A new method for aircraft noise synthesis

D. Berckmans1, K. Janssens2, P. Sas1, W. Desmet1, H. Van der Auweraer2

1 K.U.Leuven, Department of Mechanical Engineering,Celestijnenlaan 300 B, B-3001, Leuven, Belgium2 LMS International, Interleuvenlaan 68, 3001 Leuven, Belgiume-mail: Dries.Berckmans@mech.kuleuven.be

AbstractThis paper presents a method to synthesize aircraft noise. The method provides designers with a tool forsound quality evaluation with which target sounds for future aircraft design can be developed. Quick andeconomic evaluations concerning the quality of sounds of different design alternatives or improvements onexisting aircraft become possible. The method has the potential to become a crucial tool in the determinationof the primary factors that determine the quality of aircraft sound.

1 Introduction

The noise associated with civil aircraft operations in the vicinity of airports has been the major environmen-tal noise problem since the late 1950s, when turbojet aircraft entered service [1]. The take-off noise of theearliest jet aircraft, expressed in maximum A-weighted sound level, was about 20 dB greater than that of thepropeller aircraft that they replaced. The noise of the earlier jets was controlled by multiple and corrugatednozzle schemes that shifted much of the sound energy to higher frequencies that travel less far in the atmo-sphere. However, these devices had significant performance penalties of about 1% thrust lost per decibelreduction. By the late 1960s, the world’s leading engine manufacturers had developed high-bypass-ratio en-gines, which were much quieter than the earlier engines, particularly on take-off, and provided much higherpropulsion efficiency. Also, concerted government and industry research lead to the development of quieterfans and turbines, providing a significant reduction in the pure tones that were characteristic for the earlierturbofan engines. Aircraft noise perceived on the ground is an issue of continuously growing concern andannoyance. In the period of 1960 to today, the effort to reduce the noise around airport continued to increase.A lot of programs including regulations pertaining to noise limits for aircraft types, time schedules for phas-ing older, noisy aircraft out of the fleet, detailed environmental assessment procedures, and the funding andmanagement of airport specific projects for the control of noise were developed. By continuously fightingthe loudest noise sources in aircraft, we reached the point where a lot of noise sources have an almost equalloudness nowadays, this in contrast with the situation 40 years ago. Fan, turbine, compressor, jet noise andaerodynamic noise due to flows around the body of the aircraft can all be dominant depending on the modeof operation. To achieve a noise reduction noticeable by humans on the ground, several of these sources haveto be reduced simultaneously. The fact that technological break-through is needed in several different areasat the same time causes pessimistic predictions about future achievable noise reductions of the total noiseof passenger aircraft. Efforts to reduce the annoyance caused by aircraft noise, should nowadays focuss onimproving the quality of the produced sound, rather than on lowering the sound levels only. The quality ofthe total produced aircraft noise can be improved by the modification of single noise sources; nowadays thisis in contrast with the sound levels of the total sound which can only be lowered by the concurrent abatementof several noise sources.

The human perception of sound is a complex mechanism, with an impressive sensitivity and dynamic

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range [2]. The human hearing is not equally sensitive to all frequencies, it is most sensitive to frequen-cies around 4 kHz. Humans perceive broadband noise by dividing the frequency axis in bands. Researcherdeveloped different types of bands to imitate and describe the functioning of the human hearing. Completeoctave bands are frequency bands of which the central frequency equals the double of the central frequencyof the previous band. Third octave bands are partial octave bands, the ratio between two successive centralfrequencies being 21/3. Third octave bands describe quite well the human hearing and are used in this re-search. When hearing broadband noise without dominant frequencies, the human ear perceives the centralfrequencies of all covered third octave bands. Several effects like masking, sensitivity, expectation pattern,mood. . . make the human hearing far more complex. Masking is a phenomenon that occurs frequently and,in hearing, it is generally defined as the interference with the perception of one sound (the signal) by anothersound (the masker) [2]. The interference may decrease the loudness of the signal, may make a given changein the signal less discriminable, or may make the signal inaudible. Despite the current knowledge about thehuman hearing, the human perception of sound is still too complex to be understood as adequately as neededfor accurate predictions of perceived sound quality in different circumstances by the present state-of-the-art.Not only loudness, but several other noise characteristics like roughness, tonality, sharpness determine thissubjective sound quality perception. Today researchers infer the quality of a sound by a jury of listenersthat evaluates the sound subjectively. Different attempts have been undertaken to infer perception-relevantmetrics from a sound fragment, but at present these metrics don’t succeed in reflecting the complete humansound quality perception. These metrics are however useful to determine specific aspects of sound qualitylike roughness, tonality, sharpness. . . .

This paper presents a synthesis method for aircraft sound. The method allows to quantify the subjectivehuman perception of aircraft noise by performing jury tests with well chosen synthesized sounds. Section 2formulates the objectives of the performed research. This is followed by a section that gives a descriptionof the time-frequency spectrum of modern passenger aircraft sounds. Section 4 discusses the developedsynthesis method and the next section presents the validation of this method. Section 6 provides someconcluding remarks. This research makes use of aircraft noise fragments recorded within the framework ofthe European FP6-STReP project SEFA (Sound Engineering for Aircraft). This project aims at developingmethods for sound synthesis of aircraft noise and models of human perception of noise annoyance that willhelp aircraft engineers to enhance the sound design of modern aircrafts.

The analysis of an aircraft design with respect to its sound quality is a very expensive and time-consumingproces. Since aircraft sound is produced by several different sources that are almost equally loud nowadays,the designer should be able to evaluate the influence of each individual source in several conditions in a fastand affordable way. Up to now, it is difficult to assess the impact of the improvement of one source on thequality of the total produced aircraft noise in different conditions. Several examples exist where changes toaircraft in the scope of noise reduction missed their effect completely due to a misjudgement of the impact onthe total produced noise. Since sound quality is not yet described as adequately as needed by sound metrics,real hearing sensations seem to be necessary to compare the sound quality of different designs and hence,a sound synthesis method is an essential tool. Design decisions shouldn’t be based on metrics or figuresany longer, but on the aurelization of the sound produced by each new design, with a focus on the soundproduced during take-off and approach because of the huge annoyance caused during these phases. Existingtechniques are not able to do this and have the shortcoming that a lot of technical knowledge is needed tointerpret metrics and figures in order to form proper conclusions about sound quality.

2 OBJECTIVES

The main objective of this research was the development of a synthesis method for aircraft noise up to a levelwhere humans can no longer hear differences between a measured sound and its synthesized counterpart.The envisaged aircraft are all aircraft types in the fleet of civil aviation anno 2005. Since the origin of almostall components present in aircraft noise is quite easy to determine nowadays, the designer should be able to

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carry out specific modifications to all desired noise sources to simulate a physical change of the concordantsound source in an existing aircraft or in a design alternative. In this way it should be possible to weighseveral design alternatives or modifications to existing aircraft. It should be possible for the designer, forinstance, to modify all tonal components in turbine noise to simulate what would happen if the turbine is lessnoisy, contains less high-frequency components, has a lower sharpness, etc. As a result, designers should beable to aim already at the beginning of the aircraft design towards a certain target sound of high quality. Thiswill accelerate the design cycle and make thorough design modifications affordable as they can be performedalready at the design stage. A synthesis method should facilitate the comparison and evaluation of severalchanges to existing aircraft or new designs in a quick and affordable way by performing a virtual simulationinstead of an expensive and time consuming change on real aircraft. In addition, it should be possible todetermine the ’average perceived sound quality by citizens’ by jury testing.

3 AIRCRAFT SOUND SPECTRA

This section analyses the spectral content of recorded aircraft noise fragments of different aircraft, represen-tative for the fleet of passenger aircraft in the year 2005. The actual method to synthesize aircraft soundsstarts from these recorded fragments and is explained in section 4. Different types of passenger aircraft havebeen studied, mainly aircraft with jet engines but also some smaller propeller driven aircraft. Both take-offand approach events are captured and the noise recordings are made according to annex 16 of the Inter-national Civil Aviation Organization (ICAO) convention. The sample frequency used to record the soundpressure is 44.1 kHz, the microphone positions and heights (1.2 m above ground level) are taken accordingto the standards [7].

Figure 1 shows a typical time-frequency spectrum of aircraft noise, measured during take-off. This spectrumshows the evolution of the distribution of energy in the sound across frequency. Figure 1 is obtained byconsecutive Hanning windowed discrete Fourier transforms (DFT) on short fragments of the recorded aircraftnoise [8]. The Hanning window is used to diminish the end effects in the DFT calculation. Each time-frequency spectrum is achieved by executing successive DFT’s. The frequency resolution is chosen to be3 Hz so the fragments are all 1/3 s long, overlapping fragments are used in this research. Only the mostrelevant part of the frequency axis is shown.

As a consequence of using the DFT, the energy distribution across frequency is considered to be constantwithin the duration of each fragment. Although this is not entirely correct, the introduced error will be smallbecause the fragments used here are short enough not to contain huge variations in the sound. Note that theupper and lower limits of the plotted dB scales are not taken constant throughout the various time-frequencyspectra in this paper for the sake of clarity. Figure 1 reveals the three major components in ground-perceivedaircraft noise: broadband noise, some tonal components and an interference pattern. Although the latterisn’t really a kind of noise source but rather the result of interference between direct and reflected noise, itis treated nevertheless as a different ’component’ in the synthesis method. In this figure, the aircraft passesthe microphone at around the twentieth second, corresponding with the bending points in the interferencevalleys and in the tonal components.

Broadband noise arises a.o. from the combustion chamber during the combustion process, from the turbu-lence in the jet of the engines and from air flow around the body of the aircraft.

Tonal components are mainly caused by several noise sources in the engine such as the turbine, the compres-sor and the fan. Moreover, they can arise from flows over cavities and over non-aerodynamic components ofthe aircraft (e.g. flows over the cavity where the landing gear is stored during flight and flows around the flapson the wings). Sometimes the tonal components don’t show up in a narrow frequency region as in figure 1,but seem to be rather smeared out over a larger frequency interval in the time-frequency spectrum. This canoccur for example when two tonal components with closely related frequencies exist (e.g. sources in left vs.right engine) or when the frequency of the source is changing fast around some average frequency. Figure 2shows an example of a recorded noise with two closely spaced tonal components, one from the left engine

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Figure 1: Time-frequency spectrum of aircraft noise measured during take-off, sound pressurelevel dB (re. 2 · 10−5 Pa)

and one from the right engine. In figure 2 the tonal components cover only an interval width of 40 Hz butsometimes this width can be well over 200 Hz. Human hearing isn’t always able to distinguish two closelyspaced components from each other and several psycho-acoustic effects may occur. Very often, the listenerhas the impression to hear one frequency modulated tone instead of two distinct tones with nearly the samefrequency.

The interference pattern in figure 1 is due to the fact that the recording microphone isn’t positioned at groundlevel, but at 1.2 m above this level. The time delay between the indirect noise that first reflects on the groundand then impinges on the microphone and the noise which impinges directly on the microphone results in aninterference pattern. The time and frequency dependence of the interference pattern can be explained by thereflection characteristics of the ground and the trajectory of the aircraft. Some huge aircraft develop a specifickind of tonal components. During high load conditions of the engine, i.e. primarily at take-off, shock wavesdevelop at the front of the fan blades when conditions of supersonic tip speeds occur. Each pressure wavehas the shape of a saw tooth and the produced tonal components with a very characteristic noise are thereforecalled buzz saw components [4]. ’Buzz saw’ is an effect that develops because the produced pressure wavesimpinge on the engine inlet, resulting in a clear directivity towards the front of the aircraft. Figure 3 showshow this phenomenon is visible in a time-frequency spectrum of recorded noise originating from a hugeaircraft during take-off. A discrete tone at the rotational speed of the axis and several of its harmonics arisein the spectrum. Besides the buzz saw components, also 2 conventional tonal components and an interferencepattern are clearly visible in figure 3.

The fact that the frequency spacing between the buzz saw components (approximately 100 Hz in figure 3) issometimes rather small requires a slightly different synthesis strategy as compared to the synthesis of othertonal components, see section 4. Because of the pronounced directivity of this noise, these components areonly audible when the aircraft approaches the (ground) observer. As soon as the aircraft passes the observer,this is approximately from the twentieth second in figure 3, the components are no longer perceived anddisappear in the time-frequency spectrum. The impact of buzz saw components on sound quality is clearlydistinctive from the impact of conventional tonal components. Literature already revealed that buzz saw isvery annoying for passengers inside the aircraft [4]; future research can reveal the influence of buzzsaw on

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Figure 2: Recorded time-frequency spectrum that exhibits two tonal components with closelyrelated frequencies, sound pressure level dB (re. 2 · 10−5 Pa)

the quality of the sound heard on the ground, by means of the developed synthesis method.

4 SYNTHESIS METHOD

The developed synthesis method always starts from recorded aircraft noise fragments. The impact of per-forming modifications to aircraft on the noise produced by the aircraft can be studied by this method anda target sound for future aircraft development can be defined. The synthesis method starts from recordedaircraft noise fragments. All fragments used here are recorded according to annex 16 of the InternationalCivil Aviation Organization (ICAO) convention. The noise is sampled at 44.1 kHz and all microphones arepositioned 1.2 m above ground level. To reach a synthetic aircraft sound which cannot be distinguished froma real recorded sound, it was found necessary to reconstruct all tonal components, broadband noise and theinterference pattern up to about 10 kHz. Although humans can hear noise up to approximately 20 kHz, the10 kHz threshold appeared to be sufficient for a good synthesis of aircraft noise as perceived heard on theground due to several masking effects that occur and the fact that there is almost no energy left in the soundabove 10 kHz. This section explains how each component has been synthesized. The synthesis of tonal com-ponents and broadband noise is explained first, followed by a description of the modeling of the interferencepattern.

4.1 Tonal components

To obtain a correct synthesis of a tonal component, both the frequency and the amplitude have to be re-constructed correctly in function of time. Special care must be taken in cases of smearing of the tonalcomponents over more than 10 Hz.

As can be seen in figures 1 and 3, all tonal components exhibit a curved shape in the time-frequency spectrum.This curve shaping is introduced by the Doppler effect. In the Doppler formula (see eq. 1), fo is the frequency

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Figure 3: Time-frequency spectrum exhibiting the buzzsaw effect, recorded during take-off, soundpressure level dB (re. 2 · 10−5 Pa)

in Hz measured at the position of the observer, fb is the broadcasted frequency in Hz, c is the speed of soundin the propagation medium in m/s and cso is the speed of the source in the direction of the observer in m/s.As long as the aircraft is approaching the observer (i.e. before the twentieth second in figures 1 and 3), ahigher frequency with regard to the actual broadcasted frequency of the source is perceived. After passingthe observer however (i.e. cso < 0 ), a lower frequency is observed.

fo = fb · c

c− cso(1)

Equation 1 cannot be used directly to calculate the Doppler shift in the envisaged synthesis since the speedof the aircraft towards the observer (i.e. the microphone here) isn’t known in practice. In the implementationused here, the user describes the frequency vs. time behaviour of one tonal component by indicating somepoints of the component in the time-frequency spectrum. By performing a lowpass interpolation, the time-frequency behaviour of the tonal component is inferred from the points indicated by the user. The obtainedcurve is then corrected based on available information in the time-frequency spectrum and the correctedcurve is used for further synthesis. The speed of the aircraft towards the observer in function of time isinferred from this curve by using the Doppler formula, eq. 1. After indicating the behaviour of this first tonalcomponent in the time-frequency spectrum, the user indicates one additional point for each additional visibletonal component in the spectrum. Tonal components that are not visible in the time-frequency spectrum arenot considered because it is assumed that those components do not contain enough energy to be perceivedby a human observer. This assumption didn’t lead to any audible inaccuracies in the synthetic sounds sofar. The time-frequency pattern of each additional tonal component is then calculated starting from thisadditional point, the Doppler formula (eq. 1) and the previously derived frequency vs. time behaviour ofthe first tonal component which determines the evolution of the speed of the aircraft in the direction of themicrophone.

Once the frequency vs. time behaviour of each visible tonal component is known, the amplitude of each tonalcomponent can be estimated. The evolution of the amplitude in function of time is not only important for

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the loudness perceived by a listener; also for example the amplitude rate of change determines the perceivedroughness. Using the DFT has the disadvantage that the time evolution of a non-stationary signal cannotbe covered. To estimate the amplitude of the tonal components though, the DFT was used despite thisshortcoming. The amplitude of every tonal component is estimated after a frequency dependent time interval,namely every 20 periods of the signal. The DFT is calculated on a 20 period fragment of the sound whichmeans that only a poor frequency resolution, dependent on the previously derived frequency of the tonalcomponent at that time, can be achieved. In practice, instead of calculating all values of the DFT, the DFTis only evaluated for the interval which contains the frequency of the tonal component at that time, to speedup the computation since the amplitudes at the other frequencies are not used. The amplitude of the tonalcomponent at a particular time is considered equal to the modulus of the DFT in the frequency interval wherethe component lies at that time. These energy-based calculations give only an indication of the amplitude,not a fully correct value because the results are (1) function of the frequency resolution, (2) are DFT basedwhile the signal is not stationary, (3) are erroneous if neighboring broadband frequencies are playing anon-negligible role in the energy calculations. Because the amplitude can only be estimated and cannot becalculated exactly, an additional correction factor is introduced. The value of the correction factor at eachdiscrete time step is found by dividing the energy of the tonal component in the recorded noise by the energyof the synthesized tone. The width of the tones along the frequency axis varies in time and plays an importantrole in the energy calculations. The correction factor is limited between 0.2 and 1.2 and the amplitude of thetone is finally found as the product of the amplitude before correction and the limited correction factor.

Because the time variation in the time-sequence of these components isn’t very accurate yet after these steps,each value of the estimated amplitude is replaced by the average of its own value and its adjacent values. Theaverage of only 3 values is used as this proved to give the best results during some trial and error tests [8]. Theuse of more values in the average causes less time variations and a sound that corresponds less with reality.The final synthesis of the tonal component is done as a sinus with time varying amplitude and frequency.

Buzz saw components are synthesized in a very similar way compared to the above discussed ’conventional’tonal components. Because of the small spacing between the buzz saw components however, the risk ofcross-talking appears, i.e. the amplitude estimation of a buzz saw component can be wrongly influenced bysome of its neighbouring buzz saw components. The higher frequency resolution needed for the estimationof the amplitude can only be reached by considering longer fragments. This is why 100 periods instead of20 periods are used for the amplitude estimation of the buzz saw components and the amplitude is only esti-mated every 100 periods. Further extension of the fragments isn’t advisable since the noise is not stationary.Fortunately, buzz saw noise is very tonal and it has been observed that it is not that critical to determine fastamplitude fluctuations of these components [8].

When a tonal component is smeared out over a frequency interval larger than 10 Hz, an additional operation isexecuted to simulate this smearing. Different techniques, like e.g. adding sine signals of various frequencieshave been tried, but finally adding white noise up to 100 Hz came out as the best solution for an adequatesynthesis. The amplitude of the added noise determines the width of the smearing and this can be adapted foreach individual component to achieve the best results. In the future also the 100 Hz threshold can be adaptedto achieve even better results; this was however not further evaluated here because of the already satisfyingresults for all noise fragments considered in this research.

4.2 Broadband noise

Broadband noise is synthesized in third-octave bands because of the analogy with the human hearing system.To be able to synthesize the broadband noise, only the amplitude in function of time has to be known foreach frequency band, the covered frequencies are determined by the limits of each third-octave band consid-ered. Although humans are able to perceive sounds up to 20 kHz, only the bands up to 10 kHz have beensynthesized. This threshold appeared to be sufficient since there are a lot of masking effects in aircraft noiseand since there is almost no energy left in aircraft noise above 10 kHz. In practice the synthesis happens

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from 35.5 Hz up to 11.220 Hz, because these are the lower, respectively, upper limits of the 40 Hz and the10 kHz third octave bands.

The amplitude of the broadband noise in each third-octave band in function of time is determined basedon the average energy that remains in each band after removing all tonal components from that band. Thisaverage value is scaled with the ratio of the total number of spectral lines in the band and the number ofspectral lines in the band not covered by a tonal component to estimate the total broadband energy in thatcomplete band at that instant in time. The energy on frequencies equal to the frequency of a tonal componentcannot be used in the average because it is impossible to distinguish how much of the energy belongs tothe tonal component and how much of the energy belongs to the broadband noise. The synthesis of thebroadband noise is accomplished by filtering white noise with the correct band pass filters and shaping theamplitude of the signal in function of time. Butterworth filters are used to perform the filtering because ofthe smooth characteristics of these filters and the flat magnitude response in the pass band [8]. Finally, allthird-octave band syntheses are summed together to reach the total sound synthesis of the broadband noise.

4.3 interference pattern

Interference is the effect that occurs when two waves that travel trough a medium interact with each other.The interference observed in the recorded aircraft noise arises from the combination of a direct and a reflectedwave. Smith [9] showed that the interference pattern in these sounds is caused by reflections on the ground.In his test set-up, aircraft sounds were measured with several microphones placed at different heights abovethe ground. Formula 2 and 3 indicate the frequencies in Hz at which constructive, respectively, destructiveinterference occurs. In both formula, c is the speed of sound in the propagation medium in m

s and ∆l is thepath length difference between the direct and the reflected sound in m.

fcon,j = j · c

∆lwith j = 1, 2, 3, ... (2)

fdes,k = (12

+ k) · c

∆lwith k = 0, 1, 2, 3, ... (3)

Figures 1 and 3 show both the time and frequency dependence of the interference pattern. To be able toresynthesize the interference pattern, the time delay of the reflected sound with respect to the direct soundin function of time has to be known. In addition, information about the reflection characteristics of thereflecting ground is needed. This research aims at developing a method that does not require additionalmeasurements besides noise measurements. The synthesis method makes reasonable assumptions aboutreflection characteristics of the ground and tries to infer all other information that is needed out of the time-frequency spectrum of the recorded noise.

All noise fragments used here are recorded with microphones that are placed 1.2 m above the ground andall aircraft pass almost right above the microphones. The required time delay is inferred from the timevs. frequency behaviour of one interference valley in the time-frequency spectrum. In the implementationused here, the designer indicates the behaviour of one interference valley by indicating some points of thatvalley. A polynomial of order 15 is fitted through the indicated points and this polynomial is used for furthersynthesis. The ground curve of the interference pattern (with k = 0 in formula 3) is inferred from thispolynomial, with the knowledge that the microphone is positioned 1.2 m above ground level and the factthat all aircraft pass almost right above the microphone. This means fdes,0 ≈ (1

2 + 0) · 3432.4 = 71.5 Hz at

flyover because the path length difference at flyover is about 2.4 m (twice the height of the microphone).Formula 3 gives an easy way to calculate the path length difference in function of time when the frequencyof a destructive interference valley in function of time is known. The time delay of the sound that is reflectedon the ground vs. the sound that is directly impinging on the microphone is then calculated by dividing thistime dependent path length difference by the speed of sound in the propagation medium.

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Figure 4: Frequency weighting factors for synthesis of the interference pattern. ——– weightingfor the part of the sound where interference is modeled. - - - - weighting for the part of the soundwhere no interference is modeled.

Figures 1 and 3 show that the interference pattern is no longer visible at higher frequencies due to the ab-sorption characteristics of the air and the ground. It became clear throughout the research that the frequencydependence of the interference pattern is not that critical to get a good sound synthesis [8]. The modelingof the frequency dependence of the interference pattern is nevertheless performed to reach visual agreementof the time-frequency spectra of the measured and synthesized sounds on top of the aimed auditive agree-ment. Most of the time no difference between the sounds with and without the modeling of this frequencydependance was heard by the listeners however. The time dependence on the other hand is more critical andcannot be neglected for good sound synthesis.Both the frequency up to where the interference pattern is clearly visible and the frequency from where theinterference pattern disappears in the time-frequency spectrum are indicated by the user. Inbetween thosefrequencies a transition region for the interference pattern is assumed. The synthesis method divides the sumof the synthesized broadband sound and all syntheses of tonal components into two parts: a low-frequencypart where interference is modeled and a high-frequency part were no interference modeling happens. Thefrequency variation of the reflection coefficient is modeled by the two simple weighting functions, shown infigure 4. The dashed line is the weighting for the part of the sound where no interference exists, while thesolid line shows the weighting for the part of the sound for which interference will be modeled. The sum ofboth weighting functions is always one, so that after modeling the interference pattern, both syntheses canbe summed together.

Usually, both weighting functions are applied on the sum of all broadband syntheses and syntheses of alltonal components. Here, only the broadband noise is used to illustrate the weighting. Figure 5 shows thetime-frequency spectrum of the broadband noise synthesis on which the dashed weighting of figure 4 wasperformed. On this part of the sound, no interference pattern is modeled. Figure 6 shows on the other handthe same broadband synthesis, now weighted with the solid line of figure 4. On this part of the sound, aninterference pattern will be modeled by using a time dependent reflection coefficient and the time delayderived earlier. The time dependence of the reflection coefficient is caused by the movement of the aircraftwith respect to the microphone. The reflection coefficient depends on the angle of incidence, which changescontinuously over time by the movement of the aircraft. It can be noticed that no interference is modeled yet

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Figure 5: Example of a part of broadband noise on which no interference will be modeled, soundpressure level dB (re. 2 · 10−5 Pa).

in figure 6 which serves only as the starting point for the interference modeling. The low-frequency patternsimilar to the interference pattern arises in the broadband spectrum because the third octave bands are verynarrow in this low-frequency region.

The time dependency of the reflection coefficient is assumed to behave like a Hanning curve. In this research,no measurements of the reflection coefficient were made, but good syntheses were achieved by assuming aHanning shaped time dependence of the reflection coefficient. The variation of the reflection coefficient ismodeled by using two half Hanning curves. The use of two half Hanning curves instead of one Hanningcurve is needed because the flyover point is not always in the middle of the recorded noise fragment sothat one symmetric Hanning curve cannot always be used. The reflection coefficient used in the developedsynthesis method has a shape as shown in figure 7. Both the time and frequency dependence are clearlyvisible.

To synthesize the interference pattern on the part of the sound shown in figure 6, half the sound is assumedto reach the microphone in a direct way and the other half is assumed to first reflect on the ground. Multiplereflections together with reflections on other obstacles besides the ground are not considered in this synthesis.

The part of the sound on which interference occurs needs both a synthesis for the reflected sound and asynthesis for the direct sound. The interference pattern is synthesized by using both sounds and the timedelay derived earlier. The reflected sound is achieved by weighting half the broadband signal with thereflection coefficient shown in figure 7. The direct sound is synthesized by dividing the solid line weightedbroadband noise by two.

After applying the earlier derived time delay by the use of a time delay filter, the direct and the reflectedsignals are summed together. The root mean square (RMS) of this summed signal is made equal to the RMSof the measured signal to reach the final sound synthesis.

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Figure 6: Example of a part of the broadband noise on which interference will be modeled, soundpressure level dB (re. 2 · 10−5 Pa).

Figure 7: Assumed behaviour of the reflection coefficient (both time (varying reflection anglebecause of movement of the aircraft) and frequency dependent).

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5 VALIDATION

During the execution of the above mentioned SEFA project, researchers measured the noise of 87 eventsof 45 different types of passenger aircraft. The measurements took place in Germany during 3 succesivedays in August 2004. The recordings include the noise of 50 take-offs, 34 approaches and 3 fly-overs. Allfragments are recorded according to annex 16 of the International Civil Aviation Organization convention.The validation of the developed synthesis method is executed by using 12 of these measured aircraft noisefragments that are representative for the diversity in the fleet of passenger aircraft in the year 2005. Thegroup of 12 fragments was chosen by a team of 8 international experts, with the purpose of aircraft noisesynthetization. Within the SEFA project, there exist strict agreements not to mention the names of the aircraftand hence all sounds are numbered.

After decomposition of the noise into its different components, no changes were made to any componentto be able to validate the synthesis method itself. The decomposition was immediately followed by resyn-thesis of the total sound. In case of a perfect synthesis method, no difference between the original and theresynthesized noise can be observed. This presumption is evaluated by a jury of listeners. Ref. [10] in-dicates that a jury should consist of 20 to 50 persons. Here the jury consists of 23 listeners between 16years old and 55 years old, all with normal hearing. Because the human brain is not able to accuratelyremember sounds longer than a few seconds, both the measured and the synthesized aircraft sounds havebeen divided into sections of 5 seconds. The jury has been asked to compare the synthesized fragment of5 seconds with the appropriate section in the measured sound. Each listener had to give his appreciationwith one of the following answers: totally different (TD), different (D), slightly different (SD) or similar(S). The instruction was to only use the score S (similar) in the case that absolutely no difference could beheard between the signals. Headphones were used in the test, since they are generally cable of reproducingaircraft noise with lower distortion, over a wider frequency range, and at higher intensity levels than are mostloudspeaker systems [11]. All members of the jury did the test independent of each other and could listento the sounds as much as wanted to form a final conclusion. In this first test, 71 fragments of 5 seconds arecompared with the corresponding fragment in the measured sound. In total, the jury of 23 persons answered3 times TD, 102 times D, 503 times SD and 1025 times S, as table 1 indicates. Although those scores arenot that bad, further examination revealed that the scores of this first validation test are heavily biased by thesound of a propeller driven aircraft (sounds 3 & 4) which was not adequately synthesized. The very rough,low-frequency propeller noise needs further research in order to achieve a good synthesis for this kind ofaircraft noise. Beside this roughness, another reason why propeller noise is not adequately synthesized isthe fact that the very-low-frequency tonal components are often embedded in the interference pattern in thetime-frequency spectrum, so that both amplitude and frequency determination are harder to accomplish. Forthose very-low-frequency components it is possible that a good sound synthesis cannot be reached withoutadditional measurements. Another shortcoming of this first synthesis results is that all sounds used in thisfirst evaluation test were only synthesized up to 7079 Hz. The reason for this is that all noise fragments thatwere used for initial development of the synthesis method had no significant amount of energy above 7000Hz. However 4 out of the 12 sounds that are used in this first validation test did contain a significant amountof energy between 7000 Hz and 10.000 Hz and most of the D (different) scores were due to these 4 soundsand the propeller sound. A new short jury test with sound syntheses up to 11.220 Hz showed that the actualscores of similarity between the 4 synthesized sounds and its measured counterparts can be highly improvedcompared to the results of the first test, without changing the basics of the synthesis method.

6 conclusions

Based on the performed validation test, the conclusion can be drawn that the developed synthesis methodis adequate for all jet engine aircraft in the fleet of passenger aircraft anno 2005. The presented synthesismethod is not able to achieve adequate syntheses for propeller noise. Additional research is needed to achieve

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S SD D TDsound 1 75 54 9 0sound 2 57 49 9 0sound 3 70 43 23 2sound 4 89 36 13 0sound 5 96 36 5 1sound 6 86 46 6 0sound 7 75 54 9 0sound 8 84 46 8 0sound 9 102 32 4 0

sound 10 92 35 11 0sound 11 104 32 2 0sound 12 95 40 9 0

total 1025 503 102 3total (%) 62.77 % 30.80 % 6.25 % 0.18 %

total w/o propeller (3 & 4) 866 424 66 1total w/o propeller (3 & 4) (%) 63.82 % 31.24 % 4.86 % 0.07 %

Table 1: Answers of the jury of 23 persons for the 12 selected sounds (71 fragments).

this goal. The very specific buzz-saw noise is adequately synthesized and the validations show that the use ofcomplex frequency-dependant ground reflection coefficients is not necessary. The presented method seemsadequate and more efficient. The developed sound synthesis method allows to evaluate the influence ofdifferent noise sources on the perceived quality of aircraft noise.

The developed sound synthesis method creates the opportunity to check the influence of different noisesources on the quality of aircraft noise. From the results of jury tests, the engineer can carry out specificchanges to an existing aircraft, based on the knowledge of the effect of these changes on the quality of theproduced noise. In this way, a cheap method is developed to evaluate a lot of possible design alternativesand a target sound for future aircraft design can be developed. The new aircraft sounds will not necessarilybe more quiet as compared to aircraft sound nowadays, but the quality of the sound will/should improve.Although the synthesis method has been developed for aircraft noise, it should be possible to extend themethod also to other forms of transportation noise and even to industrial noise sources.

Acknowledgements

The aircraft noise recordings have been carried out in the framework of the EC-FP6 STReP project SEFA(Sound Engineering for Aircraft, coordinated by Dornier GmbH). The support of the EC is therefore grate-fully acknowledged. The author would also like to thank the Institute for the Promotion of Innovation throughScience and Technology in Flanders (IWT-Vlaanderen) for the support of his research project.

References

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[2] M. J. Crocker, Encyclopedia of acoustics, Vol. 3: Architectural acoustics; Acoustical signal processing;Physiological acoustics; Psychological acoustics, John Wiley & sons, Inc., New York (1997).

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[3] P. Nelson, Transportation noise reference book, Butterworths, London (1987).

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[6] E. Zwicker, Procedure for calculating loudness of temporally variable sounds, Journal of the acousticalsociety of America, Vol. 62(3), American institute of physics (1977), pp. 675-682.

[7] ICAO, Environmental protection. vol. I: aircraft noise - specifications for aircraft noise certification,noise monitoring, and noise exposure units for landuse planning, available on http://www.icao.int/.

[8] D. Berckmans, P. Sas, W. Desmet, Model based synthesis of aircraft noise to give a subjective appreci-ation. Master thesis K.U.Leuven, Leuven (2005).

[9] M. J. T. Smith, aircraft noise, Cambridge University press, Cambridge (1989).

[10] H. Van Der Auweraer, K. Wyckaert, Sound quality: Perception, Analysis and Engineering, LMS inter-national, Leuven (2002).

[11] H. H. Hubbard, Aeroacoustics of flight vehicles vol. 2: Noise control, Acoustical society of America,New York(1994).

[12] Y. Guo, a statistical model for landing gear noise prediction, Journal of sound and vibration, Vol. 282,No. 1-2, Academic Press (2005) pp. 61-87.

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