Active control of low-frequency broadband air-conditioning duct noise

Transcription

1 Active control of low-frequency broadband air-conditioning duct noise Juan M. Egaña, a) Javier Díaz, b) and Jordi Viñolas c) (Received 23 February 3; revised 23 July 7; accepted 23 August 5) The low-frequency broadband noise generated by an air-conditioning unit on a railway vehicle may be significant in situations where the vehicle is stopped or its speed is low. Low-frequency acoustic radiation is extremely difficult to attenuate using passive means, so in this work, active noise control (ANC) techniques were applied. Laboratory experiments were performed in which noise from two different sources, namely from loudspeakers and an axial fan, was introduced into a real air-conditioning duct, identical to that installed on a subway vehicle. The control approach used a doubled, single-, single-output (SISO), feedforward, filtered-x LMS algorithm. Control algorithms were designed using the Matlab-Simulink program and the Real Time Windows Target toolbox of Matlab in order to run the ANC in real time. Attenuations of 5-2 db at the error microphone locations were achieved when loudspeakers were used as primary noise generators. However, noise reduction was quite poor when noise was introduced via the axial fan. This was due to turbulence generated by the airflow, which has a negative influence on the performance of the control system. 23 Institute of Noise Control Engineering. Primary subject classification: 37.7; Secondary subject classification: 5.6. INTRODUCTION Although the first theoretical proposals for active noise control (ANC) were reported as early as 933, research in this field is still under development, and although certain specific ANC devices are successful, more robust practical applications have still to be widely commercialised. Focusing on one-dimensional systems, many researchers have tried to resolve such associated problems as: reference contamination; the number and arrangement of control sources and sensors, and the effect of adaptive algorithm parameter selection on stability. The purpose of the following work was two-fold: First, to design control algorithms using understandable and easy to modify software; and second, to install a complete ANC system in the laboratory so performance could be tested in real time. With respect to the software, it was decided that Matlab-Simulink, a program based on block diagrams, could be an adequate choice since this software provides a simple global display of the algorithmʼs behaviour and evolution. Two different primary noise sources were introduced: A lowfrequency broadband spectrum through loudspeakers; and a turbulent spectrum without low-frequency noise generated by an axial fan. Attenuation obtained when introducing the primary noise through the loudspeakers was quite relevant. However, the turbulence generated by the airflow provoked worsening coherence and, consequently, a reduction in the expected attenuation. 2,3 In these situations, the ANC approach is only successfully applicable to frequencies whose acoustic component is high. 4 a) CEIT, Department of Applied Mechanics, Pº de Manuel Lardizabal, 5- P.O. Box San Sebastian-Spain, jmegana@ceit.es. b) CEIT, Department of Applied Mechanics, Pº de Manuel Lardizabal, 5-P.O. Box San Sebastian-Spain; School of Engineering, University of Navarre, San Sebastian, Spain. jdiaz@ceit.es. c) CEIT, Department of Applied Mechanics, Pº de Manuel Lardizabal, 5-P.O. Box San Sebastian-Spain; School of Engineering, University of Navarre, San Sebastian, Spain. jvinolas@ceit.es. 2. THE FILTERED X ALGORITHM Widrowʼs original LMS algorithm 5 can be considered as the root of methods based on gradient descent algorithms. In real world systems, the LMS algorithm is not directly applicable since it does not converge. This is due to the delay and gain effects of the physical path taken by the control signal. The filtered X algorithm, however, includes a compensating filter, known as the cancellation path transfer function, which restores stability and produces a stable well-behaved system. As a consequence, control algorithm development is divided into two parts: the first stage is responsible for the identification of the secondary path; whilst the second concentrates on the overall control algorithm. A. Filtered-X LMS algorithm In order to enunciate the mathematical expressions that govern the operation of the algorithm, a general system, which includes K reference signals, M secondary sources and L error sensors has been considered, as shown in Fig.. The signal measured by the lth error microphone can be expressed as where d l represents the primary noise at the lth error microphone, c lmj the jth coefficient of the secondary path between the mth secondary source and the lth error sensor, and the last summation, the kth reference signal filtered through the corresponding adaptive FIR filter of I coefficients. Using matrix notation, Eq. () can be expressed as where R(n) is a matrix that includes the filtered references. Parameters included in Eq. () can be detached as () (2) (3) 292 Noise Control Eng. J. 5 (5), 23 Sept Oct

2 Disturbance signals d(n) L () with and with x(n) u(n) y(n) w(z) c(z) Σ K M L Reference signals Secondary sources Error sensors Fig. Multichannel pure feedforward ANC system. The system includes M secondary sources, K references and L error sensors. In ANC systems, the error criterion is the sum of the squared values of the error signals. Minimisation of the error criterion will lead to the minimisation of the undesirable disturbance at the error locations. A squared error criterion is employed because using the minimisation of the non-squared error signal as the control object results in a very large negative error signal, which is undesirable. Accordingly, the cost function J, which attempts to minimise the error signal at error sensors, can be defined as c(n) L (4) (5) (6) (7) (8) (9) where α represents the convergence coefficient and r the filtered reference calculated as the convolution between the reference x and the filter that identifies the associated secondary path. Figure 2 shows the diagram of a single, single output (SISO) feedforward system, similar to the system implemented in laboratory, and Fig. 3 the complete double SISO feedforward FXLMS algorithm designed in Matlab language for the particular application of the air-conditioning duct to be installed on the subway vehicle. B. Cancellation path transfer function calculation The cancellation path transfer function, also known as the secondary path, includes the physical path that the control signal must cover between the controllerʼs output and the error microphone. Its calculation is usually carried out through an FIR filter. The reason for using an FIR filter instead of an IIR fitter stems from its purely feedforward nature, where no previous outputs are required in the calculus of the current output sample. Working off-line, in order to take into account the complete performance of the control algorithm, implies advantages from the point of view of loading data, making it easier, therefore, to work in real time. Two methods were used to characterise the secondary path: the first was based on the LMS algorithm; the second consisted of capturing the error and modelling signals in order to create a transfer function via Matlab. This second method included a checking stage in order to quantify the error percentage of the secondary path filter, relative to the ideal. The diagram in Fig. 4 shows the algorithm based on the LMS strategy used to calculate the coefficients of the FIR filter that represents the path transfer function. The first step in calculating the secondary path this way consists of injecting a modelling signal, m(n), into both the physical system and the model itself. m(n) is usually a white noise comprised of a range of frequencies which are of interest from the point of view of control. Taking m(n) and the difference between the system and the model outputs, known as estimation error e (n) into account, the FIR filter coefficients, c(n), are then where E{.} denotes an expected value. The optimum set of filter coefficients is found by minimizing J through gradient descent methods. The differential of the total error with respect to the adaptive filter coefficients, known as the gradient of the error, can be expressed as Disturbance generator Structural / Acoustic system Primary disturbance d(n) Σ () Consequently, the algorithms based on gradient descent operate by adding a small percentage of the negative gradient of the error surface to the current value of the filter weights in order to calculate a better set of filter coefficients. Thus, the expression that governs the filtered-x LMS (FXLMS) algorithm can be written as Secondary path model Reference x(n) Filter weights w(n) Filtered reference r(n) Control filter Adaptive algorithm Control signal y(n) Physical secondary path Error signal e(n) Fig. 2 Adaptive feedforward active noise control system, showing integration of the main components. Noise Control Eng. J. 5 (5), 23 Sept Oct 293

3 (imput vector) Not filtered reference Error Conv. coef. Conv. coef. W Control signal FXLMS algorithm (SISO) W2 W control weights 2 Unit delay Conv. coef. Control stop output output (control output ) output output2 (control output 2) Not filtered reference 2 Error 2 Control signal 2 FXLMS algorithm (SISO) W2 control weights Fig. 3 Double SISO feedforward filtered-x LMS algorithm designed for the particular application of the air-conditioning duct to install on the subway vehicle. updated at each time step in order to minimize e (n) and, thus, characterize the secondary path. This calculation is governed by the equation (2) where c(n + ) represents the new filter weights in sample (n + ); m(n) the signal that includes the frequencies to be characterized; e (n) the value that compares the real and the model outputs, and α the convergence coefficient. Figure 5 shows the algorithm built in order to identify each of the two cancellation path transfer functions included in the system under research. In Fig. 6, the evolution and stabilisation of the identification weights of one of the two single-, single output (SISO) systems included in the air-conditioning duct can be seen. The second identification method consisted of capturing the error signal as well as the white noise introduced as modelling signal. This noise included the range of frequency between - 4 Hz. Firstly, as shown in Fig. 7, a PCI-MIO-6E-4 National Instruments Corporation board installed in the PC generated a random noise modelling signal. Secondly, this signal and the signal captured by the error microphone were appropriately treated and stored using functions computed in Matlab language in order to calculate the FIR filter model, represented in Fig.2 as the secondary path model. Thirdly, the degree of accuracy of the secondary path model already calculated was verified by means of the algorithm represented in Fig. 8: A random signal was introduced through the previously calculated filter model and, at the same time, compared to the real error signal measured by the microphone. The error percentage of the FIR filters calculated this way, using Matlab functions, did not exceed 5%-6% in any case. 3. EXPERIMENTAL LABORATORY SETUP The physical system utilized for the ANC experiments was a half air-conditioning duct intended for installation on a subway vehicle built for Metro Bilbao. The duct has a length of 6.45 m, a width of.3 m and weighs about 46 kg. A pair of 2 mm thick steel sheets compose the ductʼs wall, with a Modeling signal m (n) Secondary source Flow sense C (n) FIR filter model System output Cancellation path identification algorithm Model output Σ Error estimation e (n) Fig. 4 Secondary path identification diagram, based on LMS algorithm. 294 Noise Control Eng. J. 5 (5), 23 Sept Oct

4 Identification noise Error microphone ( ) Error microphone signal Modelling signal Error microphone Filter weights Modelling signal ( output) Filter weights Secondary path identification algorithm Fig. 5 Secondary path identification algorithm based on LMS algorithm, developed in Matlab-Simulink for a SISO system. 2 mm thick thermal insulation material between them. The duct section is partially divided into two equal parts, so two independent parallel SISO feedforward systems with their respective loudspeakers and microphones were employed. In order to avoid reference contamination, a system based on Swinbankʼs dipole 6,7 was included, for each half tube. The dipole was designed for a particular distance (2 mm) between control and delayed loudspeakers, as well as to assure linear behaviour of the whole system. The object of this dipole was to avoid the negative effect that the control signal upstream could provoke in the reference microphone. Fig. 9 is a side view photograph of both the primary and control loudspeakers arrangement. Although a dipole based on Swinbankʼs approach was applied, there are alternative ways of dealing with this problem; the use of an IIR filter is one of the most common. This method allows the feedback component of the system comprised of the control loudspeaker and the reference microphone to be identified. The primary and control sources used in this experimental work were 8-ohm RS Series loudspeakers rated at 84 db SPL at m, with a maximum peak power of 8 W. The loudspeakers were driven by LAB 3 power amplifiers with a maximum power of 5 W per channel. In addition, four PCB 3B model microphones were used; these sensors have a good response in the Hz-5 khz frequency range. The signals that came into play were band-pass-filtered between 5 and 3 Hz. The lower limit was fixed by the loudspeaker behaviour since their low frequency range of flat response is limited to about 5 Hz. The upper control frequency was determined by the dimensions of the duct, which limits the maximum frequency value to that which can assure a onedimensional wave front transmission through the duct. 8 The location of the reference microphones, error microphones and control sources was determined on the basis of the results of many experiments realized in laboratory and guidelines presented in the literature, 9, in particular, the error microphones were placed in a position in which all natural frequencies were sufficiently excited for the algorithm to respond. The relative distance between reference sensor and secondary sources was fixed so, consequently, there were no group delay problems. Figure represents the schematic arrangement of the complete ANC system connections, whilst Fig. shows the axial fan used as primary source. The ventilator, which had a speed regulator, was attached to the duct by means of a metallic joining element. The room in which the ventilator was installed, was isolated from the duct by means of a glass screen so that the signal measured by the microphones was not affected by the noise transmitted through the air. Coefficient values Identification weights (Evolution) Time (s) Fig. 6 Evolution of the secondary path identification weights in case of utilizing the LMS algorithm to minimise the estimation error. Noise Control Eng. J. 5 (5), 23 Sept Oct 295

5 (error microphone) (high-pass 5 Hz) scope Control loudspeakers (system based on Swinbanks dipole) Random noise (high-pass 5 Hz) output output (modelling signal) Primary source loudspeaker Input Fig. 7 Identifying noise and error microphone signal capture. Fig. 9 General view of the duct installed in the laboratory. Error microphone Random number (high-pass 5 Hz) (high-pass 5 Hz) W_fft(z) Secondary path model 4. EXPERIMENTAL RESULTS output output (random number) Fig. 8 Comparison between system output and model output. The following section includes experimental results achieved in laboratory when implementing the ANC technique. The layout of the results has been divided according to the primary source utilized. In the first experiment, a lowfrequency broadband signal was generated using a HP-3567A Hewlett Packard dynamic signal analyser and then introduced upstream through the primary loudspeakers placed on either side of the duct. In the second experiment, the axial fan was put into operation. The experimental procedures previously undertaken were then repeated under the same conditions, but with a different noise source. It should be clarified that the noise in the duct can arise for three different reasons: it can be generated by the system itself; it can come from external sources, and it can be produced as a consequence of turbulence due to airflow along the duct. Before reviewing the experimental results, it should be mentioned that because of the characteristics of the air conditioning duct, it was not possible to place microphones downstream of the error sensors in order to measure the attenuation effect in additional positions. A. Loudspeakers as primary source Scope First of all, the coherence between the reference and the error microphone of one of the two SISO subsystems when a broadband noise is introduced is represented in Fig.2, though it should be pointed out that this graph is representative of both subsystems. As can be seen, the coherence was sufficient at most control frequencies (above.9 for almost the entire frequency range), so ANC was expected to be a good method of attenuating noise inside the duct. Figures 3 and 4 show broadband spectra of the sound pressure level of both error microphones (re: 2 μpa) before and after control. The sample frequency utilized was khz, the secondary path modelʼs filter length was 3 and a 5-coefficient FIR filter was used during the adaptive stage. As expected, the results show attenuations concentrated on the frequencies where the sound level was highest before control. Reductions on the order of 5-2 db around the most excited frequencies were obtained in both subsystems. Egana - 9 B. Axial fan as primary source It must be mentioned that an axial fan rather than a centrifugal fan (the type installed in the real vehicle) was utilized during laboratory work because of a lack of availability. In contrast to that revealed in the previous section, the use of an axial fan as primary noise did not lead to such a good response. The origin of this poor performance was the turbulence originated by the airflow (about 7 m/s) downstream of the duct. 3,2 The flow component turned out to be higher than the acoustic component over the studied frequency range. In the absence of flow effects, to obtain an attenuation of db or more, the coherence must be greater than about.95. This characteristic is drastically reduced in the presence of local turbulence at the microphones. These problems may be reduced by attaching foam protectors to the microphones, although coherence cannot always be recovered, 3 as the work here exposed. Consideration of the results obtained (see Fig. 5) shows coherence to be very poor; consequently, the ANC systemʼs performance (see Figs.6 and 7) was also poor and only seemed to work at the blade passage frequency and at the frequency excited by the metallic element joining the fan and the duct. 296 Noise Control Eng. J. 5 (5), 23 Sept Oct

6 PC (acquisition board) Control speaker 2 Delay speaker 2 Primary speaker 2 Subsystem 2 Error micr. 2 Reference micr. 2 Subsystem Error micr. Reference micr. Out In Connection site ref. error ref.2 error2 ref. Control speaker Delay speaker Primary speaker control control2 error ref.2 3 output3 4 output4 error2 Signal feeder Amplifier 2 (channels 3 & 4) clock delay mic3 mic4 clock filter outmic3 outmic4 mic mic2 outmic outmic2 in in2 filter filter2 delay delay2 clock delay clock filter output 2 Amplifier (channels & 2) output2 clock filter Filter feeding clocks Capture, feed and microphone s to signal treatment site Filtered signals and connection site s Control signal subsystem Control signal subsystem 2 Fig. General diagram including all the connections as well as the arrangement of the different devices that take part in ANC. 5. CONCLUSIONS The active noise control technique was implemented to attenuate low-frequency broadband noise in an air-conditioning duct to be installed on a subway vehicle. The use of Matlab- Simulink to design the control algorithms was a success and the attenuations obtained were similar to those achieved with commercial devices shown in the literature. Moreover, the two methods developed to calculate the secondary path were shown to be effective. In the experiments, microphones were used as reference and error sensors, and loudspeakers as secondary or control sources. Attenuations of up to 5-2 db were obtained over the 5-3 Hz. frequency range when the primary noise was introduced via loudspeakers. This range was limited at low frequency by the non-linear performance of the loudspeakers and at high frequency by the cut-frequency of the duct. Nevertheless, the use of an axial fan as a primary source led to poor ANC performance. This low attenuation, linked with poor coherence, was a consequence of a significant turbulence component of the signal measured by the microphones. The work presented here demonstrates the implementation of specific algorithms, as well as the potential and limitations of ANC methods when factors not directly linked with noise control affect the systemʼs performance. To sum up, and in addition to the results presented in this paper, it is important to emphasise that ANC experiments are going to be carried out in the real vehicle. Consequently, axial fans will not provide the only source of noise; there will also be other sources to control, such as those from exterior sources. Axial fan Fig. Detail of the axial fan used as primary noise source. Noise Control Eng. J. 5 (5), 23 Sept Oct 297

7 Source (FFT) Date: 8/6/ Level: 6 mvpk Offset: V Time" :24: Type: random noise Save/Rec Def Disk: Internal Date: 4/6/ Time: 6:8: 2/ X:62 Hz Y: e-3 A: CH2 Pwr Spec X:37 Hz B: D2 Pwr Spec X:37 Hz 75 Y: * Y: * Coherence Avg: 4 6. ACKNOWLEDGMENTS The financial support of the Basque Government and the help of CAF Company in carrying out this research work are greatly appreciated. 7. REFERENCES D. Guicking, On the invention of active noise control by Paul Lueg, J. Acoust. Soc. Am. 87(5), (99). Save/Rec Def Disk: Internal Date: 4/6/ Time: 6:8: A: CH Pwr Spec X:38 Hz B: D Pwr Spec X:38 Hz 75 Y: * Y: * Band pressure level (db) Band pressure level (db) Fig. 2 Coherence between reference microphone and error microphone signals of one of the two subsystems of the control configuration when using loudspeakers as primary source. 2 Avg. 2 4 Fig. 4 Error microphone spectra for second SISO ANC subsystem, before control (continuous line) and after control (dashed line). 2 P. A. Nelson and S. J. Elliot, Active Control of Sound (Academic Press, New York, 992). 3 G. Leventhall and C. Carme, Active control in one dimensional flows, Proc. INTER-NOISE 2, edited by Didier Cassereau (Noise Control Foundation, Poughkeepsie, New York, 2). 4 M. Abom and O. Schiegg, Turbulence noise suppression methods for ANC in ducts, Proc. INTER-NOISE 2, edited by Didier Cassereau (Noise Control Foundation, Poughkeepsie, New York, 2). 5 Bernard Widrow and Samuel D. Steams, Adaptive Signal Processing (Prentice-Hall, Englewood Cliffs, New Jersey, 985). Disp Frmat Disp Date: Frmat 8/6/ Time: 7:32: Date: 8/6/ Time: 7:32: 2/ X:9 Hz Y: e-3 2/ X:9 Hz Y: e-3 Coherence Coherence 2 Avg. 2 4 Fig. 3 Error microphone spectra for first SISO ANC subsystem, before control (continuous line) and after control (dashed line) in case loudspeakers are used as primary source. Avg: 4 Avg: 4 Fig. 5 Coherence between reference microphone and error microphone signals of one of the two subsystems of the control configuration when using the axial fan as primary source. 298 Noise Control Eng. J. 5 (5), 23 Sept Oct

8 Save/Rec Def Disk: Internal Date: 8/6/ Time: 7:: Systm Util Date: 8/6/ Time: 7:2 Date: 8/6/ Time: 7:: A: CH Pwr Spec X:5 Hz B: D Pwr Spec X:5 Hz 7 Y: * Y: * A: CH2 Pwr Spec X:24 Hz B: D2 Pwr Spec X:24 Hz 7 Y: * Y:63.53 * Band pressure level (db) Band pressure level (db) 2 Avg. 2 4 Fig. 6 Error microphone spectra for first SISO ANC subsystem, before control (continuous line) and after control (dashed line) in case the axial fan is used as primary source. 2 Avg. 2 4 Fig. 7 Error microphone spectra for second SISO ANC subsystem, before control (continuous line) and after control (dashed line) in case the axial fan is used as primary source. 6 M. A. Swinbanks, Active control of sound propagation in long ducts, J. Sound Vib. 27(3), (973). 7 J. H. B. Poole and H. G. Leventhall, An experimental study of Swinbanksʼ method of active attenuation of soundi in ducts, J. Sound Vib. 49(2), (976). 8 Pedro Cobo Parra, Control Activo del Ruido: Principios y Aplicaciones (Instituto de Acústica. CSIC, 996). 9 A. Boudreau., A. LʼEspérance, M. Bouchard, and B. Paillard, Actuators positioning for multichannel active control system in circular ducts, Applied Acoustics 59, (2). G. Mangiante, A. Roure, and M. Winninger, Optimized unidirectional system for active control of sound in ducts, Proc. ACTIVE 99, edited by Scott Douglas (Noise Control Foundation, Poughkeepsie, New York, 999), pp P. Minogue, N. Rankin, and J. Ryan, Short duct server fan noise cancellation, Proc. ACTIVE 99, edited by Scott Douglas (Noise Control Foundation, Poughkeepsie, New York, 999), pp A. Roure, Self-adaptive broadband active sound control system, J. Sound Vib. (3), (985). Noise Control Eng. J. 5 (5), 23 Sept Oct 299