PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Prediction of maximum Fast time-weighted sound pressure levels
from time-varying structure-borne sound sources in heavyweightbuildings
Steffi REINHOLD1,2; Carl HOPKINS1; Gary SEIFFERT1
1Acoustics Research Unit, School of Architecture, University of Liverpool, UK
2

University of Applied Sciences Stuttgart, Germany

ABSTRACTAt present the prediction model in EN 12354-5 for sound transmission due to structure-borne excitation frombuilding machinery is limited to sources running under steady-state conditions. As machinery noise also
needs to be assessed under time-varying conditions, building regulations on installation noise in some
European countries set requirements based on the maximum Fast time-weighted sound pressure level in thereceiving room. This paper proposes an approach that could predict this information at the design stage andvalidates it using idealised time-varying signals applied via a shaker into a concrete floor. A heavyweight
reception plate is used to quantify the structure-borne sound power using equivalent continuous levels over
125ms time periods from which the highest value can be used as the power input into an SEA or SEA-based
prediction model. An empirical correction (developed in previous work by the authors) is then applied to theoutput from this model to estimate the maximum Fast time-weighted sound pressure level. This approach isvalidated with measurements in a room below a concrete floor (where there is suppressed flankingtransmission) from which the results show close agreement between predictions and measurements for onethird octave bands and A-weighted values.
Keywords: machinery, structure-borne sound power, time-varying signals, Fast time-weighted levels

1. INTRODUCTION
The structure-borne sound power from a high-mobility source injected into a low-mobility plate
can be determined according to EN 15657 (1) by using the reception plate method when the source
operates under steady-state conditions. This can then be used as input data to estimate the steady-statesound pressure level in a receiving room using the SEA-based prediction model described inEN 12354-5 (2). However, building machinery does not always operate in a ‘steady-state’ and often
has time-varying operating conditions. At present there is no standardised procedure with thereception plate to quantify the structure-borne sound power from time-varying sources. In addition,EN 12354-5 is not able to predict the maximum Fast time-weighted sound pressure level (L Fmax) in
the receiving room which is required in some European regulations on installation noise e.g.
VDI 4100 (3) in Germany.
In heavyweight buildings it is possible to predict the impact sound insulation due to transient
excitation in terms of maximum Fast time-weighted sound pressure levels using Transient Statistical
Energy Analysis (TSEA) (4,5). This requires measurements of the blocked force from the transient
excitation for which the approach has been validated for heavy impacts from the ISO rubber ball andthe bang machine on heavyweight floors with and without floating floors (6,7). However, there has
been a move through the EN 12354 series of standards to simplify the prediction process for thebuilding industry, such that it is not feasible to incorporate TSEA calculations in these Standards.
Hence the aim in this paper is to identify and validate a simpler procedure than TSEA which could be
used in an SEA-based prediction model like EN 12354-5 to estimate the maximum Fast time-weighted
sound pressure level from building equipment. This would require input data for time-varying
structure-borne sound power and ideally this would be based on a modified approach to the reception
plate method described in EN 15657.
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steffi.reinhold@liverpool.ac.uk, carl.hopkins@liverpool.ac.uk

The underlying principle to this new approach for time-varying structure-borne sound sources is thatbuilding machinery such as boilers, washing machines, pumps tends to have different operating cycles
between which an approximately broadband, structure-borne sound power input ramps up and down.
However, such machinery rarely introduces very short, high level transients in the power input likean impact from a dropped object such as the rubber ball which has 20ms contact time (6,7). For thisreason, it is proposed that the reception plate could be used to identify max{L eq,125ms } and that this
could be used as input data in an SEA or SEA-based prediction model (i.e. EN 12354-5) with anempirical correction to convert the estimated sound pressure level from max{Leq,125ms } to L Fmax. Thisempirical correction and the use of 125ms has been assessed in a previous investigation by the authors(8) using idealised time-varying signals which ramp up and down. This showed that the empiricalcorrection has some dependence on the ramp duration as well as the ramp levels; for ramp levels of
10dB and all ramp durations the empirical correction was 5dB, for ramp levels of 20/30/40dB and aramp duration of 125ms the empirical correction was 7.5dB and for ramp levels of 20/30/40dB with
ramp durations ≥500ms the empirical correction was 6dB.
The current paper builds on the work in (8) to use the reception plate with power injected by ashaker with idealised time-varying signals to determine the highest L eq,125ms and then predict themaximum Fast time-weighted sound pressure level in a heavyweight building-like situation using anSEA model with the empirical correction. The initial comparison is made using one-third octave bands
but practical assessments of machinery noise often require an A-weighted maximum Fast timeweighted sound pressure level; hence an energetic summation is used to assess whether an A-weighted
value could also be estimated from the frequency band data.

2. EXPERIMENTAL SET-UP
Twenty wav files of idealised time-varying signals were created in Matlab. These had different
rising and falling ramp durations of 125ms, 500ms, 1s, 2s and 5s with increasing and decreasing ramp
levels of 10/20/30/40dB as indicated by the examples in Figure 1. The signals are played into anelectrodynamic shaker on a reception plate and a floor in a building-like situation in the laboratory atStuttgart (8).

Figure 1 – Example of idealised time-varying signals for all ramp durations with a ramp level of 30dB.
2.1 Reception Plate for Structure-borne Sound Characterisation
The reception plate test rig at Stuttgart consists of three decoupled plates due to resilient supports
around the edges (1,9). In this paper, only the horizontal 100mm concrete (low-mobility) plate withan area of 5.6m² is used. Three excitation positions are taken for a shaker to quantify the injectedstructure-borne sound power in terms of max{L eq,125ms } in each one-third octave band using theproposed weighting factor in (10,11) that combines velocity measurements of all four corners andcentral zone positions (≥ 0.5m away from edges).

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2.2 Building-like Situation for Structure-borne Sound Transmission
A floor test facility is used to represent a building-like situation in which there is suppressedflanking transmission (using independent wall linings) such that only direct sound transmission fromthe floor is dominant. The concrete test floor is 140mm thick with an area of 19.4m². The receivingroom has a volume of 51.1m³.
Three positions on the concrete floor are excited by the electrodynamic shaker to determine thevibration field on the floor and the sound field in the receiving room. The spatial-average velocity
level is determined in terms of max{L eq,125ms } and L Fmax on the separating floor using sevenaccelerometer positions (two corner/edge positions and five central zone positions that are ≥0.5m
away from floor edges). The spatial-average sound pressure level is obtained in terms ofmax{Leq,125ms }and L Fmax using four microphone positions in the central volume of the room (>0.5maway from room boundaries).

3. SEA PREDICTION MODEL FOR A COUPLED ROOM-PLATE SYSTEM
To describe the steady-state sound transmission in the building-like situation, an SEA model of acoupled room-plate system is used by considering a homogenous plate (subsystem 1) coupled to areceiving room (subsystem 2) – see Figure 2.

Figure 2 – Two-subsystem SEA model for a coupled room-plate system.
The energy balance of this coupled room-plate system is determined from knowledge of thevibrational power input into the plate, the coupling between the subsystems and the power dissipatedthrough internal and coupling losses to other subsystems (12,13).
The power balance equations for a coupled room-plate SEA model are:Win,1  11 E1  12 E1  21 E2(1)12 E1   22 E2  21 E1(2)where Win,1 is the power injected into the plate (1),  11 represents the losses of the plate (internallosses and the sum of coupling losses from the plate to connected walls and floors), 22 represents thelosses of the receiving room (determined from the reverberation time),  12 and  21 are the couplingloss factors from the plate (1) to the room (2) and from the room (2) to the plate (1), respectively, andE represents the subsystem energies.
The experimentally-determined input data are the vibrational power of the source, the loss factorsof the plate and in the receiving room as well as the plate radiation efficiency. The radiation efficiency
is determined using shaker excitation with white noise from measurements of the sound pressure andthe plate velocity based on the following equation:  A p2

 4S  c v 2 20 02(2)where A is the absorption area of the room, S is the area of the plate,  0 is the air density, c 0 is thespeed of sound,〈p2 〉is the spatial-average mean-square pressure and〈v 2 〉is the spatial-averagemean-square velocity.

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4. RESULTS
4.1 One-third Octave Bands
To assess the results it is assumed that an acceptable difference between the two-subsystem SEA
prediction and the measurement is ±5dB for the low-frequency range up to 200Hz and ±3dB for themid- and high-frequency range from 250Hz to 3.15kHz. The allowable error is larger in the lowfrequency range where uncertainties are larger in reverberation time measurements and in the spatial
variation of the sound pressure and the plate velocity (13).
Figure 3 shows the difference between predicted and measured velocities in terms of L Fmax on theconcrete floor in the building-like situation. This shows that the SEA model is able to predict themeasured vibrational response of the concrete floor within the acceptable error limits for all ramp
durations with only a few exceptions (e.g. 125ms ramp at 50Hz) where the error is up to 1.4dB higher
than the acceptable error limits. In general, there is no significant offset, although for the 125ms ramp
the prediction appears to slightly overestimate between 50Hz and 100Hz and for the 1s, 2s and 5s
ramps the prediction appears to slightly overestimate between 630Hz and 3.15kHz.

Figure 3 – Difference between predicted and measured velocity levels in terms of LFmax (predicted –measured). (a) 125ms ramp, (b) 500ms ramp, (c) 1s ramp, (d) 2s ramp and (e) 5s ramp.

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Figure 4 shows the difference between predicted and measured sound pressure levels in terms ofL Fmax. These differences are similar to those observed for the plate velocity with the prediction model
having only a slightly higher overestimation than with velocity. For a 125ms ramp there are fiveexceedances of the acceptable error by up to 1.3dB whereas for ramp durations ≥500ms all ramp levels
are within the acceptable error. However, such differences are similar to SEA predictions of airborne
or impact sound insulation (steady-state sources) with only direct sound transmission (13).

Figure 4 – Difference between predicted and measured velocity levels in terms of LFmax (predicted –measured). (a) 125ms ramp, (b) 500ms ramp, (c) 1s ramp, (d) 2s ramp and (e) 5s ramp.
The above results provide evidence that by using the specific empirical correction for a known
ramp level and a known ramp duration it is feasible to estimate L Fmax within ±3dB. However, on thebasis that the ramp level and the ramp duration is not known for the majority of building equipment,
it would be convenient to adopt a single empirical correction that could be used with simplified formsof SEA such as in EN 12354-5. The empirical corrections from reference (11) range from 5dB to
7.5dB; hence it is reasonable to consider 6dB as a candidate for a single empirical correction as thisis approximately in the middle of this range. The implications of choosing this value are that for ramp
levels of 10dB it will overestimate L Fmax by ≈1dB, but it will exactly correspond to the empiricalcorrection for 20/30/40dB with ramp durations ≥500ms. The results using a single empirical correction1252

are shown in Figure 5. These show that for ramp levels of 20/30/40dB and all ramp durations the error
is within the acceptable limits. With a ramp level of 10dB, the prediction tends to overestimate andoccasionally this error is outside the acceptable error by ≈1.2dB; however, this simplification still
seems justifiable for an SEA-based approach like EN 12354-5.

Figure 5 – Difference of predicted and measured sound pressure levels, LFmax using a single empiricalcorrection of 6dB.
Note that this paper only considers direct transmission whereas structure-borne sound transmission
in the field between horizontally, vertically or diagonally adjacent rooms in heavyweight buildings
will involve flanking transmission. However, in these situations the propagation times for bending
waves across heavyweight walls and floors are sufficiently short that the use of L eq,125ms should bereasonable.
4.2 A-weighted Levels
This stage assesses whether it is feasible to estimate L AFmax from L Fmax values in one-third octave
or octave bands by subtracting the A-weighting and energetically summing them. The L AFmax
measurements are carried out with a high-pass filter above 20Hz and a low-pass filter below 6.3kHz.
For the prediction of L Fmax an A-weighting from 20Hz to 5kHz is applied. The frequency-dependent
L AFmax can be converted into a single value using an energy summation. Table 1 shows the differencesbetween the predicted and measured L AFmax. The differences are below 2.5dB which would be suitable
for most building acoustics applications.
Table 1 – Predicted LAFmax minus measured LAFmax
Ramp level

ΔLAFmax
(dB)

10dB

20dB

30dB

40dB

125ms ramp

1.9

2.4

1.5

1.6

500ms ramp

0.4

0.7

0.0-0.1

1s ramp

1.1

1.1

0.3

0.6

2s ramp

1.1

0.8

0.5

0.5

5s ramp

0.5

0.8

0.8

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5. CONCLUSIONS
Validated procedures have been developed to predict maximum Fast time-weighted sound pressurelevels in a receiving room due to time-varying vibrational power injected into a heavyweight floor.
Comparison between SEA predictions and the measured L Fmax in one-third octave bands shows thatthe difference is within ±3dB. To simplify the approach, a single empirical correction has beenassessed that could be used for simplified SEA-based models such as described in EN 12354-5. In
addition, it has been shown to be feasible to estimate L AFmax from predicted one-third octave band
L Fmax values with close agreement.
The approach described in this paper has the potential to be incorporated into EN 15657 andEN 12354-5 so that estimates of the maximum Fast time-weighted sound pressure level can be carriedout before machinery with a time-varying structure-borne sound power is installed in a heavyweightbuilding.

REFERENCES
1. EN 15657:2017 Acoustic properties of building elements and of buildings – Laboratory measurement ofstructure-borne sound from building service equipment for all installation conditions.
2. EN 12354-5:2009 Building acoustics – Estimation of acoustic performance of building from theperformance of elements – Part 5: Sound levels due to service equipment.
3. VDI 4100:2012 Sound insulation between rooms in buildings – Dwellings – Assessment and proposals
for enhanced sound insulation between rooms.
4. Robinson, M. and Hopkins, C. (2014). Prediction of maximum time-weighted sound and vibration levels
using transient statistical energy analysis – Part 1: Theory and numerical implementation. Acta Acustica
united with Acustica, 100(1), 46-56.
5. Robinson, M. and Hopkins, C. (2014). Prediction of maximum time-weighted sound and vibration levels
using transient statistical energy analysis – Part 2: Experimental validation. Acta Acustica united withAcustica, 100(1), 57-66.
6. Robinson, M. and Hopkins, C. (2015). Prediction of maximum fast time-weighted sound pressure levels
due to transient excitation from the rubber ball and human footsteps. Building and Environment, 94, 810820.
7. Hirakawa, S. and Hopkins, C. (2018). Experimental determination of transient structure-borne soundpower from heavy impact sources on heavyweight floors with floating floors using an inverse form oftransient statistical energy analysis. Applied Acoustics, 140, 74-82.
8. Reinhold, S., Hopkins, C. and Seiffert, G. (2018). Estimating maximum Fast time-weighted vibrationlevels from short equivalent continuous vibration level measurements of structure-borne sound sourceson heavyweight plates. Proceedings of the 11th European and Exposition on Noise Control Engineering(Euronoise), Heraklion, Crete, 1609-1616.
9. Späh, M. M. and Gibbs, B. M. (2009). Reception plate method for characterisation of structure-borne
sound sources in buildings: Assumptions and application. Applied Acoustics, 70, 361-368.
10. Reinhold, S., Hopkins, C. and Zeitler, B. (2017). Numerical simulation of a laboratory reception plateusing finite elements. Proceedings of the 43rd Annual Conference on Acoustics (DAGA), Kiel, Germany,525-528.
11. Reinhold, S., Hopkins, C. and Zeitler, B. (2017). Low-frequency structure-borne sound power
measurements using heavyweight reception plates. Proceedings of the 24th Congress on Sound andVibration (ICSV24), London, UK, 1-8.
12. Lyon, R. H. (1975). Statistical energy analysis of dynamical systems: Theory and applications.
Cambridge: MIT Press, ISBN 0-262-12071-2.
13. Hopkins, C. (2007). Sound Insulation. Butterworth-Heinemann, ISBN 978-0-7506-6526-1.

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