Improved methods for source characterization on trains Karl Bolin 1 , Stefan Jacob 2 and Mats Åbom 3 Dept. of Mechanics-The Marcus Wallenberg Laboratory KTH-Royal Inst. of Technology SE-100 44 Stockholm

ABSTRACT One problem for railway noise predictions is to characterize noise from various auxiliary equipment, e.g., fans, compressors, transformers. The noise from such sources can be a dominating contribution under low-speed operation or stand still. To better handle this problem the EU-project TRANSIT investigates improved methods for acoustic source characterization. As a starting point it is assumed that an acoustic source is enclosed by a control surface. The surface is sub-divided into smaller areas and each area is assumed to act as an acoustic one-port coupled to all the other areas. The properties of each area can then be described by its volume flow and internal impedance. The resulting acoustic pressure at a receiving point, can finally be expressed as a product of the source volume flows and a matrix representing the acoustic installation effects (“source+radiation impedances”). To simplify the method one can assume uncorrelated sources and use an ISO procedure for sound power to determine the volume flows. The acoustic installation effects can be obtained using a monopole point source to measure or calculate the pressure at selected receiving positions. 1. INTRODUCTION

This paper will summarize work done in the EU-project TRANSIT ( Contract No. 881771 ) concerning a source characterization method first proposed by KTH in the ACOUTRAIN project [1,2].

2. THEORY

2.1. The complete model The starting point is the assumption that we have a linear and time-invariant acoustic source or system. In the frequency domain such a system can be described as an acoustic multi-port or black- box model [3]:

, s s = + y K x y (1)

1 kbolin@kth.se 2 sjacob@kth.se 3 matsabom@kth.se

where x , y are column state vectors containing complex (Fourier) amplitudes at a certain frequency, K is a matrix relating in- and output and the sub-script s denotes the source strength. For air-borne sound which is the main interest here one can select acoustic pressure ( p ) and volume flow ( Q ) as the state variables defining the state vectors. This lead either to an impedance ( Z ) or mobility ( M ) type of source model:

, s s = − p p Z Q (2) . s s = − Q Q M p (3) Here the usual convention that the volume flow is positive out from the source regions is assumed. One can also note that: . Of course, in principle Eqs. (2) and (3) are equivalent and one can use either one. But one important difference is that Eq. (2) will express a source as a set of “dipoles”, while Eq. (3) corresponds to a set of “monopoles”. This difference is important in practice since when applying these models, the transmission to various receiving points must be known. To measure these transmissions can involve cases where it is much easier to apply reciprocity, i.e., interchange source and receiver. This is not a problem with the mobility formulation since then p and Q are used. Of course, assuming one has access to a calibrated monopole source, e.g., as described by Ref. [4]. But for the impedance formulation one needs to use reciprocity for a “dipole”, which implies to measure acoustic velocity. This is possible but certainly more difficult and sensitive to various measurement errors. Despite this drawback the impedance approach has been studied and proposed for instance by Pavic [5]. Assume now a source producing air-borne sound which can be enclosed by a reference surface. This surface is arbitrary but often chosen as the smallest volume that entirely enclose the source in question, see Figure 1. The surface of the reference surface can be subdivided into smaller patches (n=1,2,……) each corresponding to a certain acoustic pressure (average over the patch) and volume flow. Together these pressures and volume flows can be used to define the source multi-port on the reference surface as described by Eqs. (2) and (3). Of course, a detailed accuracy of the model at each frequency would require that the patches are smaller than a wavelength. However, assuming one is mainly interested in frequency band averages (say 1/3-oct) and to predict dBA-values, then a set of patches not resolving the wavelength can be sufficient. This statement can be considered to already be partly validated by the work done in the ACOUTRAIN project [1,2].

1 s s − = Z M

Figure 1: Illustration of the source multi-port model.

For each patch one can associate an impedance Z mn , i.e., relating the volume flow to the acoustic pressure received at any position m. For points on the reference surface Z mn corresponds to the radiation impedance Z mn,r or Z r . This can be used to rewrite Eq. (3) in the form:

( )

1 s s r s r s − = −  = + Q Q M Z Q Q E M Z Q ,

where E is the unit matrix. From knowledge of the volume flows on the reference surface Q one can finally compute the pressure at any receiving point using the transfer impedance Z mn,t or Z t :

( )

1 t s r s − = + p Z E M Z Q .

This is the final equation which simply can be written as:

s = p GQ , (4)

where G mathematically can be seen as the Greens-function matrix for the source under study. This matrix contains the complete information about the source ( M s ) and how it couples to the surrounding environment ( Z r & Z t ). Note that the source strengths Q s represent ideal monopoles with infinite internal impedance i.e., they are not affected by the installation.

The strategy to apply this model to characterize a source can be summarized in the following steps:

i. Decide the number ( N ) of patches or sub-surfaces (monopoles) to use.

ii. Test the source in a “free field” environment and start by determining G ff . N.B. This can be done by a reciprocal procedure and the number of reception points ( M ) can also be larger than N .

iii. The monopole source strengths are then given by Eq. (4). To be applicable to both periodic and random data this result should be rewritten in terms of auto- and cross-spectra:

( ) 1 1 , s s

c

Q Q ff pp ff − − = S G S G (5)

where c xx =  S x x is a N x N matrix and the super-script c denotes the Hermitian.

iv. The final step is to determine the Greens function G for the installation case. This is done with the machine installed (not running) or alternatively with a dummy having the same shape, volume & surface impedance. Of course G could also be computed using finite element methods (FEM) or ray tracing models.

v. The resulting sound field at the reception points is finally computed from:

c pp Q Q = S GS G (6)

. s s

Note G represents ALL the acoustic installation effects BUT for fluid machine sources, e.g., fans, we also have aerodynamic installation effects .

The multi-port model described above is similar to so called monopole or multi-pole expansion models proposed in the literature see e.g., Refs. [6]. However, an important difference is that such models are normally based on the free-field Greens function and not the actual Greens function.

2.2. The simplified model Assuming data only in frequency bands (say 1/3-oct) the full monopole model can be simplified. Averaging Eq. (6) in a frequency band b gives assuming one looks at a particular receiving point:

c pp i ij j b b i j S G S G =  , (7)

,

where G i is the Greens function between source i and the receiving point and S ij is the source cross- spectrum matrix between source i and j . The cross-terms in this sum can be expected to average out, i.e., the sources can be considered as uncorrelated, implying that:

c pp i ij j i ii b b b i j i S G S G G S = →   ,

2

,

2 i G will be referred to as the source

where the summation is over all sources and from now on

power based FRF . This result can be approximated by:

2 , , pp b i ii b b i S G S   , (8)

where the auto-spectra now refer to the entire frequency band. Although the result in Eq. (8) is derived assuming frequency bands it should be possible to apply for tonal and coherent sources assuming: i) they are connected to the receiver by multiple paths, e.g., like a source placed inside a reverberant box; ii) a spatial average is performed at the source or receiver positions. In practice there is some difficulty to apply Eq. (8) since it requires a determination of the source monopoles representing the actual source. One idea to simplify this part, proposed in the ACOUTRAIN project [1,2], is to estimate these monopoles based on standard sound power measurements. The most accurate is to use acoustic intensity scanning (ISO 9614-2:1996) [7] but an alternative is to use sound pressure (ISO 3744:2010) [8]. The measurement surface is then chosen as described by the standard and will normally be larger than then the reference surface. It will be assumed here that both the reference and measurement surfaces are rectangular boxes that are geometrically similar. If the box is on a rigid surface then there are 5 sides that needs to be measured. This will give 5 sound powers W i that can be converted to N =5 monopoles S ii by assuming an ideal monopole over a rigid plane:



W c S K

4 i b ii b

 =  , (9)

, , 2 ,

i b

where K is a correction factor which gives the increase in sound power due to a nearby rigid surface, c the speed of sound,  the density and  the angular frequency (mid-frequency of the band). The factor K is plotted and tabulated in Ref. [9], Appendix 1. Other installation cases with more than one rigid surface close to the source could be treated as described by the standards. However, since in the proposed method ALL acoustic installation effects are included in the power based source FRF, it is suggested to always test the source in question on a reflecting plane. Of course, other shapes of the reference surface than a rectangular box are possible and also for large machines to use more than 5 sources, e.g., by subdividing one of the sides of a box. Combining Eqs. (8) and (9) gives:



W c S G K

4 i b pp b i b i i b

     . (10)

2 , , 2 ,

The contribution from each source i is:



W c S G K

4 i b i pp b i b i b

2 , , 2 ,

    .

This can be rewritten using the normal definitions of sound pressure ( L p ) and sound power ( L W ) levels as:

, , 10lg p i W i i i L L PBNR K = − − , [dB] (11)

             

W c PBNR G p

2 2 4 10lg

where 2

is the power based noise reduction as defined in Ref. [4],

ref i i f ref

W ref =1 pW , 2 ref p = 20  Pa and the sub-script b denoting the frequency band is dropped. The

interpretation of PNBR is, the RMS pressure squared divided by the free field sound power of the monopole creating this pressure, expressed in dB. The total level from all 5 sides is given by:

  =       . [dB] (12)

, 5

/10 ,

p i L p tot

1 10 lg 10

i L

=

If only the total power from a machine is known one can still include the variation in transmission in different directions by using a space averaged power based noise reduction PBNR .

3. EXPERIMENTAL TESTS

In the ACOUTRAIN project the full model (Eq. 6) was tested on a train HVAC unit from Bombardier mounted in a mock-up to simulate a real installation [1,2]. This was then compared with models disregarding phase information using sound power. The results were very promising suggesting that this type of simplified approaches is possible. This motivated the effort in the TRANSIT project to further test and validate the simplified model proposed in Sec. 2.2 (Eqs. 11&12). The planned tests are split in two parts; first, controlled experiments using generic loudspeaker sources (monopole, dipole and quadrupole) in mock-ups resembling installations on a train; second, field measurements on a few selected cases in co-operation with the partners in the FINE-2 project. The first part has been finished and will be summarized here, while the second has been delayed due to Covid-19 and will be presented later.

3.1. Sound sources

Ref. microphone

Figure 2: From left to right: Calibrated monopole source [4], omnidirectional, dipole and a lateral quadrupole source. The vertical bars and horizontal strings show the measurement surface or ISO box used (0.5x0.5x0.5 m 3 or 0.35x0.35x0.35 m 3 ).

The following generic source types (see Figure 2) were used as the noise source in the tests:

• Large monopole or omnidirectional sound source: Look Line model 28-41035, s/n

14051. • Dipole : made of two identical loudspeakers (Beyma 6B30/P, φ 150 mm) face-to-face

bolted together. The two loudspeakers are driven out-of-phase. • Quadrupole : two sets of dipoles as described above placed side-by-side.

All sound sources were driven using white noise with the frequency span 0 – 12.8 kHz (or 0-10 kHz). All measurements were performed in 1/3 octave band from 100 Hz to 5000 Hz. The strengths were controlled by the settings of the signal generator and the power amplifier. Tests showed that with this arrangement, the maximum error in the repeatability is less than 0.3 dB. To determine the sound power from the source under test one needs to measure the power from each side of the reference surface. For the test presented here two cubical measurement boxes (0.5x0.5x0.5 m 3 & 0.35x0.35x0.35 m 3 ) were used and the power determined by the intensity scan method (ISO 9614-2:1996). The results for the larger box with the omnidirectional source are presented in Figure 3.

10° Frequency (Hz) (SP) TWNOLLOSYIGINWO 48mod punos jeEMeg

1

4

5

2

3

Figure 3: Partial sound powers from the 5 box sides for the tested omnidirectional source (see Figure 2).

3.2. The calibrated monopole source

An important part of the proposed method is the ability to determine the Greens function (Eq. 6) for an installation or the power based noise reduction ( PBNR ) (Eq. 11). This requires a calibrated monopole source which can built based on the recommendation of the GM standard [4]. The source at KTH consists of a high frequency compression driver (KU-516) fitted with a 570 mm and 25 mm (outer)/18 mm (inner) diameter steel pipe, see Figure 2. A ¼” microphone (G.R.A.S. 40BD- S3/26CB, sensitivity 1.85 mV/Pa) is mounted at the pipe opening to monitor the output sound pressure level. The point source is used to measure the magnitude of the transfer function or Power Based Noise Reduction ( PBNR ) as defined in Eq. (11). The first step is to calibrate the point source by measuring

the free-field sound power , free b W in some frequency band ( b ) as described in Ref. [4]. This test will

result in a power based FRF ( D W ):

  =        

W D S W

, 2 , 10 lg ( /1V )

free b W

, [dB] (13)

ee b ref

where S ee,b is the auto-spectrum of the built-in microphone voltage and W ref =1 pW. Then the point source is used to determine the acoustic installation effect, by measuring the power based FRF at the positions of the equivalent monopoles on the measurement surface ( D p ). This gives:

  =        

S D S p

,

pp b p

, [dB] (14)

2 2 , 10 lg ( /1V )

ee b ref

where , pp b S is the auto-spectrum for the pressure at the receiving position. Combining Eqs. (13) and

(14) finally gives us the power based noise reduction as defined by Eq. (11): PNBR = D p -D W . In order to suppress noise one can of course also rewrite Eq. (14) as:

    =     

2

H D p

,

pe b p

, [dB] (15)

2 2 10 lg ( /1V )

ref

where pe H is the transfer function between the built-in microphone and the pressure.

3.3. Measurements using generic sources The measurements were performed in the hemi-anechoic room at KTH. The mock-up of the train with a roof mounted box is shown in Figures 4 and 5. The idea being to represent a typical installation case for a train and include the effects of a reflecting enclosure (“roof box”) as well as diffraction in the transmission path. According to the standard ISO 3095:2005, the reference point for a stand-still test is 7.5 meters away from the track center and 1.2 meters above the track plane. The dimension of a typical railway car cross-section is about 3 meters wide and 4 meters high (above the track plane). Due to the limit of the space available, the mock-up is only two meters high (and three meters wide). In order to keep the same diffraction effects from the roof, it was decided that the position of the measurement microphone should be in the line between the top-corner of the roof and the receiver position recommended by ISO 3095:2013. This implies that the diffraction angle will be the same as specified by the standard. The reference point was therefore selected at the point 1.2 meters above the floor and 3.22 meters from the center line of the car-body (1.77 meters from the side wall), see Figure 4.

1.3 m

0.6 m

Reference microphone

2 m

h*=1.2 m

Floor of the room

4 m

h=1.2 m

3.22 m

7.5 m

Figure 4: Illustration of mock-up geometry and the position of the reference microphone.

Figure 5: The mock-up of the wagon with the roof box and reference microphone. For measures and distances see Figure 4. The generic sources were put inside the roof box. Sound sources were placed inside the roof box and excited with white noise. The equivalent monopoles were assumed to be located in the middle of the five surfaces of the measurement box used in the sound power measurements. The power-based noise reduction, PBNR , was measured by using the calibrated point source, see section 3.2.

3.3.1. Results Two different cases were studied one was a roof box with hard walls and no added damping (“reference case”). The other was the same box but with added damping and scattering objects in the box. Here only the results for the reference case using the omnidirectional source will be presented, see Figure 6. The sound source in this measurement was placed about 20 cm away from the center of the roof box. In this figure the influence of not using the correction factor K (see Eq. 9) is tested. As can be seen from Figure 6 this factor can lead to a significant improvement of the low frequency prediction.

Figure 6: Omnidirectional sound source, placed about 20 cm off box center. The sound pressure

level is predicted at the reference microphone position, see Figure 4.

In the full TRANSIT report [9] concerning this work a total of 11 different tests are presented based on different source types: monopole, dipole and quadrupole and installation conditions. Based on this one can estimate the mean error for the proposed simplified equivalent monopole source model. The error is simply defined as the difference between the predicted level at the reference microphone, based on Eqs. (11) and (12), compared to the measured.

Table 1: Summary of errors in the prediction based on all test performed [9]. The errors have

been averaged in a low 100-500 and high frequency 630-5000 Hz range.

Errors (dB) 100-500 Hz 630-5000 Hz Mean original REF.B OX 1.8 0.2 Mean original REF.B OX no K-factor 2.8 0.2 Std original REF.BO X 3.0 1.8 Std original REF.BO X no K-factor 3.0 1.8

The data in Table 1 are based on the “original”, i.e., larger ISO reference box 0.5x0.5x0.5 m 3 . Using the smaller box 0.35x0.35x0.35 m 3 did not significantly improve the results. It is clear that the errors are largest in the range 100-500 Hz and then decrease in the high frequency range 630-5000 Hz. The table also shows the reduction in mean error for low frequencies by applying the K-factor, see Eq. 9.

The main reason for the systematic error in the low frequency range is probably related to that a single coherent source was used for all tests. This implies that the tests were essentially equivalent with using a tonal source and averaging this over a frequency band. In particular, for low frequencies this will not so efficiently remove the correlation between different propagation paths and introduce bias errors. In practice as long as one is dealing with non-coherent sources this type of bias error should be less important. For pure tonal sources on the other hand it might be necessary to include the phase in the modelling, i.e., use the full model (Eq. 6).

In practice when A-weighted results are of interest, errors in the low frequency range (100-500 Hz) will also be supressed.

‘Sound pressure level (dB) = Predicted simpliied model Predicted no fee-feld correction —— Measured 10° 10° Frequency (Hz)

4. SUMMARY AND CONCLUSIONS

Based on the work in the previous project Acoutrain [1,2] a simplified equivalent monopole method is presented, see Eqs. (11) and (12). The method is based on determination of monopole source strengths, by measuring the partial sound power from various sides of the machine or device of interest. This is done using an appropriate ISO standard [7,8] and defining a measurement surface around the machine. This surface can be in the form of a rectangular box normally located on a hard floor. In that case there will 5 sides and 5 partial sound powers for each frequency band of interest. The sound powers are then converted into 5 monopole source strengths by assuming each side of the box radiates as over a reflecting plane. The position of the monopoles is assumed to be in the middle of each of the 5 sides. To describe the acoustic installation effects a calibrated monopole source is used [4]. Using this source the frequency response, between pressure at a receiving position and the monopole volume flow producing this pressure, is measured for each of the 5 monopole positions and expressed as a Power Based Noise Reduction ( PBNR ), see Eqs. (13-15). Once the partial sound powers and corresponding PBNR :s are known the resulting sound pressure at the receiving position can be predicted using Eqs. (11) and (12). The proposed simplified model is based on averaging the complete equivalent monopole model (see Eq. 6) in frequency bands, e.g., 1/3-octave. This removes the phase information which is appropriate for sources with broad-band noise character, e.g., a HVAC fan. Tonal noise and coherent sources should also be possible to handle, assuming that either there are a number of tones in the frequency band or multiple source- receiver transmission paths, e.g., like a source placed inside a reverberant box. For cases where these conditions are not satisfied it is recommended to use the complete equivalent monopole method (see Eq. 6), e.g., by applying iterative Bayesian focusing [10-12].

To validate the proposed method tests using generic sources (see Sec. 3.1) excited by coherent noise and installed under different conditions were conducted at the Marcus Wallenberg Laboratory at KTH. The details and results are summarized in Section 3.3, see Table 1. Based on the investigation done it is concluded that the simplified equivalent monopole method has been validated for generic sources under laboratory conditions. Since the tested sources represent the three basic sources (monopole, dipole, quadrupole) from which any real sources can be built up, it is believed that the results also support that the method will work for real sources. The effort to validate this last statement is delayed due to Covid-19, but is planned to be finished before June 2022. An important part of the field tests will also be to test the method for tonal sources and to compare it with results from the iterative Bayesian focusing method.

The source characterization methods studied in TRANSIT will be introduced into the global train noise modelling tool developed in the ACOUTRAIN project [13].

5. ACKNOWLEDGEMENTS

The authors acknowledge the contribution from Dr. Leping Feng who performed the experiments presented in this paper.

6. REFERENCES

1. Feng L., Åbom, M., Final report WP 3.1: Source model for cooling fans suitable for integration

in the global simulation model. European project ACOUTRAIN (contract number: FP7- 284877), 2014. 2. Feng L., Åbom M., Orrenius U., Engineering methods to predict noise levels at reference

points with known source properties. Applied Acoustics 96 , 68-74 (2015). 3. Bodén H., Åbom M., Modelling of fluid machines as sources of sound in duct and pipe

systems. ACTA ACUSTICA-LES ULIS 3 , 549-560 (1995). 4. GM Worldwide Engineering Standards. Sound Power to Pressure Transfer Function Master

Test Procedure. GMW14174 Oct 2005. 5. Du L., Pavić G., Experimental characterization of air-borne sound sources via surface coupling.

Applied Acoustics 134 , 97–109 (2018). 6. Yves J, Gounot R, Musafir R.E., Simulation of scattered fields: Some guidelines for the

equivalent source method. Journal of Sound and Vibration 330 , 3698–3709 (2011). 7. Acoustics – Determination of sound power levels of noise sources using sound intensity - Part

2: Measurement by scanning (ISO 9614-2:1996). 8. Acoustics – Determination of sound power levels and sound energy levels of noise sources

using sound pressure – Engineering methods for an essentially free field over a reflecting plane (ISO 3744:2010). 9. Åbom M., et al., Final report D1.1: Validated procedure for source characterization based on

equivalent monopoles and tests involving generic sources. European project TRANSIT (contract No. 881771), 2020. 10. Le Magueresse T., Outrequin A., Thivant M., Antoni J., Jouvray J-L., Rober E., 3D acoustical

characterization of an electrical motor by Bayesian Focusing, BeBeC 2020 . 11. Antoni J., Le Magueresse T., Leclère Q., Simard P., Sparse acoustical holography from iterated

Bayesian focusing, Journal of Sound and Vibration , 446 , 289-325 (2019). 12. Pereira A., Antoni J., Leclère Q., Empirical Bayesian regularization of the inverse acoustic

problem, Applied Acoustics , 97 , 11-29 (2015). 13. Thompson D., Squicciarini G., ACOUTRAIN project Deliverable D4.7 – Basic global

prediction tool and user manual (final update of D4.2), 2014.