÞ

(4)

where Xb(z) in Eq. (4) is the reference signal in the feedback structure synthesized by ^ X b ðzÞ ¼ EðzÞ–SðzÞY ðzÞ

(5)


 ^ X b ðzÞ ¼ EðzÞ–SðzÞ X ðzÞW f ðzÞ þ X b ðzÞW b ðzÞ

(6)

Substituting Eqs. (2)–(4) into Eq. (5) gives

Rearranging Eq. (6), one has X b ðzÞ ¼

^ EðzÞ  SðzÞXðzÞW f ðzÞ ^ 1 þ SðzÞW ðzÞ

(7)

b

Substituting Eqs. (2)–(4) and (7) into Eq. (1) yields "

^ EðzÞ  SðzÞXðzÞW f ðzÞ W b ðzÞ EðzÞ ¼ DðzÞ þ VðzÞ þ SðzÞ XðzÞW f ðzÞ þ ^ ðzÞ 1 þ SðzÞW

#

b

EðzÞW b ðzÞ þ XðzÞW f ðzÞ ¼ DðzÞ þVðzÞ þ SðzÞ ^ 1 þ SðzÞW b ðzÞ

(8)

After some further rearrangement, one obtains EðzÞ ¼

^ 1 þ SðzÞW SðzÞW f ðzÞ b ðzÞ ½DðzÞ þ VðzÞ þ XðzÞ ^ ^ 1 þ½SðzÞ SðzÞW b ðzÞ 1 þ½SðzÞ SðzÞW b ðzÞ

^ If SðzÞ ¼ SðzÞ and D(z) ¼X(z)P(z) are applied in Eq. (9), the error signal of the tHybrid ANC system is then given by   EðzÞ ¼ ½1 þSðzÞW b ðzÞV ðzÞ þ ½1 þ SðzÞW b ðzÞP ðzÞ þSðzÞW f ðzÞ X ðzÞ

(9)

(10)

Eq. (10) shows that the feedforward control filter Wf(z) and the feedback control filter Wb(z) are coupled in the tHybrid ANC system. In order to control the noise d(k), the term [1þS(z)Wb(z)]P(z)þS(z)Wf(z) should approach zero, and then the feedforward control filter becomes W f ðzÞ ¼ 

½1 þSðzÞW b ðzÞPðzÞ  PðzÞ ¼ SðzÞ SðzÞ=½1 þ SðzÞW b ðzÞ

(11)

In a single feedforward structure ANC system, the optimal feedforward control filter is Wf(z)¼ P(z)/S(z) [1], thus in the traditional method the effect of the coupling is that the feedback control filter Wb(z) influences the feedforward control filter Wf(z) by changing the secondary path from S(z) to an “equivalent secondary path” S(z)/[1þ S(z)Wb(z)]. Even assuming that S (z) is stationary, the “equivalent secondary path” changes when Wb(z) is adapted online. During the convergence of the adaptive filter Wf(z), the updating of Wb(z) might sometimes cause the phase difference between S(z) and S(z)/[1 þS(z)Wb(z)] to be larger than π =2 radians, resulting in the divergence of the feedforward structure [1–2]. The coupling between Wb(z)

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and Wf(z) happens because the reference signal xb(k) is synthesized using both the secondary signals of the feedforward and feedback structures, yf(k) and yb(k) as shown in Eqs. (2)–(5). In addition, Eqs. (1) and (2) show that the error signal also depends on the secondary signals of both structures.

2.2. The simplified combination method based system An intuitive approach for alleviating the coupling is to remove the reconstruction of the reference signal in the feedback structure. This results in the simplified combination method based system (sHybrid) shown in Fig. 2, where the feedback structure is a simplification of that in the tHybrid system and the reference signal xs(k) in the feedback structure now comes from the error signal directly, i.e. X s ðzÞ ¼ EðzÞ

(12)

Repeating the derivation of Eq. (10) but replacing Eq. (5) with Eq. (12), the error signal in the sHybrid ANC system can be ^ derived as (also assuming SðzÞ ¼ SðzÞ and D(z)¼X(z)P(z)) EðzÞ ¼


 1 1 VðzÞ þ PðzÞ þ SðzÞW f ðzÞ XðzÞ 1 SðzÞW s ðzÞ 1  SðzÞW s ðzÞ

(13)

The simplification decouples the feedforward and feedback structures and the feedforward structure does not impact the feedback structure directly. The benefits of the decoupled structure can be observed from Eq. (13), where the feedforward and feedback structures can be updated independently. The feedback structure aims to control the uncorrelated disturbance v(k) and its ideal solution is to update the controller Ws(z) to have a large gain over the frequency range of interest and to make the term 1/[1 S(z)Ws(z)] as small as possible [14], while the feedforward control filter Wf(z) approximates  P(z)/S(z) to attenuate d(k). The term [P(z)þS(z)Wf(z)]/[1  S(z)Ws(z)] in Eq. (13) is a product of P(z) þS(z)Wf(z) and 1/[1  S(z)Ws(z)], i.e., the feedforward and feedback structures are cascaded. In addition, the term [P(z) þS(z)Wf(z)]/[1 S(z)Ws(z)] can also be considered as an IIR filter by embedding Wf(z) and Ws(z) in the numerator and denominator respectively [15,16]. In that case, Wf(z) approximates P(z)/S(z) to make the numerator approach zero, and Ws(z) is optimized so as to have the denominator as large as possible. As a result, both the structures tend to drive the term [P(z)þS(z)Wf(z)]/[1  S(z)Ws(z)] to zero, and contribute to the overall attenuation of the noise with an uncorrelated disturbance. The feedback structure in Fig. 2 is the same as the one in a recent publication [14] where a simplified adaptive feedback ANC system is presented. It was shown that the simplification features low computational load and ease of implementation in comparison with the feedback structure of the tHybrid ANC system due to the elimination of the convolution operation ^ (SðzÞYðzÞ) required in Fig. 1. But there are several drawbacks as reported in [14] caused by the simplification of the feedback structure. From the results given in [14], the stability condition for the feedback structure in Fig. 2 is    ^ jω Þ o π =2 8 ∠½Sðejω Þ  ∠½1 Sðejω ÞW s ðejω Þ  ∠½Sðe (14) ω

Fig. 2. Block diagram of the single channel hybrid ANC system based on the simplified combination method (the feedforward structure is shaded gray).

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^ jω Þ and ∠½1  Sðejω ÞW s ðejω Þ denote the phase of S(z), SðzÞ ^ where ∠½Sðejω Þ, ∠½Sðe and 1  Sðejω ÞW s ðejω Þ at frequency ω ^ ¼ SðzÞ is satisfied, Eq. (14) reduces to respectively. If SðzÞ   (15) 8 ∠½1  Sðejω ÞW s ðejω Þ o π =2 ω

If the control filter Ws(z) is updated at some iteration and Eq. (15) is violated, the feedback structure may be unstable. On the other hand, Ws(z) is updated to have a large gain to make the term 1/[1 S(z)Ws(z)] as small as possible. It is also found in [14] that if the gain of Ws(z) is unlimited, the feedback structure will be unstable, so the leaky FxLMS [14] algorithm was used to update Ws(z) because the leaky FxLMS algorithm can limit the gain of the adaptive filter. However, the leaky FxLMS algorithm does not minimize the squared error signal directly, and, consequently the cost of using the leaky FxLMS algorithm is the introduction of bias into the convergent control filter which causes the noise attenuation performance of the feedback structure to decrease. 2.3. The decoupled traditional combination method based system In order to enhance the noise reduction performance of the feedback structure in the sHybrid system, a hybrid ANC system based on the decoupled traditional method (dHybrid) is now proposed as an alternative (see Fig. 3), where the error ^ signal in the dHybrid ANC system is derived as (again assuming SðzÞ ¼ SðzÞ and D(z)¼X(z)P(z))
 EðzÞ ¼ ½1 þ SðzÞW d ðzÞV ðzÞ þ ½1 þ SðzÞW d ðzÞ P ðzÞ þSðzÞW f ðzÞ X ðzÞ (16) The first difference between Figs. 1 and 3 is that the reference signal xd(k) is synthesized by only the secondary signal of the feedback structure yd(k), i.e. ^ X d ðzÞ ¼ EðzÞ–SðzÞY d ðzÞ

(17)

so the feedforward structure does not impact the feedback structure directly. The second difference is that Xd(z) above is not only the reference signal for the feedback structure, but also the error signal for the feedforward structure. Assuming ^ SðzÞ ¼ SðzÞ, this results in Ef ðzÞ ¼ X d ðzÞ ¼ EðzÞ–SðzÞY d ðzÞ
 ¼ DðzÞ þ V ðzÞ þ SðzÞ Y f ðzÞ þY d ðzÞ –SðzÞY d ðzÞ ¼ DðzÞ þ V ðzÞ þ SðzÞY f ðzÞ

(18)

Eq. (18) indicates that xd(k) is the “true” error signal exactly as if the feedforward structure were operating alone. Therefore, using xd(k) as the error signal can further reduce the effects of feedback structure on the feedforward structure without introducing any extra computation load. Eq. (16) demonstrates that the decoupled traditional method has two advantages. First, the feedforward and feedback structures can be updated independently. The feedback structure aims to control the uncorrelated disturbance v(k) and its ideal solution is Wd(z)¼  1/S(z), while Wf(z) approximates  P(z)/S(z) to attenuate d(k). Second, the feedforward and feedback structures are also cascaded, i.e., the term [1þS(z)Wd(z)][P(z)þS(z)Wf(z)] in Eq. (16) is a product of the feedforward and feedback structures, Wf(z) approximates  P(z)/S(z) to let [P(z)þS(z)Wf(z)] be close to zero, and Wd(z) approaches 1/S(z) to make [1þS(z) Wd(z)] tend to zero. Therefore both the structures are able to contribute to the overall attenuation of the noise independently.

Fig. 3. Block diagram of the single channel hybrid ANC system based on the decoupled traditional method (the feedforward structure is shaded gray).

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The stability condition of feedback structure in the dHybrid system is [14]   n o  ^ jω ÞW ðejω Þ ∠½Sðe ^ jω Þo π =2 8 ∠½Sðejω Þ ∠ 1  ½Sðejω Þ  Sðe d

(19)

ω

^ Comparing Eq. (14) with Eq. (19), it is clear that if the difference between SðzÞ and S(z) is small, Eq. (19) approaches zero and is always satisfied, so the stability of feedback structure in the dHybrid system is better than that in the sHybrid system.

3. Simulations and discussions Simulations were carried out to examine the properties of the three combination based hybrid ANC systems. The primary noise d(k) was a 400–700 Hz wideband noise and the uncorrelated narrowband disturbance v(k) was a 100–150 Hz narrowband noise signal. The sample rate was 16,000 Hz. The primary path P(z) and the secondary path S(z) were respectively modeled by a 256 taps FIR filter and were measured from an ANC headset. The estimation of secondary path ^ SðzÞ is obtained by adding white noise to S(z), which is to simulate the condition that S(z) is estimated with errors. Fig. 4 shows the impulse responses and frequency responses of P(z) and S(z) respectively. The feedforward control filter Wf(z) was selected to be an FIR filter with 512 taps and the feedback control filter (Wb(z), Ws(z) and Wd(z) in Figs. 1–3) was selected to be an FIR filter with 256 taps. For clarity, in the legends of the figures below, the following abbreviations are defined and listed in Table 1.

0.15 0.1

Value

0.05 0 −0.05 −0.1 −0.15 −0.2

0

50

100

150 Taps

200

250

300

5 0

Magnitude (dB)

−5 −10 −15 −20 −25 −30 −35 −40

0

500

1000

1500 2000 2500 Frequency (Hz)

3000

3500

4000

Fig. 4. Primary and secondary path used in the simulations, (a) impulse responses and (b) frequency responses.

L. Wu et al. / Journal of Sound and Vibration 350 (2015) 1–10

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Table 1 Explanation of abbreviations. Abbreviations Explanations ANC off FF tFB sFB itHybrid isHybrid idHybrid FF-tHybrid FB-tHybrid FF-sHybrid FB-sHybrid FF-dHybrid FB-dHybrid

Without ANC Single feedforward structure Traditional feedback structure shown in Fig. 3 The simplified feedback structure shown in Fig. 2 Use the “FF” and “tFB” control filter coefficients in the tHybrid system directly to control the noise Use the “FF” and “sFB” control filter coefficients in the sHybrid system directly to control the noise Use the “FF” and “tFB” control filter coefficients in the dHybrid system directly to control the noise Feedforward structure in the tHybrid system Feedback structure in the tHybrid system Feedforward structure in the sHybrid system Feedback structure in the sHybrid system Feedforward structure in the dHybrid system Feedback structure in the dHybrid system

3.1. Results of feedforward or feedback structure alone The single feedforward structure was first tested for the control of noise accompanied by an uncorrelated narrowband disturbance. The FxLMS algorithm was employed to update the control filter and the step size was chosen experimentally as 0.005 to guarantee that the algorithm was stable and converged fast [1,2]. The converged feedforward control filter coefficients are plotted in Fig. 5(a) and the power spectra of the residual error signal at steady state is shown in Fig. 6(a). It can be seen from Fig. 6(a) that the noise within the 400–700 Hz frequency band is reduced by 15 dB while the uncorrelated disturbance within the 100–150 Hz frequency band cannot be the controlled by the single feedforward structure. Given the demonstrated failure of the single feedforward structure, the tFB and sFB structures were then utilized to control the uncorrelated disturbance within the 100–150 Hz frequency band. The FxLMS algorithm was also employed to update the control filter in the tFB structure and the step size was again chosen experimentally as 0.005 for stable and fast convergence. The leaky FxLMS algorithm (with leakage coefficient 0.9999) was employed to adapt the control filter in the sFB structure as suggested in [14] (again with a step size of 0.005). The converged control filter coefficients for the tFB and sFB structures are plotted in Fig. 5(b) and the disturbance within 100–150 Hz frequency band is attenuated by 10 dB and 5 dB by the tFB and sFB structures respectively. This is in accordance with the observation in [14] that the sFB structure may have a lower noise reduction performance than the tFB structure because the quality of the simplified reference signal xs(k) in Eq. (12) is worse than the reference signal in the “tFB” structures (xd(k) in Fig. 3). In addition, the leaky FxLMS algorithm introduces bias into the convergent control filter because it does not minimize the squared error signal directly. 3.2. Results of the three hybrid systems Simulation results from the tHybrid ANC system are illustrated in Fig. 6(a). Fig. 5(a) compares the feedforward control filter coefficients of FF and FF-tHybrid structures, Fig. 5(b) compares the control filter coefficients of the tFB and FB-tHybrid structures. The mismatch between the vector of reference filter coefficients wo and the comparative filter coefficients w was measured by M ¼ 20log10

‖w wo ‖2 ‖wo ‖2

(20)

where ‖‖2 is the Euclidean norm. If wo and w are identical, then M tends to  1, thus the closer to 1 M is, the better the w matches wo. The mismatch of control filter coefficients between the FF and FF-tHybrid structures is 6.1 dB, and that between the tFB and FB-tHybrid structures is  1.6 dB. In order to demonstrate the coupling effects in the tHybrid system, the FF structure coefficients in Fig. 5(a) and tFB structure coefficients in (b) were used directly as the converged ones in the tHybrid system to control the noise. The results are shown by the “itHybrid” curve in Fig. 6(a). Comparing the tHybrid curve with the itHybrid curve, it can be seen that for the 400–700 Hz frequency range, the tHybrid achieves 15 dB noise reduction while that of itHybrid is 17 dB. The reason is that the FF structure coefficients of itHybrid are obtained by setting the secondary path to be S(z). However, as mentioned in Section 2, the true secondary path should be changed to S(z)/[1 þS(z) Wb(z)] due to the coupling effect. On the other hand, for the 100–150 Hz frequency range, itHybrid achieves 10 dB noise reduction and that of tHybrid is 2 dB. Hence, the results of Fig. 6(a) further confirm that the FF and FB structures are coupled in the tHybrid system and that both the structures must be updated simultaneously. The simulation results of the sHybrid ANC system are presented in Fig. 6(b). A comparison of the control filter coefficients from the FF and FF-sHybrid structures is given Fig. 5(a), and the mismatch between the FF and FF-sHybrid structures is 29.5 dB, indicating that the coefficients of the FF-sHybrid structure match those of the FF structure better than that of the tHybrid ANC system. Fig. 5(b) compares the control filter coefficients between the sFB and FB-sHybrid structures, and the mismatch is  18.5 dB, also indicating an improved matching. The FF structure coefficients in Fig. 5(a) and the sFB structure

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0.25 FF FF−tHybrid FF−sHybrid FF−dHybrid

0.2 0.15

Value

0.1 0.05 0 −0.05 −0.1 −0.15

0

100

200

300 Taps

400

500

600

0.06 tFB FB−tHybrid FB−dHybrid sFB FB−sHybrid

0.04 0.02

Value

0 −0.02 −0.04 −0.06 −0.08 −0.1 −0.12

0

50

100

150 Taps

200

250

300

Fig. 5. The converged control filter coefficients of (a) feedforward structures and (b) feedback structures.

coefficients plotted in (b) were inserted directly into the sHybrid system to control the noise and the results are shown by the “isHybrid” curve in Fig. 6(b). It was found that the sHybrid curve is very close to the isHybrid curve. For the 400–700 Hz frequency range, both the sHybrid and isHybrid can achieve 15 dB noise reduction while for the 100–150 Hz frequency range, the noise reduction of both the sHybrid and isHybrid is 5 dB. Fig. 6(b) confirms that the coupling between feedforward and feedback structures is alleviated in the sHybrid system, where one structure does not affect the other so both structures can be designed individually. Especially, for the low cost hybrid system using analog circuits [10,11], the ability to optimize the feedforward and feedback parts separately brings some convenience for practical ANC design. Fig. 6(b) also presents the simulation results of the dHybrid ANC system. The control filter coefficients of the FF and FFdHybrid structures are also compared in Fig. 5(a), and the mismatch is  24.4 dB which is 18.3 dB less than that of the tHybrid system. Fig. 5(b) compares the control filter coefficients of the tFB and FB-dHybrid structures and the mismatch between them is 16.7 dB, showing that the coefficients of the FB-dHybrid structure are very close to those of the tFB structure. The FF structure coefficients in Fig. 5(a) and the tFB structure coefficients in (b) were inserted directly into the dHybrid system to control the noise and the results are shown by the “idHybrid” curve in Fig. 6(b). The curves of the dHybrid and idHybrid structures are in agreement with each other and the average difference between the two curves is within 1.5 dB. Therefore, the feedforward and feedback structures are decoupled and they can be optimized individually. Aiming to derive the converged controller coefficients in the tHybrid ANC system mathematically, a modification was performed on the tHybrid system where the reference signal in the feedback structure is also generated by its own secondary signal alone [17]. It was confirmed [17] that the converged solution of each filter in the feedforward and feedback structures is then the same as that when each filter is operating separately. Based on the work in [17] and the findings in this

L. Wu et al. / Journal of Sound and Vibration 350 (2015) 1–10

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15 ANC off FF tHybrid itHybrid

Magnitude (dB)

10

5

0

−5

−10

−15

0

200

400 600 Frequency (Hz)

800

1000

15 ANC off sHybrid isHybrid dHybrid idHybrid

Magnitude (dB)

10

5

0

−5

−10

−15

0

200

400 600 Frequency (Hz)

800

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Fig. 6. Power spectra of the residual noise signals controlled by (a) single feedforward structure and traditional combination method based hybrid system and (b) simplified and decoupled traditional combination method based hybrid systems.

paper, it is clear that the two methods presented in this paper can decouple the feedforward and feedback structures and both the structures can be optimized individually. Comparing the power spectra of the residual noise signals from the tHybrid, sHybrid and dHybrid systems shown in Fig. 6, it is found that for the 400–700 Hz frequency range, the noise reduction of the tHybrid system is 2 dB lower than that of the other systems. The reason may be that the converged feedforward controller is influenced by the feedback controller as mentioned in Section 2.1. For the 100–150 Hz uncorrelated narrowband disturbance, the noise reduction of the dHybrid system is 8 dB and 5 dB higher than the tHybrid and sHybrid systems respectively, while the FF structure does not have the capability to attenuate such uncorrelated disturbance. Finally, the performance of the FF structure, the tHybrid, sHybrid and dHybrid systems under the condition that the broadband and narrowband disturbances are not separated in frequency domain is compared. The uncorrelated narrowband disturbance v(k) was a 500–550 Hz narrowband noise signal, the other simulation settings are the same as before. Results are plotted in Fig. 7, where it is clear that the FF structure cannot attenuate the 500–550 Hz narrowband disturbance, while the dHybrid system achieves the best performance and it can attenuate the 500–550 Hz narrowband disturbance about 10 dB. 4. Conclusions The commonly used hybrid ANC system combines the feedforward and feedback structures directly so the coupling effects exist. In order to alleviate the coupling, two alternate integration methods are presented in this paper. The simplified

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method excludes the secondary signals from the synthesis of the reference signal in the feedback structure but uses the error signal directly. The advantages of the method are low computational load and ease of implementation. The decoupled traditional method generates the reference signal for the feedback structure with its own secondary signal and uses the generated reference signal as the error signal for the feedforward structure. The benefit of this method is that the influences between the feedforward and feedback structures are further reduced. Both the methods can alleviate the coupling of the feedforward and feedback structures so that each structure can be designed individually. Acknowledgments The project was funded by Natural Science Foundation of Jiangsu Higher Education Institutions, China (13KJB510018), the Priority Academic Program Development of Jiangsu Higher Education Institutions and KHYS1302. This research was also supported under Australian Research Council's Linkage Projects Funding Scheme (LP140100987) and National Natural Science Foundation of China (11474163). Great thanks to Mr. Xin Mao and Zhongfeng Qiu for the help on this work. References [1] S.M. Kuo, D.R. Morgan, Active Noise Control Systems: Algorithms and DSP Implementations, Wiley, New York, 1996. [2] S.J. Elliott, Signal Processing for Active Control, Academic Press, London, UK, 2001. [3] S.M. Kuo, Y. Song, Y. Gong, A robust hybrid feedback active noise cancellation headset, IEEE Transactions on Speech and Audio Processing 13 (2005) 607–617. [4] C.Y. Chang, S.T. Li, Active noise control in headsets by using a low-cost microcontroller, IEEE Transactions on industrial electronics 58 (2011) 1936–1942. [5] R. Castae-Selga, R. Pena, Active noise hybrid time-varying control for motorcycle helmets, IEEE Transactions on Control Systems Technology 18 (2010) 602–612. [6] Y. Zhou, Q. Zhang, X. Li, W. Gan, On the use of an SPSA-based model-free feedback controller in active noise control for periodic disturbances in a duct, Journal of Sound and Vibration 317 (2008) 456–472. [7] J. Romeu, X. Salueña, S. Jiménez, R. Capdevila, L.I. Coll, Active noise control in ducts in presence of standing waves, its influence on feedback effect, Applied Acoustics 62 (2001) 3–14. [8] M. Akhtar, W. Mitsuhashi, Improving performance of hybrid active noise control systems for uncorrelated narrowband disturbances, IEEE Transactions on Audio Speech and Language Processing 19 (2011) 2058–2066. [9] Y. Kajikawa, W.S. Gan, S.M. Kuo, Recent advances on active noise control: open issues and innovative applications, APSIPA Transactions on Signal and Information Processing 1 (2012) 1–21. [10] M. Winberg, S. Johansson, T. Lago, I. Claesson, A new passive/active hybrid for a helicopter application, International Journal of Acoustics and Vibration 4 (1999) 51–58. [11] C. Carme, The third principle of active control: the feed forback, Proceedings of ACTIVE 99, Ft. Laudaredale, 1999, pp. 885–896. [12] L.R. Ray, J.A. Solbeck, A.D. Streeter, R.D. Collier, Hybrid feedforward–feedback active noise reduction for hearing protection and communication, Journal of the Acoustical Society of America 120 (2006) 2026–2036. [13] L. Liu, K. Beemanpally, S.M. Kuo, Application of multi-channel hybrid active noise control systems for infant incubators, Noise Control Engineering Journal 61 (2013) 169–179. [14] L. Wu, X. Qiu, Y. Guo, A simplified adaptive feedback active noise control system, Applied Acoustics 81 (2014) 40–46. [15] C. Hansen, S. Snyder, X. Qiu, L. Brooks, D. Moreau, Active Control of Noise and Vibration, second edition, CRC Press, Boca Raton, 2013. [16] J. Lu, C. Shen, X. Qiu, B. Xu, Lattice form adaptive infinite impulse response filtering algorithm for active noise control, Journal of the Acoustical Society of America 113 (2003) 327–335. [17] H. Sakai, T. Someda, S. Miyaga, Analysis of an adaptive filter algorithm for hybrid ANC system, Proceedings of International Conference on Acoustics, Speech and Signal Processing, Orlando, 2002, pp. 1553–1556.