Simulation and experimental study of active noise barrier based on multiple-channel and decentralized system design

Active noise barrier (ANB) was helpful to enhance the noise reduction performance of noise barrier especially in low-frequency range. But it was quite difficult to realize an ideal effect in the far-field as most of the exiting work of ANB took the realization of soft boundary at the edge of noise barriers as the target. An active control strategy based on the decentralized system design was proposed in this paper. The virtual sensor technology was used in order to obtain the far-field noise signal with the help of near-field sensor, while multiple-channel design of both centralized system and decentralized system was studied. An experimental ANB system was then built in semi-anechoic chamber. The performance of the above control strategies was calculated with the actual measured parameters, and the advantages and disadvantages of different systems were compared and studied. The effectiveness of the new strategy was verified through the noise reduction tests of active noise control. The ANB established in this paper which was based on decentralized system design, could be extended to large scale usage directly in the future.


Introduction
Noise barrier is a common control measure of occupational noise or traffic noise.Noise barriers can usually effectively isolate the sound propagation of medium or high frequency, but the effect decreases in the low frequency range, while active noise control technology usually has better performance in the low frequency band [1] due to its own characteristics.So, they can be combined in the form of hybrid active-passive design to improve the noise reduction performance of noise barriers.
A lot of work has been done on active noise barriers.Researchers of Nanjing University have carried out relevant research work on virtual noise barriers, and have conducted research on the application of engineering examples of virtual noise barriers for application scenarios such as sound insulation windows.Most of the established work revolves around the influence of the structure and physical placement of the noise barrier on the noise reduction [2][3][4][5][6][7].Some work has also entered the stage of product-type experiments, such as Ohnishi [8], who designed a feedback active noise barrier system, and installed a 20 m-long active noise barrier on a road for experiments.Duhamel et al. [9] adopted FxLMS algorithm to make the noise attenuation exceed 10 dB.Ohnishi et al. [10] adopted the feedback algorithm with an insertion loss of 4-5 dB.Kwon et al. [11] adopted the multichannel FxLMS algorithm, using 6 microphones and 4 speakers, and achieved 20 dB(A) noise reduction at 190 Hz.Zou et al. [12] adopted the decentralized feedforward ANC system to reduce the transformer line spectrum noise, with a noise reduction of 15 dB in the near area.One common drawback of these work is their poor far-field performance.
From the current research, the application of active noise control (ANC) technology in noise barriers mainly take two forms, named centralized system design and decentralized system design.The centralized system uses a multiple-channel centralized system in the form of a unified processing unit for all channels and combines the near-field or (and) far-field error sensor signals to implement noise reduction in a specified area, which can usually achieve some optimal strategy, but the disadvantage is that the system is more complex and also limited by the number of channels, which is difficult to be applied in practical large-scale situations.The decentralized design [13][14][15] decomposes the centralized calculation of a single controller into a number of controllers, typically by using a series of single-channel controllers to control the sound field at localized points in the near field to realize a soft boundary at the top of the barrier.The decentralized design is often less effective than the centralized system design in the target area because it uses only a local noise reduction strategy.
Based on the non-stationary and non-deterministic characteristics of actual sound sources and the demand of large-scale of actual noise barriers, a decentralized adaptive active noise control system is studied in this paper, which incorporates the centralized pre-parameter design and virtual sensing methods.An ANB is established in semi-anechoic chamber, then control strategies are studied, and several typical methods are compared with the new strategy based on the parameters of the experimental ANB.

Method
Berkhoff proposed a virtual sensor technique in active noise barrier systems and compares the noise reduction effects of three cases where the error signal is the far-field sensor signal, the near-field sensor signal and the virtual sensor signal, and points out that the use of virtual sensors can achieve the same effect as using the far-field sensor.The active noise control system in this paper is based on Berkhoff's architecture of a single-channel decentralized system and uses virtual sensing in order to achieve a larger control area in the far field.
In a single-channel system, the variables can be defined, such as the primary acoustic disturbance d, the reference signal x, the secondary source control signal u, the near-field error signal and the farfield error signal .From the physical model, minimizing the near-field error signal does not mean the minimum of far-field error signal .In order to minimize the far-field error signal , the transfer matrix between the near-field to far-field signals should be constructed, and it can be used to predict the far-field error signal in real time.The relationship of the parameters can be described by (1) where , , and denote the transfer functions between the primary acoustic disturbance to the reference microphone, the near-field error microphone, and the far-field error microphone, respectively.
, and denote the transfer functions from the secondary source control signal to the reference microphone, the near-field error microphone and the far-field error microphone, respectively.
The active noise barrier noise reduction model is shown in Figure 1, denotes the transfer function between the positions of the near-field error microphone and the far-field error microphone.and denotes the acoustic contributions of the primary and secondary sources at the far field, respectively.The predicted far-field error signal ̂ is given by the sum of and ̂ in real time and used in the coefficient update calculation of the adaptive filter.The predicted can be obtained using the predicted value by .The estimated ̂ can also be obtained by using the estimated value ̂ by ̂ ̂ .̂ is determined by and the real-time value of u, then can also be obtained.So, the key to implement the system is , and , which can be obtained by off-line identification.The above method did not consider the effect of multiple-channel system strictly.A common diagram of a multiple-channel system is shown in Figure 2, where the wide arrow denotes an array of signals.Consider the simplest multiple-channel near-field noise reduction strategy first, in which the error signal of near-field microphones is minimized to achieve noise reduction.There is only in the control system, while is out of the control system.The block diagram is illustrated in Figure 3.
The matrix and represents primary path transfer functions, from the primary source to error sensors.The matrix and represents secondary path transfer functions, from secondary sources to error sensors.For simplicity, the matrix and which represents feedback paths from secondary sources to reference sensors is ignored here.The matrix W represents adaptive filters, as there are K×J channels in the control system, each has a separate filter.
When using a simplified system design in which the reference signal, secondary source and error signal correspond to each other one by one, that is, when J=K=M, W is an M×M matrix.Since each error sensor is most sensitive to its corresponding secondary sound source, when the effect of other secondary sound sources is ignored, the system can degenerate into a decentralized system.The W of a decentralized system degenerates into an array with a length of M, while each unit is a single channel filter.
When virtual sensor is used, the above system needs two more parameters and , which are both N×M matrix.The calculation of the system becomes more complex, as shown in Figure 4.In each iteration of the algorithm, it is necessary to calculate K×J filters based on the real-time value u to obtain the estimated value of and .After that, 2×N×M filters should be calculated to obtain the estimated value of and .Generally, N ≥ M is required to ensure the stability of the data system.Therefore, a centralized system needs to run a large amount of real-time computing.As the above processing is quite complicated, the algorithm is usually unable to execute in real time with numerous channels, so it needs to be simplified.Similarly, the implementation of the system is expected to adopt a decentralized system, where J=K=M and W is an M×M matrix, as shown in Figure 5. Since each error sensor is sensitive to its corresponding and perhaps several nearby secondary sound sources, W behaves as a banded sparse matrix.Similarly, if the influence of other secondary sound sources is ignored, the system can further degenerate into a decentralized system, where W degenerates into an array with a length of M. The overall system behaves as a combination of a series of single channel systems.The simplified system needs to be checked whether its noise reduction performance is still well.This article establishes an actual system, the simulation and experimental verification is done.

Noise barrier setup
In the semi-anechoic chamber (cut-off frequency less than 80Hz), a noise barrier of 5.0 m in length and 1.6 m in height is installed.The primary sound source is a loudspeaker, with a height of 1.2 m and a straight-line distance of 2.0 m from the noise barrier.As the secondary sources, 8 loudspeakers are arranged with an interval of 0.6 m at the top of the noise barrier.The photo of the noise barrier arrangement is shown in Figure 6.Measurement diagram is shown in Figure 7. Considering the limitation of the cut-off frequency of the semi-anechoic chamber and the spacing of the secondary sources should be less than half of the wavelength, the design frequency band of the active noise control system is set to 100-300Hz.The simulation of the noise reduction performance of the active noise control models can be directly calculated from theoretical models of sound radiation and sound barrier diffraction.However, in order for the actual application, the parameters such as , , , , , and were measured, and the simulation was conducted using the actual tested parameters.

Simulation results
The theoretical noise reduction of each system is discussed in the form of simulation based on the experimental system, and the key parameters are obtained through actual measurement.The simulation mainly considers the following system designs: centralized system, decentralized system near-field optimization algorithm and decentralized system combined with virtual sensor algorithm.Due to the actual measurement of the parameters, when the primary sound source is set up, the noise transmission of different active noise control methods to the far-field evaluation point can be calculated.
The feedback term in the active noise control model can be suppressed by using techniques such as directional microphones, so the feedback pathway will not be considered here for simplicity.
The theoretical noise reduction of the centralized system at the far-field evaluation points is shown in Figure 8, with 8 curves representing the frequency-based noise reduction effect of 8 far-field evaluation points.Due to the more ideal assumption, the insertion loss of active noise control system is quite high.The theoretical noise reduction of the decentralized system with near-field optimization is shown in Figure 9.The theoretical noise reduction of the decentralized system combined with virtual sensor algorithm is shown in Figure 10.From comparison and analysis of the above algorithms, the centralized system has the best theoretical noise reduction performance, the decentralized system with near-field optimization has very little noise reduction effect at far-field evaluation points, and the decentralized system with virtual sensor still has significant noise reduction performance at far-field evaluation points.Due to its simple structure, it has more practical value compared to the centralized system.

Experiment and discussion
The assessment of the active noise control was carried out by means of a comparison test with the active control off and on.The measurement point was located of different height and different distance.The implementation of the single-channel algorithm is based on BMILP ANC2.0 controller, which is developed by the Institute of Urban Safety and Environmental Science, Beijing Academy of Science and Technology.The circuit of BMILP ANC2.0 controller is based on ADSP21489 chip with an adaptive active noise control code inside, the sampling rate is adjustable up to 48 kHz.The controller also has a high-quality power amplifier.It can support the implementation of the algorithm in this paper.The distribution of insertion loss of the active control system was further tested, as shown in Figure 12.Due to the size limitation of the semi-anechoic chamber, the experiment range is up to 4.0 m in the horizontal direction, with a maximum height of 3.1 m.The noise reduction performance is good in the shadow zone behind the noise barrier and decreases with height.Since each controller takes the point with distance of 2.0 m as the target control point, the experimental results also show that the noise reduction performance is best inside this range, which is consistent with the design.
The comparable simulated distribution of the sound field is shown in Figure 13.The experimental results and simulated results show a quite similar distribution pattern.From the experimental results and simulated results, the noise reduction strategy based on decentralized system in this paper can achieve effective noise reduction in a large area.Overall, the additional noise reduction is more balanced in the whole test area than other methods.The active noise barrier design of this paper can be easily extended to a larger size of noise barrier in noise reduction practice.

Conclusions
Based on the decentralized system architecture, an active control strategy for noise barriers was proposed.In this method, a virtual error signal was derived from the near-field microphone at the top of the noise barrier and thus far-field sound pressure reduction was achieved using active noise control.The effectiveness of this method is verified through simulation and experimental tests.The results show that the active noise barrier system achieves effective noise reduction in a wide range of space behind the noise barrier in the design target frequency band.
Compared with the common centralized system active noise barrier, the method avoids the problem of sophisticated system design and pre-testing as well as the large demands of real time computation, and it can be directly extended to large scale noise barrier applications.Compared with the common decentralized active noise barrier, the method can realize noise reduction in a longer distance range after the barrier, avoiding the problem that the current active noise barrier is only efficient to near-field noise reduction.
The verification has been carried out only in the semi-anechoic chamber at present.For the application over longer distances and wider frequency bands, the further verification and optimization work of the algorithm should be continued in the future.

Figure 1 .
Figure 1.Model of active noise control.

Figure 2 .
Figure 2. Structure of a multiplechannel ANC system.

Figure 4 .
Figure 4. Block diagram of adaptive multiple-channel feedforward ANC system with virtual sensor technology (centralized system).

Figure 5 .
Figure 5. Block diagram of adaptive multiple-channel feedforward ANC system with virtual sensor technology (decentralized system).

Figure 6 .
Figure 6.Photo of noise barrier experiment.

Figure 8 .
Figure 8. Insertion loss of centralized ANC system.

Figure 9 .
Figure 9. Insertion loss of decentralized ANC system with near-field optimization.

Figure 10 .
Figure 10.Insertion loss of decentralized ANC system with virtual error sensor.

7
The noise reduction result is shown in Figure11, which gives the noise reduction in frequent domain at each evaluation point located behind the noise barrier at a distance of 1.0 m, 2.0 m, 4.0 m, respectively.Because of the small size of the secondary source in the experiments, the noise reduction decreases at lower frequency.

Figure 11 .
Figure 11.Frequency related noise reduction of active noise control by experiment.

Figure 12 . 8 Figure 13 .
Figure 12.Noise reduction distribution of active noise control by experiment.