Performance Evaluation of Selective Fixed-filter Active Noise Control based on Di ff erent Convolutional Neural Networks

Zhengding Luo 1 , Dongyuan Shi 2 , Woon-Seng Gan 3

School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore.

Libin Zhang 4

Huawei Technologies Co., Ltd.

Qirui Huang 5

Huawei International Pte. Ltd.

ABSTRACT Due to its rapid response time and a high degree of robustness, the selective fixed-filter active noise control (SFANC) method appears to be a viable candidate for widespread use in a variety of practical active noise control (ANC) systems. In comparison to conventional fixed-filter ANC methods, SFANC can select the pre-trained control filters for di ff erent types of noise. Deep learning technologies, thus, can be used in SFANC methods to enable a more flexible selection of the most appropriate control filters for attenuating various noises. Furthermore, with the assistance of a deep neural network, the selecting strategy can be learned automatically from noise data rather than through trial and error, which significantly simplifies and improves the practicability of ANC design. Therefore, this paper investigates the performance of SFANC based on di ff erent one-dimensional and two-dimensional convolutional neural networks. Additionally, we conducted comparative analyses of several network training strategies and discovered that fine-tuning could improve selection performance.

1. INTRODUCTION

Acoustic noise problems are becoming more prevalent as the quantity of industrial equipment increases [1]. The attenuation of low-frequency noises is quite di ffi cult and expensive for passive noise control techniques such as enclosures, barriers, silencers, etc. Di ff erent from passive techniques, active noise control (ANC) involves the electro-acoustic generation of a sound field to cancel an unwanted existing sound field [2]. Moreover, ANC can o ff er a possible lower-cost alternative for the control of low-frequency noises. Thus, it attracts much interest from the industry. When dealing

1 luoz0021@e.ntu.edu.sg

2 dongyuan.shi@ntu.edu.sg

3 ewsgan@ntu.edu.sg

4 zhanglibin@huawei.com

5 huang.qirui@huawei.com

a slaty. inter.noise 21-24 AUGUST SCOTTISH EVENT CAMPUS O ¥, ? GLASGOW

Error signal +

( ) x n Primary noise ( ) e n

( ) d n Disturbance

Primary path ( ) P z

_

' ( ) y n Secondary path

Control filter ( ) W z ( ) S z

Anti-noise

Co-processor

Min-max operation

Pre-trained

Filter index

CNN Control filter

database Control filter

database

Figure 1: Block diagram of the CNN-based SFANC algorithm.

with di ff erent types of noises, traditional ANC systems typically use adaptive algorithms to adjust control filter coe ffi cients to minimize the error signal [3]. Among adaptive algorithms, the filtered-X least mean square (FxLMS) and filtered-X normalized least-mean-square (FxNLMS) algorithm are commonly used since they can compensate for the delay involved by the secondary path to increase the system robustness [4]. However, due to the least mean square (LMS) based algorithms’ inherent slow convergence and poor tracking ability [5], FxLMS and FxNLMS are less capable of dealing with rapidly varying or non-stationary noises. Their slow responses to noises may impact customers’ perceptions of the noise reduction e ff ect [6]. Fixed-filter ANC methods [7] can be adopted to tackle slow convergence, where the control filter coe ffi cients are pre-trained rather than adaptive updated. However, the pre- trained control filter is only suitable for a specific noise type, resulting in the degradation of noise reduction performance for other types of noises. To rapidly select di ff erent pre-trained control filters given di ff erent noise types, a selective fixed-filter active noise control (SFANC) method based on the frequency band matching was proposed in [8]. Though the SFANC method [8] selects the most suitable pre-trained control filters in response to di ff erent noise types, several critical parameters of the method can only be determined through trials and errors. Considering the limitations, deep learning techniques, particularly convolutional neural networks (CNNs) [9–12], appear to be powerful in classifying noises in SFANC methods. Automatic learning of the SFANC algorithm’s critical parameters based on deep learning would broaden its applications in real-world scenarios. With the learning ability of CNN models, the SFANC algorithm can automatically learn its parameters from noise datasets and select the best control filter given di ff erent noise types without resorting to extra-human e ff orts [13]. Additionally, a CNN model implemented on a co-processor can decouple the computational load from the real-time noise controller. Therefore, in this paper, we compared the performance of several one-dimensional (1D) CNNs and two-dimensional (2D) CNNs in the SFANC method. Also, di ff erent network training strategies are tried to choose the best one for training the networks. Experiments show that the SFANC method based on CNN not only achieves faster responses than FxLMS and FxNLMS but also exhibits good robustness. Thus, it is expected to be used for attenuating dynamic noises such as tra ffi c noises and urban noises, etc.

2. CNN-BASED SFANC ALGORITHM

The overall architecture of the CNN-based SFANC algorithm is depicted in Figure 1. Throughout the control process, the real-time controller conducts filtering to generate anti-noise while simultaneously sending the primary noise to a co-processor (e.g., a mobile phone). Given the primary noise, the co- processor employs a pre-trained CNN to produce the index for the most appropriate control filter and

Figure 2: Markov model of the ANC progress.

delivers it to the real-time controller. The controller then adjusts the control filter coe ffi cients based on the received filter index. Notably, if the network is a 1D CNN, its input is the raw waveform [14]. However, if the network is a 2D CNN, its input is the Log Mel-spectrogram [15].

2.1. Concise Explanation of SFANC An ANC progress can be abstracted as a first-order Markov chain [16] as shown in Figure 2, where w o ( n ) represents the optimal control filter to attenuate the disturbance d ( n ). To achieve the best noise reduction performance, the best control filter w o ( n ) can be selected from a pre-trained filter set { w i } C i = 1 . Hence, the SFANC method can be represented as follows:

w o = argmin w ∈{ w i } C i = 1 E  h d ( n ) − x T ( n ) w ( n ) ∗ s ( n ) i 2  , (1)

where argmin( · ) operator returns the input value for minimum output; ∗ , x ( n ), and s ( n ) represent the linear convolution, the reference signal, and the impulse response of the secondary path, respectively. The reference signal is assumed to be the same as the primary noise. In practice, d ( n ) is typically seen as the linear combination of x ( n ). Thus, Equation 1 equals to

w o = argmax w ∈{ w i } C i = 1 P [ w | d ( n )] = argmax w ∈{ w i } C i = 1 P [ w | x ( n )] , (2)

which means that the selected control filter is the one with maximum posterior probability in the presence of reference signal x ( n ). Moreover, according to Bayes’ theorem [17], the posterior probability can be replaced with a conditional probability as

w o = argmax w ∈{ w i } C i = 1 P [ x ( n ) | w ] , (3)

which predicts the most suitable control filter straight from the primary noise x ( n ). A classifier model ˆ P [ x ( n ) | w , Θ ] can be developed to approximate P [ x ( n ) | w ] from the pre-recorded sampling set { x j ( n ) , w j } N j . The Θ denotes the parameters of the classifier and can be obtained through maximum likelihood estimation (MLE) [18] as

N X

1 N

j = 1 log ˆ P h x j ( n ) | w j , Θ i . (4)

Θ = argmax

Therefore, we can utilize deep learning approaches to lean the classifier model from the training set { x j ( n ) , w j } N j .

2.2. CNN-based SFANC algorithm Motivated by the work [13], this paper compares some 1D CNNs and 2D CNNs used for classifying noises in the frequency domain and time domain, respectively. The min-max operation firstly

Hidden state Optimal control filter >: ) Ew, (nr): wi(n—1 d(t) d(n — 1) d(n) Observation Disturbance J

Figure 3: Architecture of the proposed 1D CNN. The configuration of convolution layer is denoted as: (kernel size, channels, stride, padding).

Figure 4: The frequency bands of the noise tracks for pre-training control filters.

normalizes the input of the network:

ˆ x ( n ) = x ( n ) max[ x ( n )] − min[ x ( n )] , (5)

Noise waveform (1 second) Conv Layer (80, 128, 4, 38) v BatchNorm y ReLU Max Pooling v Residual Block v Residual Block t Max Pooling y Adaptive Avg Pooling FC Layer Filter index Residual Block: Input Conv Layer (3, 128, 1, 1) v BatchNorm 4 ReLU Conv Layer (3, 128, 1, 1) v BatchNorm y ReLU BatchNorm Output

where max[ · ] and min[ · ] mean obtaining the maximum and minimum value of x ( n ). It aims to rescale the input range into ( − 1 , 1) and retain the signal’s negative part that contains phase information. Phase information is quite critical for ANC applications. A lightweight 1D CNN illustrated in Figure 3 is proposed. Every residual block in the network comprises two convolutional layers, subsequent batch normalization, and ReLU non-linearity. Note that a shortcut connection is adopted to add the input with the output in each residual block since residual architecture is demonstrated easy to be optimized [19]. Additionally, the network uses a broad receptive field (RF) in the first convolutional layer and narrow RFs in the rest convolutional layers to fully exploit both global and local information.

2.3. Training of CNNs The primary and secondary paths used in the training stage of the control filters are band-pass filters with a frequency range of 20Hz-7 , 980Hz. Broadband noises with 15 frequency ranges shown in Figure 4 are used to pre-train 15 control filters. The FxLMS algorithm is adopted to obtain the optimal control filters for these broadband noises due to its low computational complexity. Subsequently, the 15 pre-trained control filters are saved in the control filter database. A noise dataset including synthetic and real noise tracks is used in this work. Specifically, 80 , 000 synthetic noise tracks and 80 , 000 real noise tracks are used for training, 2 , 000 real noise tracks for validation, and 2 , 000 real noise tracks for testing. The synthetic noise tracks are randomly generated with various frequency bands, amplitudes, and background noise levels. The SFANC system’s sample rate is 16 , 000Hz, so each noise track of 1-second duration consists of 16 , 000 samples. Each noise track of 1 second duration is taken as primary noise to generate disturbance. The class label of a noise track corresponds to the index of the control filter that achieves the best noise reduction performance on the disturbance.

7.08 kHz C, C60, €,,6, CP 10~ 11 Vy 137 147 15

3. EXPERIMENTS

The Adam algorithm was employed to optimize the network during training. The training epoch was set to be 30. The glorot initialization [20] was used to avoid bursting or vanishing gradients. Additionally, to prevent overfitting, the weights of CNNs were subjected to ℓ 2 regularization with a coe ffi cient of 0 . 0001.

3.1. Comparison of Di ff erent Training Schemes Four di ff erent training schemes are compared in training the proposed 1D CNN. The comparison results are summarized in Table 1. According to Table 1, training firstly on the synthetic noise tracks and then fine-tuning on the real noise tracks achieves the highest testing accuracy. Noted that simultaneously using synthetic dataset and real dataset for training has not obtained a superior testing accuracy since the characteristics of synthetic noises and real noises are quite di ff erent. As discussed above, in the SFANC system, the CNN models can be firstly trained with the synthetic dataset and then fine-tuned with the real noise dataset.

Table 1: The performance of di ff erent network training schemes.

Training Scheme Testing Accuracy

Only using synthetic dataset 46.4%

Only using real dataset 94.6%

Fine-tuning method * 95.3 %

Simultaneously using synthetic dataset and real dataset 94.5%

* Training firstly by the synthetic dataset and then fine-tuning by the real dataset.

3.2. Comparison of Di ff erent Networks Based on above fine-tuning training scheme, we compared several di ff erent 1D networks utilizing raw acoustic waveforms: the proposed 1D CNN, M3 [21], M5 [21], M11 [21], M18 [21], and M34- res [21]. Also, some light-weight 2D networks including Shu ffl eNet v2 [22], MoblieNet v2 [23] and Attention Network [24] are compared in the SFANC method. The performance of these networks on the real testing dataset are summarised in Table 2.

Table 2: Comparisons of di ff erent networks used in the SFANC system.

Network Testing Accuracy Network Parameters

1D Convolutional Neural Networks

Proposed 1D Network 95.3 % 0.21M

M3 Network 93.7% 0.22M

M5 Network 94.9% 0.56M

M11 Network 94.5% 1.79M

M18 Network 93.8% 3.69M

M34-res Network 94.4% 3.99M

2D Convolutional Neural Networks

Shu ffl eNet v2 95.5 % 0.25M

MoblieNet v2 95.6% 2.89M

Attention Network 94.9% 4.95M

As shown in Table 2, the proposed 1D network obtains the highest classification accuracy of 95 . 3% with the fewest network parameters among the 1D networks. As for 2D networks, the Shu ffl eNet v2 achieves a similar classification accuracy as MoblieNet v2 and requires far fewer parameters. By considering both the testing accuracy and the number of parameters, the Shu ffl eNet v2 performs best on the testing dataset among the 2D networks. Compared to the proposed 1D network, the Shu ffl eNet v2 obtains a slight improvement in classification accuracy but requires a little more network parameters. Therefore, it is found that the proposed 1D network and Shu ffl eNet v2 perform better in classifying noises in the SFANC system. The two light-weight networks can be implemented on mobile platforms, but using acoustic models directly from the raw waveform data is more convenient [25]. Hence, the proposed 1D network is preferred.

3.3. Non-stationary Noise Cancellation This section uses the SFANC algorithm based on the proposed 1D network, FxLMS algorithm, and FxNLMS algorithm to attenuate a recorded aircraft noise. The aircraft noise is non-stationary and has a frequency range of 50Hz-14,000Hz. It does not belong to the training dataset. The step size of the FxLMS and FxNLMS algorithm is set to 0 . 0001, and the control filter length is 1 , 024 taps. The noise reduction results using di ff erent ANC methods on the aircraft noise are shown in Figure 5. From the results in Figure 5, we can observe that the SFANC method responds to the aircraft noise much faster than the FxLMS and FxNLMS algorithms. Also, the SFANC method consistently outperforms the FxLMS and FxNLMS algorithm in the noise reduction process. In particular, during 1s-2s, the averaged noise reduction level achieved by the SFANC algorithm is about 7dB and 8dB more than that of FxLMS and FxNLMS, respectively. Therefore, the results on the aircraft noise confirm that the SFANC method can rapidly select the most suitable pre-trained control filter given the noise type. In contrast, adaptive algorithms show slow responses to the aircraft noise due to adaptive updating.

(a) The SFANC Algorithm

(b) The FxNLMS Algorithm

ANC off ANC on

ANC off ANC on

0.5

0.5

Magnitude

Magnitude

0.0

0.0

0.5

0.5

0 2 4 6 8 10 Time (seconds)

0 2 4 6 8 10 Time (seconds)

(d) Averaged Noise Reduction Level of Every 1s

(c) The FxLMS Algorithm

Noise Reduction Level (dB)

20

SFANC FxNLMS FxLMS

ANC off ANC on

0.5

15

Magnitude

10

0.0

5

0.5

0

0 1 2 3 4 5 6 7 8 9 10 Time (seconds)

0 2 4 6 8 10 Time (seconds)

Figure 5: (a)-(c): Error signals of di ff erent ANC algorithms, (d): Averaged noise reduction level of every 1 second, on the aircraft noise.

4. CONCLUSIONS

Active noise control (ANC) technologies have been widely used to deal with low-frequency noises. However, adaptive ANC algorithms are typically limited by slow convergence speed. In this paper, CNNs are used to automatically select the best pre-trained control filters given di ff erent noises. Also, light-weight CNNs implemented on a co-processor can decouple the computational load from the real-time noise controller. Numerical simulations show that the CNN-based SFANC method improves response time while maintaining low computational complexity and high robustness. Additionally, the e ff ectiveness of the proposed 1D network and the fine-tuning training strategy are confirmed in the SFANC method. In future works, we will explore more e ffi cient and robust ANC algorithms based on deep learning.

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