WO2018178809A1

WO2018178809A1 - Noise level simulation method as well as computer readable medium and system therefore

Info

Publication number: WO2018178809A1
Application number: PCT/IB2018/051866
Authority: WO
Inventors: Christian Hegner; Peter JÄGER; Micha KÖPFLI; Jean-Marc WUNDERLI; Christoph ZELLMANN
Original assignee: Bundesamt Für Zivilluftfahrt
Priority date: 2017-03-28
Filing date: 2018-03-20
Publication date: 2018-10-04
Also published as: CH713630B1; CH713630A1

Abstract

The present invention relates to a Method for computing for at least one receiving point (R) a noise level generated by a sound source (S, 111), in particular an aeroplane, moving along a defined trajectory (116) with respect to the at least one receiving point (R), the method comprising the steps of: providing a sound propagation model for an airspace extending between the at least one receiving point and at least one estimated trajectory (115) along which the sound source is expected to be moving with respect to the receiving point; computing the noise level by entering the defined trajectory (116) into the sound propagation model and calculating a sound propagation between the sound source (S, 111) and the at least one receiving point (R) for each one of a number of different sound source locations (114) arranged along the defined trajectory. Furthermore, the present invention relates to a computer-readable medium containing computer readable instructions for enabling a computer system to carry out a method according the present invention. Finally, the present invention related to a computer system (117) adapted to carry out a method according to the present invention.

Description

NOISE LEVEL SIMULATION METHOD AS WELL AS COMPUTER READABLE MEDIUM AND SYSTEM THEREFORE

The present Invention relates to a method for computing for at least one receiving point a noise level generated by a sound source, in particular an aeroplane, moving along a defined trajectory with respect to the at least one receiving point. Furthermore, the present invention relates to a computer-readable medium containing computer readable instructions. Finally, the present invention relates to a computer system.

BACKGROUND

Under presently prevailing circumstances in densely populated areas, such as e.g. Europe, traffic managing and planning is subject to multiple influencing factors. One of these influencing factors, having a high importance and being treated with increasing sensitivity are noise levels caused by the traffic as they are perceived by the public in domestic as well as business areas. In particular for airborne traffic, noise levels generated by aeroplanes as sound sources perceived in areas near airports are determining the public acceptance of existing or planned take-off or landing routes, i.e. trajectories of the planes during take-off and landing.

Management and planning of such trajectories is further complicated particularly for traf- fic in that passenger numbers per year our steadily increasing. In the year 2016, approximately 3.5 billion passengers were travelling planes worldwide. It is being estimated that in 20 years, i.e. by the year 2036, passenger numbers in air traffic will increase to around 7 million passengers per year. Hence, the number of take-offs and landings will most likely increase as passenger numbers increase in a more or less proportional manner. The trajectories of aeroplanes during take-off and landing are from a technical perspective in general statically dependent on certain individual conditions of a respective airport and its surroundings, such as the orientation and length of runways or geological conditions, such as mountains, hills etc. Furthermore, from a technical point of view, a dynamic dependence of the trajectories results from certain temporal conditions, such as metro- logical conditions and traffic load. In addition to these technical conditions, the trajectories must meet legal conditions imposed by geographical parameters, such as international borders and further and boundaries, for example military zones, as well as temporal parameters, such as curfews. Especially the latter are mainly imposed by allowable noise levels near airports. Already today, aeroplane trajectories, particularly take-off and landing routes are being discussed on a highly emotional level between airport operators and airline carriers on the one hand, and the public on the other hand, while politicians may be regarded as a third party somewhere in between. In view of that aeroplane courses and hence their trajectories are more or less defined by predefined take-off and landing routes are crossing borders between countries and states, respective discussions take place on an international level.

Due to their high emotional level, such discussions, and hence recursively also the planning and management of the trajectories is cumbersome and time consuming. The discussing parties are often not capable of finding solutions or compromise due to a lack of objective data available on noise levels in affected residential and business areas. Instead, the discussions are held mainly based on mere assumptions and subjective interpretations of possible noise levels in respect of receiving points.

An objectification of the discussions is desirable in order to streamline the process of decision-making and to render it transparent for making fair decisions where no party feels overlooked, consequently enabling to increase planning certainty and thus saving costs and efforts. One way for providing a basis for objective decisions is the calculation of noise levels caused by aeroplanes at certain receiving points. Aircraft noise calculations according to the prior art are already being used as essential tools for land-use planning and management worldwide. They allow to assess and optimize noise abatement procedures for a quieter environment. Both topics are important elements of the Balanced Approach to Aircraft Noise by the ICAO. The former element is well established by conventional im- mission models, which are developed to calculate the sound level at the receiver. For this purpose, international harmonized methods such as ICAO Doc. 991 1 resp. ECAC Doc. 29 are used, but also national guidance as the AZB in Germany and national pro- grams like FLULA2 in Switzerland are applied. For the latter element, more sophisticated models, which describe the sound source and propagation separately, are needed to accurately calculate single flights. ANOPP, SIMUL, and PANAM are current programs which fulfil this condition. They all use similar semi-empirical emission models in their frameworks to describe the main sources of an aircraft. However, immission models for legal compliance as well as sophisticated semi-empirical models for scientific purposes have their limitations for the assessment of noise abatement procedures. For instance, the influence of the speed of the aircraft or its configuration on sound emission is not accounted for in the noise prediction by emission models, and is therefore missing in the calculation of the respective immissions, which is a major limitation. In addition, the acoustical description is simplified to generalized spectral classes (Doc. 991 1/ Doc. 29) or fixed to a standard atmosphere (FLULA2), which both increase the model uncertainty. These shortcomings are no issue for emission models, which predict spectra and directivity for each source on a high level of detail. However, they require very detailed input data of geometry as well as physical flight parameters (e.g. primary jet speed or airflow mass) for accurate predictions. Another drawback of noise calculation programs according to the prior art is the limited accessibility of these programs to other users and a very limited data base. SUMMARY

It is an objective of the present invention to remedy at least some of these disadvantages and drawbacks of noise calculation programs according to the prior art described above.

According to the present invention, this objective is at least partially achieved through the provision of a method according to independent claim 1 , a computer-readable medium according to claim 41 and a computer system according to claim 42.

According to the present invention, the above mentioned objectives are particularly achieved in that a method for computing for at least one receiving point a noise level generated by a sound source, in particular an airplane, moving along a defined trajectory with respect to the at least one receiving point, comprises the steps of:

- providing a sound propagation model for an airspace extending between the at least one receiving point and at least one estimated trajectory along which the sound source is expected to be moving with respect to the receiving point;

- computing the noise level by entering the defined trajectory into the sound propaga- tion model and calculating a sound propagation between the sound source and the at least one receiving point for each one of a number of different sound source locations arranged along the defined trajectory.

For a computer-readable medium, the above-mentioned objections are at least partially achieved in that the computer-readable medium contains computer readable instructions for enabling a computer to carry out a method according to the present invention.

For a computer system, the above-mentioned objections are at least partially achieved in that the computer system is adapted to carry out a method according to the present invention. This solution has the advantage over the prior art that in a first step, for the estimated trajectory, general parameters of an immission model for the calculation of a noise level at the at least one receiving point can be calculated with desired detail of an emission model, predicting spectra and directivity for the sound source at each point of the prede- fined trajectory on a high detail level. Furthermore, a simulation of sound propagation between the number of different sound source locations along the defined trajectory and the at least one receiving point can make use of a detailed acoustical description of the atmosphere and geological conditions to a degree of detail that requires and amount of computing power which does not allow for spontaneously adjusting model parameters because of relatively long calculation durations of e.g. several hours or days.

When the sound propagation model for the airspace extending between the defined trajectory and the at least one receiving point is at hand, then in a second step, actual sound propagation between a defined trajectory and the at least one receiving point can be calculated based on said sound propagation model. The defined trajectory may at least slightly differ from the estimated trajectory. However, the sound propagation model for the airspace is applied to the defined trajectory which can be easily altered and modified while benefiting from the desired detail of sound emission and immission calculation. This enables a fast simulation of noise levels and at least one receiving point which can be altered and recalculated virtually immediately, or at the most within minutes and hours. In other words, in a first step, based on general parameters applying to the estimated trajectory, the framework for sound propagation is calculated in a sufficiently detailed manner. In a second step, additional model parameters, such as fine adjustments of the trajectory of a vehicle and the type of vehicle are defined and actual sound propagation between the vehicle travelling along the defined trajectory and the at least one receiving point are being simulated within a very short timeframe based on the defined framework. Different scenarios for air spaces may be calculated for estimated trajectories at hand as a preparation for the simulation of a noise level generated by different kinds of sound sources and defined trajectories.

Thereby, on the one hand, any kind of planning and management facilities can quickly simulate noise levels for certain receiving points under different conditions, in particular by using different defined trajectories in order to optimise a route of a vehicle, e.g. an aeroplane, in terms of noise immission. On the other hand, respective simulations can be quickly provided to the public and altered according to public concerns of submissions. This helps in particular in objectifying the discussions between operators, carriers, politicians and the public regarding aeroplane routes and thus facilitates planning and man- agement of airborne traffic.

The inventive solution may be combined and improved by the following further embodiments, which are each advantageous on their own.

In some embodiments, the sound propagation is calculated based on at least one sound emission value of the sound source. The sound emission values may comprise overall sound level, frequency spectrum and directivity characteristics of a sound source. Sound emission values of certain sound sources may be modelled based on back propagated fly over measurements, which are separated into airframe and engine noise by means of a novel separation technique applied during the model development. Therefore, no complex measurements with microphone arrays are necessary and the model can be applied to any turbofan powered aircraft type.

In some embodiments, the at least one sound emission value is calculated in dependence of a sound radiation pattern associated with a type of the sound source for each one of a number of different sound source locations arranged along the defined trajectory. As the sound source travels along the defined trajectory, its sound radiation pattern may change. Such changes can be due to changes of operational modes and arrangements within the sound source as well as due to changes of an orientation and location of the sound source within the airspace. In regards of aeroplanes, operational modes, parameters, and arrangements may change along the defined trajectory and that throttle and flap settings as well as the state of landing gears are changed, thus altering respective sound emissions. Furthermore, by different orientations and locations of the aeroplane along the defined trajectory, the direction of jets from the engines and the orientation of slats as sound sources are altered.

In some embodiments, the sound radiation pattern is based on a sound power level associated with the type of the sound source. Certain types of sound sources may be as- sociated to certain sound power levels. The sound power levels may change along the defined trajectory.

In some embodiments, the sound power level is estimated based on travel parameters of the sound source derived from the defined trajectory. Such travel parameters may include but are not limited to e.g. client angles, rates of descent, top of descent, speeds and alike of an aeroplane. These travel parameters allow for estimating operational modes, parameters and arrangements, such as weight, throttle, flap and gear settings.

In some embodiments, the sound radiation pattern is based on a directivity pattern associated with the type of the sound source. Certain types of sound sources may have certain directivity patterns. For example, the jets or fans of an aeroplane may direct the sound in a certain manner. The different ways in which they direct sound and in which the direction of sound as alternated according to operational and travel parameters may be taken into account when calculating the sound radiation pattern.

In preferred embodiments, the sound propagation model comprises a direct propagation scenario and a complex propagation scenario; - wherein for the direct propagation scenario, a direct sound propagation between the sound source and the at least one receiving point is assumed; and

- wherein for the complex propagation scenario, a complex sound propagation between the sound source and the at least one receiving point is assumed. The direct propagation scenario may be applied for calculating the direct sound propagation either as a part of complex sound propagation at a certain point of time and location of the sound source with respect to the receiving point or in addition to complex sound propagation. In complex sound propagation, all kinds of reflections and other effects on sound travelling through the airspace can be taken account of. Thus, complex sound propagation is in general far more demanding in terms of computing power than direct sound propagation. In deciding between scenarios where complex some propagation can be neglected due to that direct some propagation delivers sufficient accuracy, omitting to calculate complex some propagation can help to minimise computing efforts and thus save time and energy when simulating noise levels in line with a method ac- cording to the present invention.

In some embodiments, for each one of the number of different sound source locations, an angle of sight is determined between the sound source and a horizon;

- wherein the direct propagation model is applied for angles of sight greater than a negligibility threshold; and - wherein it is being assumed that for angles of sight greater than the negligibility threshold, complex sound propagation becomes neglectable.

Using the angle of sight for distinguishing the scenarios for applying the direct sound propagation model and the complex sound propagation model is a simple condition for switching between the models according to the different sound source locations along the defined trajectory.

In some embodiments, for the direct propagation scenario, a homogeneous atmosphere within the air-space is assumed. Using a homogeneous atmosphere for direct sound propagation simulation helps to minimise complexities of the calculations involved. In turn, complex sound propagation simulation is preferably based on the assumption of an inhomogeneous, i.e. heterogeneous atmosphere within the airspace. Alternatively, or additionally, if desired, also the direct propagation scenario can make use of calculations which are based on the assumption of a heterogeneous atmosphere within the airspace. In some embodiments, the direct propagation scenario comprises at least one of a geometrical divergence model, a dissipation model, a barrier effects model, a foliage attenuation model, and a ground effects model for the airspace. Thereby, effects of geometrical divergence and a dissipation of sound within the airspace may be considered. Barrier effects, i.e. effects of any kind of obstacles, such as buildings, geological formations or alike, bordering the airspace can be considered. Foliage attenuation modelling is particularly helpful when calculations should be provided for different primary surfaces and/or seasons, where surrounding vegetation is assumed as carrying foliage or not. Modelling ground effects helps to simulate damping and reflection of sound according to the individual characteristics of the ground bordering the airspace. In some embodiments, the ground effects model comprises at least one of a spherical wave propagation determination, an uneven terrain model, a surface property variation, and coherence loss model for modelling a loss of coherence of different sound paths between the sound source and the receiving point. Spherical wave propagation determination involves the assumption that sound is emitted by the sounds source and then travels with respect to the sound source as a spherical wave through the airspace. Modelling an uneven terrain bordering the airspace enables to simulate reflection and damping of the sound on the ground. This may involve surface property variations, since e.g. roughness and composition of the ground may change along the airspace and with time. When travelling between the sound source and the at least one receiving point, sound propagation may be divided into different path by certain obstacles which lead to that the sound waves travelling along these paths are separated from each other such that they lose cohesion. Then, sound propagation is to be calculated separately for each of the paths.

In some embodiments, the complex propagation scenario comprises at least one of a meteorological effects correction model, an obstacle reflection model, and a forest diffusion model for the airspace. In the metrological effects correction model, particularly tem- poral changes in the atmosphere of the airspace are considered. In the obstacle reflection model, any reflections and obstacles between the sound source and the at least one receiving point are considered. With the forest diffusion model, diffusion effects in connection with sound waves impinging on forest structures are being simulated.

In some embodiments, the meteorological effects correction model adapts a calculation of sound dissipation within the airspace to local temperature and humidity values of the airspace. The propagation of sound within the airspace depends on the temperature and humidity of the air. Hence, by considering local temperature and humidity values, sound propagation within the airspace can be precisely simulated for different metrological conditions, such as wind, precipitation, fog, as well as different day times and seasons where some propagation is altered according to the respective metrological conditions.

In some embodiments, the meteorological effects correction model adapts a calculation of barrier effects within the airspace to vertical gradients of at least one of wind speed values and temperature values of the airspace. Wind and temperature within the airspace determine the reflection and diffraction of sound at obstacles bordering the air- space. Taking into account temperature and/or wind speed values in the calculation of barrier effects, helps to precisely simulate noise levels at the at least one receiving point for different metrological conditions.

In some embodiments, barrier effects include an acoustical shadow zone effect for at least one acoustical shadow area within the airspace where sound rays directly and/or indirectly emitted by the sound source do not directly reach the at least one receiving point due to upwind conditions identified based on the vertical gradients of the at least one wind speed value. In other words, under certain metrological conditions, the at least one receiving point may be shielded from sound waves by an obstacle in a way that the sound waves pass above and/or beside the at least one receiving point located in the acoustic shadow area of the obstacle.

In some embodiments, a residual sound exposure of the at least one receiving point located within the at least one acoustical shadow area is calculated based on at least one of a diffraction effects model and a scattering effects model applied to a sound ray passing along the at least one acoustical shadow area. Hence, even if the at least one receiving point located in an acoustic shadow area is not directly affected by sound passing and obstacle, that fraction and scattering effects on the sound by the obstacle may lead to residual sound waves reaching the at least one receiving point and at least partially contributing to the noise level simulated for the at least one receiving point.

In a preferred embodiment, a method according to the present invention further com- prises the steps of

- dividing the airspace into subspaces adjoining each other;

- calculating for each of the subspaces a subspace model for determining a finite sound propagation within each of the subspaces; - composing the sound propagation model from the subspace models with at least one boarder region between adjacent subspaces representing at least one of a virtual sound source and a virtual receiving point for a virtual sound transfer value representing a virtual sound power level transferred between at least two adjacent sub- spaces.

Thereby, calculating operations for simulating some propagation within the airspace can be distributed to the subspaces such that overall some propagation is calculated in an iterated manner. The bordering regions between the subspaces become virtual sound sources and virtual receiving points, via which sound waves are transferred from one subspace to the other. The bordering regions may be e.g. corners of the subspaces sharing same or adjacent coordinates as neighbouring subspaces, whereby the bordering regions of the subspaces form a three-dimensional grid. The subspaces may be regarded as cells within which attenuation factors for sound propagation is calculated according to the properties of each cell. The airspace is hence represented by a cell model. Attenuations may be calculated between every edge, vertex or corner point of the three- dimensional grid of the cell model and each receiving point. Based on these iteratively calculated attenuations, and overall attenuation of sound between the sound source and the receiving point may be calculated. The overall attenuation can then be used for computing for the at least one receiving point a noise level generated by a sound source moving along a defined trajectory with respect to the at least one receiving point. This computation based on the overall attenuation can be conducted instantaneously, i.e. iterative calculations between corner points of the subspaces are not necessary when the overall attenuation is at hand.

During calculation of immissions, i.e. noise levels at the at least one receiving point, which are caused by an aircraft in dependence of the position of the aircraft at a certain point along a trajectory, attenuations with respect to the at least one receiving point or a plurality of receiving points can be interpolated from the attenuations of the eight surrounding corner points of the three-dimensional grid. For computing immissions, receiving points may also be arranged along a grid of receiving points arranged at the ground. A sound source grid and a grid of receiving points may be independent of each other. In some embodiments, a transfer of virtual sound power values is calculated for a number of possible combinations of virtual sound sources and virtual receiving points. Especially after sound deflection, diffraction and scattering or alike, the sound ways may travel along different paths through the airspace. These different paths lead to a number of possible combinations of sound propagation from one space to another. In taking into account all possible combinations, sound propagation within the airspace can be precisely simulated.

In some embodiments, a virtual attenuation is calculated for each of the virtual sound sources and/or virtual receiving points, the virtual attenuation representing an attenuation of the virtual sound power value upon transfer between the virtual sound sources and/or virtual receiving points. In other words, within each subspace and/or for each transfer of sound between subspaces, a virtual attenuation of sound is calculated according to properties within the subspace and between subspaces, respectively. Such properties may again comprise any kind of metrological or other values discussed herein for simulating the propagation of sound with air while taking into account any boundaries and obstacles bordering the airspace.

In some embodiments, virtual attenuations are stored in a subspace database. In storing the virtual attenuations within a subspace database, the virtual attenuations may be promptly and quickly retrieved from the subspace database. This helps in quickly calculating some propagation within the airspace by relying on the virtual attenuations stored within the subspace database. Virtual attenuations may be used for computing and overall attenuation, as already outlined above. Receiving points may be grouped in sub-territories into which a landscape bordering an airspace around the trajectories can be divided. The sub-territories may constitute a tile pattern on the ground. For each sub-territory, overall attenuations derived from the virtual attenuations of the subspaces and/or the overall attenuations can be stored in the subspace database and/or a supplemental database enabling an efficient parallelisation of computing steps in a method according to the present invention. For receiving points within a sub-territory, attenuations with respect to all corner points of the three-dimensional virtual sound source grid can be stored in the same database. In some embodiments, during calculation of the noise level, the virtual attenuations are read from the subspace database. Thereby, the noise level simulation can be conducted instantaneously, i.e. more or less in real time based on the virtual attenuations stored in the subspace database. The subspace database may be updated according to a change of environmental conditions affecting the airspace. In some embodiments, the propagation model includes an intermediate attenuation interpolated between the defined trajectory and the at least one border region. It may be assumed that the actual defined trajectory crosses through the subspaces. Hence, the defined trajectory for most of the locations of a vehicle does not coincide with the border regions. For remaining segments of the sound paths between the actual location of the vehicle along a defined trajectory and respective border regions, and intermediate and attenuation is calculated in order to provide a precise simulation of sound propagation.

In some embodiments, the airspace is divided into the subspaces along a homogeneous horizontal grid with constant distances between the subspaces in a lateral direction and a transverse direction of the airspace. The division of the airspace along a homogeneous horizontal grid facilitates the definition of the subspaces which are thereby distributed on an equal manner and can have the same sizes along the horizontal grid. In some embodiments, the airspace is divided into the subspaces along a heterogenic vertical grid with an increasing height of the subspaces along a height direction of the airspace. In other words, the height of the subspaces increases with a growing distance of the subspaces from the ground. This helps to minimise the overall numbers of sub- spaces necessary to be established for representing the airspace. By minimising the overall numbers of subspaces, calculating efforts are reduced. Such a minimisation of the number of subspaces takes into account that with increasing height above the ground, the airspace and atmosphere may be regarded as becoming more and more homogenous. Furthermore, the higher above the ground, the fewer obstacles have to be taken into account when modelling the airspace. Hence, with the increase of height from the ground, the subspaces may become bigger while still providing sufficient increments for simulating sound propagation within the airspace.

In some embodiments, the subspaces have a cuboid shape. The cuboid shape results from that the horizontal and the vertical grid are comprised of straight lines which are arranged at rectangular angles with respect to each other. In other words, the horizontal and vertical grid are arranged so as to form a Cartesian coordinate system which facilitates calculations.

In some embodiments, the border regions are constituted by eight corners of each one of the cuboid sub-spaces. Thereby, the border regions can be easily defined. Sound propagation within the airspace divided into the subspaces is simulated by regarding the corners of the subspaces as virtual sound sources and virtual sound receiving points. Virtual attenuations may be calculated between the virtual sound sources and the virtual sound receiving points. However, as already outlined above, a grid of virtual sound sources can be different to a grid of receiving points. Furthermore, as receiving points also frontage points of surrounding buildings and/or other obstacles or any point located in a desired manner, e.g. measurement or recording points, can be used. In some embodiments, sound propagation between the sound source and the at least one receiving point is calculated both in the time domain and in the frequency domain. Thereby, time domain effects and frequency domain effects of the sound propagation, in particular attenuation of sound when travelling to the subspaces can be simulated. In some embodiments, a frequency spectrum of the sound propagation in the frequency domain is divided into frequency bands and the sound propagation is calculated for each of the frequency bands. By dividing the frequency spectrum to be considered for sound propagation in the frequency domain into different frequency bands, different sound wave characteristics as a function of wave length may be considered. Accordingly, cer- tain parameters and/or constants of the propagation model may change depending on the wave length and thus frequency band. Furthermore, computing operations necessary for simulating the sound propagation can be facilitated and minimised in that e.g. for lower frequency bands, other algorithms are applied then for middle and high frequency bands. For example, the frequency bands may be divided into a spectrum of thirds. This enables a one-third octave analysis and calculation in the frequency domain.

In some embodiments, the sound propagation is calculated with unweighted sound pressure levels and the noise level is displayed with A-weighted sound pressure levels. The calculation of some propagation with unweighted sound pressure levels allows for a simulation of sound propagation based on purely physical properties, whereas displaying sound pressure levels and/or noise levels with A-weighted sound pressure levels helps to illustrate the perception of the respective noise levels by human beings. Thereby, the actual perception of the noise level for human beings at a certain receiving point can be precisely simulated.

In preferred embodiments, the noise level is weighted with a human population value representing an estimated population of the at least one receiving point with a number of human beings at a predefined time when the sound source moves along the defined trajectory. When the at least one receiving point is a residential area, then it may be assumed that that residential area as a certain population value according to the number of human beings being present at the at least one receiving point at a certain time of day and/or year. Residential areas are for example highly populated, i.e. the actual popula- tion numbers more or less match a theoretical of human beings officially registered in the residential area, in general during night times and/or weekends, whereas during working or business hours, such as e.g. from 9 AM to 5 PM, residential areas are rather less populated. On the contrary, business areas are normally highly populated during the working or business hours, such that it may be assumed that in general during night times and/or weekends, the business areas are scarcely populated. Hence, weighing the noise level with a human population value representing the estimated population of the at least one receiving point at a predefined time helps to simulate the actual impact of the noise level in the population.

In preferred embodiments, calculating the sound propagation is distributed between a client device providing a number of client FLOPs per cycle and a computer cluster and/or mainframe computer providing a number of cluster FLOPs per cycle, wherein the number of client FLOPs per cycle is smaller than the number of cluster FLOPs per cycle. The client device may be a personal computer and an office over service provider who provides e.g. engineering services including the simulation of noise levels as discussed herein. The computer cluster may be any cluster of interconnected computers or data centres providing computing power measured in FLOPS which exceeds the computing power of the client device.

It is particularly of advantage, when the calculation of the sound propagation model for the airspace extending between the at least one receiving point and at least one esti- mated trajectory along which the sound source is expected to be moving with respect to the receiving point is carried out in the computer cluster, which provides sufficient com- puting power while being less accessible and flexible in terms of operation and intervention in the calculations as the client device. The client devices is then used for computing the noise level by entering the defined trajectory and the sound propagation model provided by the computer cluster. The computing power of the client device should be suf- ficient for calculating the sum propagation between the sound source and the at least one receiving point for each of a number of different sound source locations arranged along the defined trajectory which can be altered according to respective requirements as desired for simulating different sound sources and defined trajectories.

In some embodiments, at least one total sound attenuation data set representing an at- tenuation of sound along at least one sound path established between the sound source and the receiver is calculated from a number of partial attenuation value datasets generated by the computer cluster and representing different sound attenuation characteristics of the airspace for a respective scenario. The receiver may be the at least one receiving point. The partial attenuation value datasets may comprise the subspace da- tasets providing virtual attenuations for the individual subspaces of the airspace. In addition, the partial attenuation value datasets may represent different sound attenuation characteristics for respective scenario and that different metrological and/or population scenarios are considered. By pre-processing the scenarios with the computer cluster, they can be made readily available for the client device in order to swiftly simulate noise levels at the least one receiving point by making use of the at least one total sound attenuation dataset.

In some embodiments, the total attenuation value dataset is calculated by the computer cluster and transferred to the client device or calculated on the client device. In other words, the total attenuation value dataset can be completely calculated by the computer cluster in order to be then transferred to the client device, i.e. by downloading the total attenuation value dataset from the computer cluster by the client device or uploading the total attenuation value dataset onto the client device by the computer cluster. Furthermore, any total attenuation value dataset stored in a client device may be updated in a similar manner. On the other hand, at least some steps in the calculation and updating of the total attenuation value dataset may be performed on the client device. For example, if a transfer band with between the client device and the computer cluster has certain limitations, which do not allow for transferring the total attenuation value dataset from the computer cluster to the client device on a regular basis, certain calculation and update procedures may rather be performed locally on the client device by e.g. only differentially recalculating or updating the total attenuation value dataset. In some embodiments, a sound footprint is provided comprising at least one mean noise level at the at least one receiving point; and wherein the at least one mean noise level is associated to one of a bundle of sound source trajectories. The sound footprint may be calculated with a plurality of estimated and/or defined trajectories. For each estimated and/or defined trajectory, a mean noise level may be calculated for the at least one re- ceiving point. Therefore, when carrying out the actual simulation of the noise level, the footprint may be used for swiftly calculating noise levels based on the at least one mean noise level associated to at least one of the plurality of estimated and/or defined trajectories. This helps in minimising computing efforts and facilitating, thus accelerating simulation operations according to the present invention. In other words, a calculation of sound propagation as well as a calculation of footprints, representing average immissions caused by an aeroplane of a certain type traveling along a certain trajectory, i.e. route, based on pre-calculated attenuations, is advantageously carried out on a computer cluster or mainframe computer. Simulation of single flights and calculations of superimpositions of footprints based on traffic ratios for com- putation of a traffic scenario may be carried out on a client device for easy accessibility and alterability In some embodiments, the sound footprint is calculated by the computer cluster and transferred to the client device. Thereby, the computer cluster has two sound prints available for quickly altering and then computing different scenarios of sound propagation is leading to respective noise levels at the at least one receiving point, based on the re- spective footprint. The footprint may therefore be transferred to the client device from the computer cluster as described above with relation to the total attention value datasets.

In some embodiments, a superposition of at least two footprints is calculated by the client device. In other words, the client device may superimpose several footprints in order to interpolate simulations or quickly provide different but superimposing simulations of the sound propagation and thus noise levels at the at least one receiving point. This helps to quickly provide and swiftly adjust noise level simulations according to the present invention.

In preferred embodiments, a method according to the present invention further comprises a data preparation step, wherein a number of source points corresponding to the different sound source locations along the defined trajectory is defined. Through defining the number of source points, sound propagation simulations maybe calculated for each one of the number of source points. In view of the high computing efforts involved therein, such calculations may e.g. be done by the computer cluster in order to be made readily available for the client device. In some embodiments, the sound propagation model is calculated based on at least the number of source points, a number of receiving points, and a geo data set representing a geological environment of the airspace. Thereby, the sound propagation model initially considers the source points, the receiving points and the geo data in a pre-calculated manner. Based on such pre-calculations, any further data, such as sound source param- eters, trajectories, and/or metrological data may be entered into the sound propagation model in order to refine the model. Since the initial consideration of source points, receiving points and geo data can require far more computing power than refining the model by the sound source parameters, trajectories, and/or metrological data, such a pre-calculation helps to minimise computing efforts and time when refining the model according to the desired source parameters, trajectories, and/or metrological data.

In a preferred embodiment, the at least one sound source is an airborne vehicle. Such an airborne vehicle may be an aeroplane, such as a civil or military use jet plane, or a helicopter, or alike. According to the present invention, numbers different types of such airborne vehicles may be modelled. For sound source modelling, acoustic overfly meas- urements may be conducted, for measuring sound emissions based on recordings of real air traffic near airports or alike.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to describe the manner in which advantages and features of the disclosure can be obtained, in the following a more particular description of the principles briefly described above will be rendered by reference to embodiments thereof which are illustrated in the appended drawings. These drawings depict only exemplary embodiments of the present disclosure and are not therefore to be considered to be limiting of its scope.

In the drawings: Fig. 1 shows a schematic illustration of a ray tracing algorithm to derive the sound path from source S to receiver R in a method according to an embodiment of the present invention; Fig. 2 shows a schematic illustration of a measurement layout in line with a method according to an embodiment of the present invention;

Fig. 3 shows a schematic illustration of flight-path axis system with longitudinal and lateral polar angles Θ and φ; Fig. 4 shows a schematic illustration of an angle coverage by a given measurement setup for a short take off (left) and two flights with different lift off points (right), for two microphones (I: φ ~ 40°; II: φ ~ 0°);

Fig. 5 shows schematic diagrams illustrating Directional uncertainty for radar data in a distance of 1 km (left) and 5 km (right) before touchdown; Fig. 6 shows a schematic illustration of a far range measurement setup at an airport in line with a method according to an embodiment of the present invention;

Fig. 7 shows a flowchart illustrating steps of data processing from measurements to an emission data set at the source according to an embodiment of the present invention; Fig. 8 shows diagrams illustrating results from engine run-up test conducted with exemplary aircrafts A330-300;

Fig. 9 shows two diagrams illustrating an exemplary influence of N1 on L

Fig. 10 shows two diagrams illustrating an exemplary influence of Ma on the sound emission level of the A320 aircraft; Fig. 1 1 shows two diagrams illustrating an exemplary distribution of measured flap handle positions of the A320 aircraft in dependency of the Ma-Number; Fig. 12 shows two diagrams illustrating an exemplary influence of gears on the sound emission of the A320 aircraft at approach in idle;

Fig. 13 shows a diagram illustrating steps of a process of model development and data separation according to an embodiment of the present invention;

Fig. 14 shows three diagrams illustrating a data separation example for the A320 at

100 Hz;

Fig. 15 shows a diagram illustrating an exemplary correction factor for energy mean over frequency for the A320 aircraft;

Fig. 16 shows two diagrams illustrating an exemplary coefficient of determination over frequency;

Fig. 17 shows two diagrams illustrating exemplary spectral directivity patterns of the

A320 aircraft for departure at high power setting;

Fig. 18 shows two diagrams illustrating exemplary spectra for final approach and take-off at high power setting for the A320 aircraft;

Fig. 19 shows two diagrams illustrating exemplary spectra for final approach and take-off at high power setting for the E170 aircraft;

Fig. 20 shows two diagrams illustrating exemplary spectra of an approach of an

A320 aircraft with full flaps and extended gears at Θ = 130°;

Fig. 21 shows two diagrams illustrating exemplary spectral directivity patterns for a departure at low power setting; Fig. 22 shows two diagrams illustrating exemplary Longitudinal directivity of the overall L_w for three different take-off power settings of the A320 aircraft;

Fig. 23 shows two diagrams illustrating exemplary lateral directivity of the overall L_w for three different take-off power settings of the A320 aircraft;

Fig. 24 shows six diagrams exemplarily illustrating two approaches in idle power setting and extending gears and high lift elements at a receiver approx. 15 km in front of the runway threshold;

Fig. 25 shows two diagrams illustrating exemplary spectra of an approach of an

A320 aircraft with idle power approx. 15 km in front of the runway threshold;

Fig. 26 shows two diagrams illustrating exemplary spectra of an approach of an

A330 aircraft with idle power approx. 15 km in front of the runway threshold;

Fig. 27 shows two diagrams illustrating an exemplary radiation balance for an exemplary day in combination with the wind speed and meteorological classes representing different conditions during daytime;

Fig. 28 shows three diagrams illustrating exemplary temperature, wind and humidity profiles for an exemplary day at 10 a.m.;

Fig. 29 shows three diagrams illustrating exemplary temperature, wind and humidity profiles for an exemplary day at 9 a.m.;

Fig. 30 shows two diagrams illustrating exemplary selected temperature and humidity profiles for an exemplary day between 9 a.m. and noon;

Fig. 31 shows a schematic illustration of a calculation scenario based on a flight path; Fig. 32 shows a diagram illustrating an exemplary variation of air absorption of a homogenous atmosphere shifted to momentary conditions to a uniform atmosphere with averaged conditions;

Fig. 33 shows a diagram illustrating an exemplary variation of air absorption of a homogenous atmosphere shifted to momentary conditions to a uniform atmosphere with averaged conditions;

Fig. 34 shows two diagrams illustrating exemplary differences in air absorption between a homogenous atmosphere at momentary conditions and COSMO-2 profiles;

Fig. 35 shows two diagrams illustrating exemplary differences in air absorption between idealized profiles and COSMO-2 profiles;

Fig. 36 shows a diagram illustrating an exemplary influence of the variance of dissipation on the A-weighted spectrum at a receiver;

Fig. 37 shows a schematic perspective view of a subspace used in model for calculating attenuations in line with a method according to the present invention;

Fig. 38 shows a schematic perspective view of an air space divided into subspaces in line with a method according to the present invention; and

Fig. 39 shows a schematic diagram illustrating a system for performing a method according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE DRAWINGS

One embodiment of the present invention is a method and a corresponding computer- implemented time-step program for aircraft noise calculation, in which sound source and propagation computation are strictly separated from each other. In contrast to the simu- lation model FLULA2, previously developed at the Swiss Institute for Materials Science and Technology (EMPA) for the acoustic investigation of complex scenarios such as yearly air traffic, the program according to an embodiment of the present invention focuses on single flight events to investigate and optimize noise abatement procedures by using either generic data, e.g. from a full flight simulator, or cockpit data from real flights. The aircraft as a sound source is described by physical laws and empiric data to scale with flight parameters such as power setting or speed and aeroplane configuration (slats, flaps, landing gear). To gain a sufficient database for different aircraft and engine types, extensive measurements under real air traffic at Zurich airport have been conducted.

A highly sophisticated sound propagation model is adapted to the special characteristics of aircraft noise calculations. The sound emission and propagation model are combined in a geographical information system. This interface will allow for the preparation of projects, perform the execution of calculation tasks and yield helpful tools for the analysis and presentation of results. Besides single flight events, the algorithms and program structure will also allow calculating complex scenarios such as yearly air traffic. While the emission model causes higher effort in preparing the input data, it has no relevant effect on calculation time. In contrast, the efficiency of propagation model is crucial. Sound Emission Model

A semi-empirical sound emission model according to an embodiment of the present invention is based on a combination of data measured under real air traffic with generalized physical laws establishing the relation between flight configuration and sound emission, including information on the frequency spectrum and directivity. Thereby, also results and experiences of the MODAL research program of the German Aerospace Center are considered. In the close vicinity of the airport, 3D sound directivity patterns are established, which represent the stationary flight conditions of initial climb and final approach. In larger distances to the airport, it is not possible to cover a wide range of polar angles. Possibly, sound directivities cannot be established. However, measurements are still of interest to determine the sound emission for different flight conditions. Therefore, mobile measurement stations are used at numerous different locations in distances up to 25 km from the airport. If directivity cannot be determined at far-away locations, spectral sound level differences are used as a fall-back option to account for changes in flight configu- ration.

Cockpit data is used to determine the flight configuration of the measured aircraft events. Such cockpit data is available for example for the Swiss aircraft fleet, namely for the Airbus A320 family, the A330-300, the A340-300 and the Avro RJ100. The cockpit data covers all necessary information in high time-resolution, such as flight path, orientation in space, true airspeed, rotary speeds of the engines as well as the position of flaps, slats and gears. For airplanes of other airlines, where cockpit data is not available, the ground speed and the bank angle can be derived from the flight path. Additionally, the low compressor speed (N1 ) will be estimated by spectral evaluation of the acoustical data as an indicator for power setting. This method works accurately in close vicinity of the airport. In larger distances with highly attenuated signals, the evaluation of N1 is more challenging. Sound Propagation Model

Calculation of sound propagation in a method and computer-implemented program according to an embodiment of the present invention is developed based on a model named sonX, having a propagation core which is being optimized from an acoustic point of view as well as in terms of performance.

The propagation model of sonX applies to point sources. Direct sound is calculated on the basis of vertical terrain sections from source to receiver including buildings and other barriers. The calculation is conducted in two steps. In a first step, a calculation under the assumption of a homogenous atmosphere is performed. Thereby geometrical diver- gence, dissipation according to ISO 9613-1 , barrier and ground effects as well as foliage attenuation according to ISO 9613-2 are taken into account. Barrier effects can be calculated e.g. as implemented in ISO 9613-2. For the calculation of ground effects, an analytical solution for spherical waves is used, which has been extended for uneven terrain and varying surface properties. In a second step the meteorological effects on sound propagation are determined, namely, the influence of local temperature and humidity on dissipation and consequences of vertical gradients of wind and temperature on shielding effects. The latter is done using a ray tracing algorithm, which derives the sound path from source to receiver including possible barrier edges for a given profile of the effective speed of sound. Fig.1 shows a ray tracing algorithm to derive the sound path from source S to receiver R. As an additional effect the evolution of acoustical shadow zones can be derived. Reflections at buildings and walls are taken into account. The model distinguishes between coherent, specular reflections and scattering. Diffuse reflections from forest edges and cliffs are represented by two separate models. The sound propagation modelling is per- formed in one-third-octave bands. For aircraft noise a frequency range from 20 Hz to 5 kHz is applied. Simulation Tool

According to the time-step concept, a single flight is represented by source positions that follow the aircraft trajectory with a given time step, typically of one second. At each position the angle-dependent sound emission is calculated with the momentary power set- ting, aeroplane configuration and orientation. At a given receiver location, the contributions from each source position are summed up in chronological order. From the resulting level-time histories, acoustical quantities such as equivalent continuous sound pressure level or maximum sound pressure level can be derived.

The resulting simulation tool is used for the detailed analysis of single flights, as well as for the calculation of complex scenarios, processing several 10Ό00 flights to produce noise maps of large areas of several tens of square kilometres. In the latter case the computing time is a major issue, which will be reduced by two measures.

Firstly, a distinction of the propagation situation is introduced. If sound propagates close to the ground, a direct model as described above in relation with Fig. 1 is used. For large aircraft heights, in contrast, the situation is much simpler because no shielding effects occur and the laborious processing of terrain profiles can be omitted. Furthermore, the influence of temperature and humidity on the dissipation is the only relevant meteorological effect. In addition, direct sound dominates and reflections can be neglected. Therefore, a simplified approach is applied, accounting only for geometrical divergence, dissi- pation and a standardized ground effect. As a criterion for the distinction of complex and simplified situations, the angle of sight relative to the line of horizon is used.

Secondly, the detailed or complex sound propagation calculations are done prior to the actual aircraft noise calculations and the resulting attenuations are stored in a look-up database. For that purpose, an airspace is subdivided into basic volumes of rectangular shape each constituting a cell-like subspace. A sound propagation calculation is performed for each of the eight corners of those cells that are actually flown through by aircraft. During the simulation of single flights, the relevant attenuations are derived by interpolating at the actual source position from the values of cell corners according to the database.

To avoid inconsistencies at the transition from the simplified to the sophisticated or complex model, dissipations per meter are pre-calculated with sonX for given meteorological conditions and stored in a look-up table for different layers of the atmosphere. During the single flight simulation, attenuations are either be accessed from the database or, in the simple case, directly calculated using the latter dissipation values.

Measurement Concept

Measurements are done at a public airport, e.g. Zurich Airport, under real air traffic, which allows collecting the dominant commercial aircraft types operating on comparable air- ports. Due to different runway lengths, operational concepts and destinations at the airport, a large variety of flight parameters can be gathered for the development of the semi- empiric sound source model. Independent measurements are done in small as well as in large distances from the airport.

Fig. 2 shows a measurement layout on runways 16, 28 and 34 of the airport. In close vicinity of the airport, data for 3D directivity patterns are collected by placing six to eight microphones next to the runways. The angles covered depend on the microphone position as well as on the take-off point that varies up to 500 m for the same aircraft type and up to 1500 m between different aircraft types, mainly because of different take off weights and thrust levels. Therefore, the microphones are located not only at the end of the runways, but also alongside the runways to catch early take-offs. During daytime, most of the data can be collected on runway 28 (departures to the west) and on an additional runway (approaches from the north, not shown). Due to German air traffic restrictions during early daytime hours (6 to 7 a.m.), some aircraft types are approaching from the south only (runway 34). Besides, heavy aircraft types such as the A330 or A380 normally take off to the south from runway 16. Because these types are acoustically relevant, measurements are conducted on runway 16/34, too. To cover a wide range of polar angles and hence cumulate enough data for the 3D directivity patterns, the locations of the microphones can be optimized.

For larger distances, approximately twelve microphone locations up to 25 km from the airport are installed, which cover different flight configurations. Departures are measured along the nominal flight track to the west of runway 28 and to the east from runway 16. Approaches are only measured on runway 34, as sufficient data for all aircraft types are available there.

Flight paths are determined in close vicinity of the airport (time and position) by an optical tracking system. In large distances from the airport the requirements in terms of the accuracy of the flight path localization are lower and radar data should be sufficiently accurate. These systems are needed particularly for the aircraft of airlines where no cockpit data are available. For validation of tracking data derived from different sources, a mobile multilateration system is used. Prediction of Angle Variety for 3D Directivities

To establish reliable 3D directivity patterns, a wide range of polar angles has to be covered. The microphone positions have been optimized accordingly, using a Matlab program predicting the coverage of the polar angles. As the take-off positions are very var- iable, flight paths derived from radar data of different aircraft types and with an early and a late take-off point per type are used as input data for the prediction tool. For each discrete source position (n) of the selected flight path, a relative vector to a micro

phone is was determined described in aircraft-carried normal earth coordinates (index g) as defined in DIN9300-1 according to equation (1 ) below. As all exemplary data is given in Swiss coordinates CH1903, the x_g-axis is oriented to true north.

With above equation (2), the vector is transformed into the Cartesian flight-path axis

system (index k, cf. Fig. 3) to determine the polar angles from each source position to the microphone. As information of the inclination angle is usually unavailable, the influence on aircraft orientation is neglected but subject to future investigations. The transformation matrix is transformed into the flight-path.

Fig. 3 shows a schematic illustration of a flight-path axis system with longitudinal and lateral polar angles Θ and φ. The polar angles Θ and φ for each discrete point of the flight path are determined by the law of cosines with the vector r_k,mi_C (Eq. 2) respectively the vector r_k,mic,yz and the unit vectors Xk and z_k as shown in Fig. 3 and in accordance to equations (3) and (4) below.

In the calculations, the part of the flyover from shortly after take-off up to 1500 ft height above runway is considered. This flight segment represents an almost stationary flight with constant speed and power setting. The aerodynamic noise of the gears, which are retracting in this phase, may be neglected due to the dominance of the engines. A height of 30 ft or a climb angle of 10° is proposed as criterion to start the evaluation, while the cutback at 1 ,500 ft is the criterion to end the measurement.

Fig. 4 exemplarily shows results of the prediction tool, namely, the resulting polar angles for given flight paths, plotted in flight-path axes with normalized vectors on a one side of the half sphere that represents the bottom side of the aircraft. (Only one side is plotted, as the sound directivity will be modelled symmetrically along the longitudinal axis, Xk). For a flight path with a short lift off, almost all microphones show a good coverage in Θ because of their location in front of the lift off point. While the data will be limited for angles of Θ between 15° and 170°. However, these angles are negligible with respect to their sound contribution. Further, even if the angle coverage of a single flyover is insufficient, the variation of the flight paths of a statistical adequate number of events will fill this gap, as shown in Fig. 4 (right). Within the marked surfaces for two exemplary microphone positions, good data coverage can be predicted. For the optimization of the microphone positions shown in Fig. 2, all eight microphones of a given setup are calculated. The positions are being optimized for different flight paths of different aircraft types on each runway covered by the measurements. In addition, an example of a final layout as illustrated in Fig. 2 also depends on various other conditions such as safety restrictions at the airport, inaccessibility of some areas and acoustically disadvantageous locations with reflections or high background noise.

Directional Uncertainty

Reliable 3D directivity patterns require a precise determination of the aircraft position, which affects the accuracy of the polar angles. Their standard uncertainties, ue and u₉ (68% confidence interval) may be estimated by the law of propagation of uncertainty, based on the uncertainties of the horizontal and vertical aircraft position, by applying below equations (5) and (6) to above equations (3) and (4).

where Xk is the longitudinal axis, yk the lateral axis and z_k the vertical axis of the flight- path axis system (Figure 3). The quantities of ue and _υφ are quantified for radar data which has a lateral tolerance of 230 m and a vertical tolerance of 46 m. This estimation yields an upper limit for ue and u₉, as other positioning systems such as cockpit data are more accurate. Assuming a rectangular distribution within the tolerance limits, the conversion from tolerances t to standard uncertainties u_t can be calculated according to below equation (7) as

Fig. 5 shows schematic diagrams illustrating directional uncertainty for radar data in a distance of 1 km (left) and 5 km (right) before touch down. The microphone position is shifted sidewise from 0 to 100, 200 and 300 m. Top: Glide path; Middle: Uncertainty ue; Bottom: Uncertainty u₉. (Note the different scales of the standard uncertainties for 1 km.)

Intermediate Conclusion regarding Data Acquisition

The above described model for a method and computer-implemented program according to an embodiment of the present invention accounts for flight configuration parameters and hence fulfils the requirements to acoustically optimize flight procedures. For the de- velopment of such a model, the sound emission model in function of the flight configuration and the underlying sound source data base are crucial. Extensive measurements are therefore to be carried out in close vicinity and far away from the airport in question, e.g. Zurich. A particular focus is set on the development of reliable 3D sound directivity patterns. The latter requires optimized microphone positioning for large polar angle cov- erage. The prediction of the polar angle coverage of a certain measurement layout is of great help to optimize the measurement setup. Furthermore, the determination of polar angles itself must be reliable. Their uncertainties are therefore estimated exemplarily for a typical approach. The results show that radar data is sufficiently accurate for measurement positions far away from the airport (uncertainties of 0.6°), while other systems are required in close vicinity of the airport.

Using a hybrid, case sensitive propagation model in combination with an attenuation database, it is possible to provide a simulation tool with high flexibility and accuracy without increasing the computational demand. A major advantage of the attenuation database is that once established for an airport, it can be reused for numerous calculations. Further steps are the evaluation of the sound source data in combination with the tracking data, the development of the sound emission model and the integration into the simulation tool in line with a method and computer-implemented program according to an embodiment of the present invention.

Sound Source Model for Aircrafts in Dependency on Flight Conditions

Based on the above-described measurement set-up and data sources, a sound source model for vehicles, in particular airborne vehicles or aircrafts in line with a method and computer-implemented program according to an embodiment of the present invention takes into account respective flight conditions of the aircraft.

Input Data - Measurements and Data Sources

As already outlined above, acoustic overfly measurements of real air traffic are performed around a public airport, e.g. Zurich. To cover a wide range of typical flight condi- tions, microphones are placed in the vicinity of the airport but also far away in distances of up to 20 km.

Fig. 6 depicts the measurement setup in the far range of the airport, including approaches from south and two departure routes, covering wide- and narrow-body aircraft. Microphone locations 1 -10 (circles) and typical flight tracks for departures from runway 16 (solid lines) and runway 28 (dashed lines) as well as approaches on runway 34 (dash- dotted lines) are shown in fig. 6. The ten autonomous locations are equipped with omnidirectional free-field microphones at arranged at a height of 10 m above the ground. Microphone locations for departures are selected so as to cover flight conditions after cutback, during acceleration, and continuous climb in clean configuration. During approach, the microphone locations were distributed along the glide path during deceleration of the aircraft for the final approach. Measurements in close vicinity of the airport, within 2.5 km distance from lift off or touch down, provide data for the final approach as well as for initial climb over a wide range of radiation angles. For each of the three measured runway directions in the close range, eight omnidirectional free-field microphones are installed at a height of 4 m above the ground. An optical tracking system and Multilateration (MLAT) delivers position data with high accuracy in the close range of the airport. In the far range, where the accuracy of radar data is sufficient, the latter was used. FDR data with GPS based tracks is provided from International Airlines (e.g. SWISS). The FDR data also provide airspeed, engine parameters, aircraft orientation, configuration of the airframe, ambient condition, and so on. For aircraft types without available FDR data, the rotational speed of the engine N1 are extracted from short-term spectra of the acoustical measurements. In the present example measurements, in total six aircraft types are available with FDR data with 161 to 673 flights and thirteen combinations of aircraft and engine types, called reference types, which base on N1 -determination with 27 to 334 flights each (see Table 1 further down below).

Input Data - Data Processing

Fig. 7 depicts the data processing applied to back propagate the measurements and to establish the input data set for the sound emission model. The acoustic wave files are analysed with a constant time interval of 50 ms and filtered to 1/3-oct. bands with 24 mid- frequencies from 25 Hz to 5 kHz to obtain the sound pressure levels L_p(f). This frequency range is chosen to cover the characteristic of aircraft noise which contains high acoustic energy in the low frequency range from the jet. Frequencies above 5 kHz are quickly attenuated due to the normally relatively large distances between aircraft and receiver and can thus only be measured very close to the source.

To prevent a back propagation of background noise, only the part of the level-time-history (of each 1/3-oct. band) which is 6 dB above the minimum level before and after the event is selected for the analysis. In addition, events with unwanted noise are rejected. The sound propagation model sonX is modified and used to calculate the corresponding attenuations and the speed of sound for each source-receiver combination. Source positions and flight parameters are synchronized to the acoustical data and corrected for the time delay of the sound as it travels through the atmosphere.

The geometrical divergence, atmospheric absorption, ground effect, foliage attenuation, as well as the influence of vertical gradients of wind, temperature and relative humidity are accounted for. For each flight, individual meteorological profiles from the known numerical weather prediction model COSMO-2 are used to reproduce the real atmospheric conditions as precisely as possible. The atmospheric absorption coefficient is therefore calculated for particular level-surfaces with a maximum step size of 100 m. Effects due to the motion of the source were corrected by applying a frequency shift and a level amplification. In below equation (8), the Doppler factor DF is defined in dependency of the relative Mach number Ma from the source towards the receiver, where Θ is the radiation angle between the flight path and the vector from source to receiver.

Flight effects (FE), that can be classified for sound sources that move with the aircraft, consist of the kinematic effect which corresponds to the motion of the source relative to the receiver (Doppler) as well as the dynamic effect which corresponds to the motion of the source relative to the propagation medium. Combining both effects leads to the level amplification

defined in below equation (9).

Below equation (10) summarizes the back propagation procedure to obtain the sound emission levels L_em for each 1/3-oct. band. According to the present invention, the sound emission level L_em is regarded as being equivalent to a sound power level L_w, however, with directivity D already included. This description is needed as only the lower half- sphere of the aircraft can be measured from the ground.

The back propagation from the receiver to the source is performed based on short term sound pressure levels L_p for all receivers (microphone locations) which are corrected for the propagation attenuation∑A and the flight effect In line with the definition of the

sound power level, the geometrical divergence in∑A includes the conversion constant logio(4 π ). The frequency shift is defined by the frequency ratio of source and receiver which equals the inverse Doppler factor. For 1/3-oct. bands, the frequency shift was implemented under the assumption of equally distributed energy over each band. The fre- quency shift is applied after performing the back propagation to the source position according to above equation (10). Input Data - Resulting Data Set

A data set is prepared for all events of each individual combination of aircraft type and engine type as a basis for the model development. The level of detail for the classification is limited to general types of aircrafts, thus no distinction is made for optional equipment like winglets or dual annular combustors.

For instance, the A320 family by aircraft manufacturer Airbus is divided to its types A319, A320 and A321 which mainly differ in length and maximum take-off weight. For every type of this family, different engine options are available, the CFM56 or V2500, which implies six possible data sets if all combinations are measured. Each data set consists of 24 subsets for the evaluated 1 /3-oct. bands with mid-frequencies from 25 Hz to 5 kHz. A subset includes the corresponding emission levels L_em in dB from above equation (10), calculated radiation angles θ, φ in degree, flight parameters like the rotational speed of the engines N1 in %, Mach number Ma and the atmospheric parameters pressure p in Pa, temperature T in °C, density p in kg/m3 and speed of sound c in m/s. If FDR data are available also the angle of attack and sideslip as well as the setting of the configuration are available. The Ma could be related to the true airspeed (in respect to the moving air) of the aircraft for FDR data but for consistency it is related to the flight path velocity (in respect to the ground) for all aircraft.

In addition, identification numbers for the event and microphone are appended to each data point (line) for traceability during model development. An event with a flight segment of 60 s adds 1 200 data points per microphone to the data set. For all flights and measurement locations this may add up to one to two million data points per subset.

For the comparison of the model predictions with measured data in Sec. V, the data set is filtered for the corresponding flight condition and directivity angle in each frequency band. For instance, flight parameters for a typical flight phase and a directivity angle of interest are chosen to predict the sound emission level. Then, the same parameters with a certain interval around each parameter are used to create a subset from the complete data set (φ = 60° ± 5°, N1 = 93% ± 2% etc.). Afterward, the arithmetic mean L_em is cal- culated and compared with the arithmetic mean of the predicted values ^ (see below). The comparisons with measured data are not independent because the model is fitted on the same data set, but they allow to assess if the model approach is appropriate

Model Development The model is established by means of multiple linear regression. This method allows for identifying effects of different influential parameters and their interactions in great detail. It can be applied on the sound emission level because the logarithmic levels are normally distributed. In a first step, outliers are removed from the data set (see following section). Then, the parameters for the models are selected (see below). Thereafter, a novel pro- cess to separate the data set to airframe and engine noise is performed (see below). This separation of the two main source mechanisms is beneficial because it allows for a more precise description of each mechanism. For instance, both models may include different parameters or may account for different relations of the same parameter.

Data processing, data analysis and fitting of the source models may be conducted e.g. by making use of the standard software Matlab 2014b for mathematical calculations. The models are e.g. fitted with the Statistical Toolbox of Matlab via the command "fitlm", which uses an ordinary least squares fit and allows for individual weighting of the data points. Outliers

Outliers are removed before estimating the model coefficients by an adaptive outlier detection which uses the robust Mahalanobis distance (RD) to automatically detect outliers. An advantage of the method is the adjusted threshold which adapts to the sample size. If the data set originates from a multivariate normal distribution, no outliers would be detected in contrast to a fixed threshold.

Data Exploration

The available parameters of the presented data set are analysed by means of explorative analysis and knowledge from literature. The findings are used to select the most important parameters for the statistical model which will be presented further down below. Also, parameters are rejected if they correlate with other parameters to ensure reliable model coefficients. Finally, to comply with the linearity of the statistical model, the relationships of the parameters to L_em are revealed. For many engines, N1 is the control parameter of the power setting. In contrast to the thrust or jet velocity of the engine, it is directly a measurable parameter. It correlates with the jet velocity, which can be regarded as the main physical cause for jet noise. Thus, for frequencies below 1 kHz where jet mixing noise is dominant, N1 can be used as substitute for the jet velocity. In addition, also the blade passing frequency (BPF) as well as the fan broadband noise with a centre frequency of 2.5 times the BPF [20] are directly connected to N1 . For most engine types, the BPF and thus the broadband noise can be found above 1 kHz, therefore N1 is a reasonable predictor for the whole engine spectra. Fig. 8 shows diagrams illustrating results of engine run-up tests conducted with the exemplary aircraft A330-300 (TRENT772B) for two exemplary 1 /3-oct. bands, L_p measured on a radius of 170 m at four different directions. The tests were Executed by SWISS, measurements were conducted by EMPA and Zurich airport. Permission on the data was kindly granted. An exemplary engine run-up test of an A330-300 with the TRENT772B is evaluated to establish the functional relation between sound pressure level and N1 for each 1/3-oct. band, as no such relation. The stationary aircraft excludes all airframe noise sources and flight effects from the measurements. Short term, linear sound pressure levels (L_p) are measured at four microphone locations at a radius of 170 m around the aircraft. The engine test is carried out twice upwards and downwards by run-up of six different engine loads from idle to the highest possible engine pressure ratio on ground. Thus, for each time interval with constant N1 two to four mean L_p are available (Fig. 3). A regression model was fitted for each direction, 0° corresponds to the aircraft's nose, with a second order polynomial fit for N1 . According to diagrams a) and b) of Fig. 8, which show two exemplary frequency bands, the functional relation is changing with frequency and direction. For 31 .5 Hz the fit is slightly parabolic to the front and almost linear to the rear of the aircraft. In addition, the slope increases to the rear. For some frequencies as at 2 kHz, the parabola actually opens downwards for 15°. For frequencies in-between, which are not shown here, the relations are very similar with mainly linear or slightly quadratic behavior (open upwards). Thus a flexible second order polynomial approach allows to represent the relation between L_p resp. L_em and N1 .

Fig. 9 shows two diagrams illustrating an exemplary influence of N1 on L_em of the exemplary aircraft E170 equipped with the turbo-engine CF34-8E for 2 kHz. The data points are filtered for 0.2< Ma < 0.24 but airframe noise might influence the levels at low N1 . In general, the turbofan engines of today's civil aircraft are very similar and the mechanisms of sound generation are the same. Therefore, it is assumed that the quadratic approach is also valid for other turbojet engines. This assumption can be tested exploratively using the back propagated data set shown in Fig. 9 for the Embraer E170 (CF34-8E) at 2 kHz. Although airframe noise is contained in the L_em for low N1 , the same trends can be found. In diagram a) of Fig. 9, the sound emission to the front is a downward open parabola, while it is the opposite for the radiation angle in diagram b) of Fig. 9. This agrees well with the results of the run-up test.

The Mach number Ma = U/c is chosen to take the speed dependent sound sources into account. It represents the mean flow speed U at the source as well as the local speed of sound c in a single, dimensionless variable. Furthermore, the Mach number is an aero- dynamic characteristic that is interpreted as compressible flow condition and therefore ensures comparable flow phenomena.

The dependency of the sound emission to Ma can be provided by an aeroacoustic analogy. The generation of sound from the fluctuating fluid is described by the classical wave equation, which is extended by three basic source terms: monopole, dipole and quadru- pole. The theoretical free-field solutions obtained for example by below equation (1 1 ) reveal that the sound power W is proportional to the air density p, a characteristic dimension of the source D, the mean flow speed U and the Mach number Ma. The exponent x depends on the source mechanism (monopole x = 1 , dipole x = 3, quadrupole x = 5).

To derive the relation for the sound power level L_w the base-10 logarithm is applied according to below equation (12). The units of the parameters are therefore normalized by po, Do, Uo.

The dependencies of equation (12) are transferred to the L_em which is proportional to L_w as defined in equation (10). In a statistical model, the implementation of U and Ma is problematic as these parameters are highly correlated (multicollinearity). The multicollin- earity can have strong effects on the estimates of the regression coefficients. Even if the model equation may still be useful in its known intervals, the individual effects of the parameters may be poorly estimated and would lead to wrong extrapolations. In order to prevent for multicollinearity, instead of logi₀(U) only logio(Ma) is accounted for. Thereby, the regression coefficient represents the power x of Ma at which the total airframe noise scales. In contrast, engine noise is mainly affected by the effect of the reduced relative jet speed. To allow an extrapolation of the model for the take-off roll, a simplified correlation of L ^« U can be used, by [22] is used. Thus, it is being assumed that L_em ^ Ma for engine noise.

Figure 10 shows two diagrams illustrating an exemplary influence of Ma on the sound emission level of the A320 aircraft at a) take-off and b) approach at 250 Hz. The dashed line is a linear regression in a) and a logarithmic regression in b). The exemplary dependency of Lem on Ma for 250 Hz for typical flight conditions of take-off with high power in is shown in diagram a) and approach with idle power in a diagram b) in Fig. 10. Engine noise is expected to be dominating in diagram a) and a linear regression seems to be reasonable to extrapolate the decrease of Ma to zero. In contrast, airframe noise is likely to be dominant for the approach in diagram b). However, a regression with the base-10 logarithm of Ma is as reasonable as a linear regression, but a linear approach would not represent the physics of the airframe noise, thus overestimating levels for lower and higher Ma.

An effect of air density is included in the airframe model to account for the generalized aeroacoustic theory in above equation (12). The air density highly correlates with the air pressure p and temperature T, which are excluded from the regression model to prevent multicollinearity of the predictors. Multicollinearity can be checked by means of the variance inflation factor (VIF), which can be determined for each possible parameter. After rejecting p and T no strong multicollinearity is left. Nevertheless, it can be decided to also reject the speed of sound c because it is already included over Ma. In fact, with the rejection of c the VIFs of Ma and p further decrease. Therefore, only p may be chosen as variable for the statistical model. From above equation (10), the logarithmic transformation is applied on p. The transformation may be needed to guarantee linear behaviour in respect to the coefficients of the airframe model. The Mach number and the air density can be transformed logarithmically, i.e. the linear coefficients express the variables' ex- ponents inside the logarithm. The air density can be normalized by the density at mean sea level as defined by the International Standard Atmosphere (p₀ = 1 .225 kg/m3) to have the variable dimensionless. For zero airspeed or density the transformations tend towards minus infinity which is physically reasonable. In practice, Ma can be set to 10-3 to obtain a real value and p should never be extrapolated that strong.

The sound emission of an aircraft has a directivity that may be best described with spherical coordinates. Particularly the longitudinal radiation, represented by the polar angle Θ, strongly changes with the aircraft type, frequency band, and power setting as shown in Fig. 10. The lateral radiation, represented by the azimuth angle φ, is also taken into account in dependency of aircraft type, frequency band, and power setting. The lateral directivity can lead to level differences up to 3 dB over φ. Additionally, the lateral directivity in may show significant discrepancies to the generalized corrections, which only distinguish between wing and fuselage-mounted engines. A Fourier series of second order can be chosen to represent the longitudinal directivity. During the model development also a higher order was tested but resulted in problematic slopes at the borders, where less data is available. In particular for conditions far away from the receivers the directivity at high frequencies was critical. The lateral directivity is modelled with a half range Fourier series (2nd order) to simplify the number of terms and also to prevent problematic slopes in areas with low data coverage.

Fig. 1 1 shows two diagrams illustrating an exemplary distribution of measured flap handle positions of the A320 in dependency of the Ma-Number. In contrast to approach, the flap handle position 1 refer to a different deflection angle of flaps at departure. The configuration of the aircraft is modelled by three categorical variables: The position of the gears (in: 0, out: 1 ), the position of the flap handle (0 to 4, fix combinations of slat and flap deflection) and the deployment of the speedbrakes (inactive: 0, active: 1 ). This information is taken from FDR data. Due to the measurement of real air traffic the data is naturally not balanced and it may not be possible to gain data for all combinations of configurations. Furthermore, the flap settings highly correlate to different intervals of Mach numbers due to the procedures and structural limits as shown in Fig. 1 1 . In addition, the flap handle position 1 for departures is indicated as 1 +F which corresponds to a different deflection angle of the flaps than for approach (10° instead of 0°). Although all difficulties, the influence of the aircraft configuration is of interest and is therefore ac- counted for with the help of a specific model structure as described more in detail further down below.

Fig. 12 shows two diagrams illustrating an exemplary influence of gears on the sound emission of the A320 at approach in idle for 250 Hz in (a) and 2 kHz in (b). Measured data and the regression lines show a clear effect on the sound emission with gears ex- tracted. The data points shown in Fig. 12 for illustrating the effect of the gears stem from measurements for approach situations with gears in and out. Each data set is fitted with a simple logarithmic regression to show the influence of the gears. In diagram a) of Fig. 12, a slightly larger slope of the regression with extracted gears can be found. For low Ma the emission levels are similar, but for high Ma of 0.3 the level difference is 2.6 dB. At 2 kHz in diagram b) of Fig. 12, the effect of the gears on the Ma-dependency of the sound generation is much stronger. At Ma = 0.3 the difference is already 6 dB. Further parameters can be considered or may be rejected during model development due to insignificance or practical reasons. In particular, the angle of attack and angle of sideslip, which are available from FDR data, can be excluded as no correlations are found to the emission level. Besides, the rejection of both angles is also reasonable as they are usually not available for predictions.

Data Separation Technique

Fig. 13 shows a diagram illustrating steps of a process of model development and data separation according to an embodiment of the present invention. The process is repeated for each 1 /3-oct. band. According to the exemplary process shown in Fig. 13 for illustrating the model development and the separation of the total emission levels from a frequency band in the data set into airframe and engine noise is shown, in a first step 1 , the data set is split into two parts: part one contains all data with the engines in idle i.e. only approach situations, and part two contains all other data from approach and departure with engines on load. A reasonable limit for the split is determined by data plots of Lem over N1 as in Fig. 14, where no correlation is found for N1 below 40 %. Therefore, it is assumed that airframe noise is dominating the total L_em for this subset.

In step 2, an initial airframe and an initial engine model are fitted on their corresponding data sets to reveal the main effects for each source. The initial models are only minor modifications of the models presented more in detail further down below. With the aid of the predicted initial airframe

g sound emission levels, a source ratio can be calculated for each data point in the original data set (step 3). The ratio q' (see below equation (15)) is defined as the predicted sound emission of the engine divided by the sum of predicted engine and airframe emission. Thus a ratio of 0 means only airframe noise contributes to the total sound emission and 1 corresponds to engine sound emission only. Note that all predictions from these models are marked by a hat to distinguish from input data; the superscript i indicates that the initial models are used.

However, this method implies that the initial models need to be extrapolated. For example, the initial airframe model was based on approaches with Ma smaller 0.35. By contrast, departures are measured up to Ma of 0.45. As a consequence, to predict

for each data point on the whole data set, the model has to be extrapolated. Nevertheless, the extrapolation for the Mach number is based on physical knowledge (see above), thus allowing for a plausible first estimation.

Based on the ratio q' two separated data sets, both including all measurements for approach and departure, are created for each 1/3-oct. band (step 4). One represents the sound emission of the engines

(see below e uation (16)) and the other represents the sound emission level of the airframe

(see below equation (17)).

Fig. 14 shows three diagrams illustrating a data separation example for the A320 at 100 Hz. The back propagated data on the top is split to estimates of the sound emission related to airframe (bottom left) and engine noise (bottom right). In Fig. 14 both data sets to the original L_em are being compared to each other. The airframe levels (bottom left) are dominating for N1 < 40%, which is the implication of the assumption in step 1 . In the example they are approx. 20 dB lower than the total levels for departures. In contrast, the engine levels (bottom right) are dominant for departures and loose influence to lower N1 . In total, by adding the individual levels of both data sets energetically, the original data set can be reconstructed. In step 5 the final models for airframe and engine noise as defined herein are fitted on the separated data sets presented in Fig. 13. Steps 3 to 5 are repeated once to improve the estimation of the ratio between airframe and engine noise, as the regular models were fitted on the whole data set in contrast to the initial models. Finally, the energetic sum of the airframe and engine model adds up to the predicted total L_em. The whole process of data separation and model fitting is performed 24 times for each 1/3-oct. band individually.

Source Models

In the following, source models according to an exemplary embodiment of the present invention which are based on findings as described above are being presented. The models are built based on knowledge of the main parameters and their interactions, e.g.

Ma-dependency of the gears. From the statistical point of view, this approach equals the forward selection with the scope to only include the relevant parameters for both sources.

Each model with a new parameter or interaction is compared to the coefficient of deter- mination R², the mean squared error σ_θ, and Akaike information criteria (AIC). All criteria should to be compared over all frequencies to find a global optimum. Compliance with the model assumptions was visually confirmed by means of residual plots.

Exemplarily, the source models are being built on the A320 data set, which provides FDR data and a high number of flights. Afterwards, they can be tested and further improved on the exemplary five other aircraft types with FDR data to confirm that the models are applicable to different aircraft and engine types. The resulting models are presented as advanced models (see further down below). If no FDR data are available, meaning the configuration of the aircraft is unknown, e.g. thirteen reduced models can be established (see further down below).

Advanced Models

The sound emission level of the airframe

can be modelled by the sum of the source terms and the radiation angle terms as summarized in below equation (18). The dependency on the frequency f indicates that all coefficients of the source and radiation angle terms are fitted for all 1/3-oct. bands, even if not further denoted due to readability.

Below equation (19) represents the source terms of the airframe model. L_a0 is the intercept and ¾i to e_a3 are the frequency dependent coefficients of all model parameters. The main parameters are the logarithmic transformations I Ma and Ip which represent the behaviour of the aeroacoustic sound generation in line with known semi-empirical models. In addition, each configuration change of gears, flaps or speedbrakes (SB) is modelled with discrete steps as these parameters are categorical. For flaps and speedbrakes, also interactions with the gears are considered to account for the changes in the absolute effect when the sound emission level is raised by the extracted gears. Further, gears and speedbrakes interact with IMa to account for the speed dependent sound generation. For the flaps, the interaction with IMa is neglected because each flap setting is only used for a certain small range of Ma-numbers (see Fig. 1 1 ), thus a Ma-interaction cannot be determined without high uncertainty. Nevertheless, the very different combinations of flap setting and Ma-number range for approach and departure of Fig. 1 1 needs to be considered in the model in one way or another. Therefore, an additional categorical parameter, the flight procedure Proc (departure: 1 , approach: 0) can be introduced, which also takes into account the different deflection angles. The parameter further accounts for the observation on the A320-family that frequency bands with cavity tones can have a strong increase in level with increasing Ma for approaches but not for departures. It can be assumed that the local flow field is different for approach and departure due to different angle of attack and flap setting.

The directivity of the airframe model (see below equation (20)) is expressed as an axially symmetric radiation along the longitudinal axis of the aircraft because the lateral directivity is mainly assigned to reflections of the engine noise on the airframe (see below). The polar angle Θ is taken into account with a 2nd order Fourier series to model the longitudinal directivity. The coefficients for the airframe directivity are k_a to n_a. No interactions are included, i.e. the shape of the emission directivity is the same for all flight conditions. This simplification is justified as the data set was already corrected for the flight effect (see above equation 10).

The sound emission level of the engine noise is modeled by the sum of source

terms and a more detailed approach for the radiation angle terms as summarized in below equation (21 ).

Source terms for engine noise (see below equation (22)) include the intercept L_e0 and three parameters with their coefficients a_ei , b_e2 The main source term of engine noise is N1 . The quadratic approach for N1 represents the jet as well as the fan noise as laid down above. In addition, the parameter Ma takes the source strength alternation of the jet mixture with aircraft speed into account.

The exemplary engine run-up test reveals that the relation of L_em to N1 is strongly dependent on the polar angle Θ. Therefore, the Fourier terms of the directivity

interact with N1 as well as N1² (see below equation (23)). The corresponding model coefficients are k_e,j to n_e,j with index j for each interaction. The lateral directivity (see below equation (23)), which represents the installation effect, is included as a half range Fourier series of 2nd order, i.e. with only sine terms of φ. Similar to the longitudinal directivity, each term has an interaction with N1 with coefficients It was can also be tested

to include the interaction with N1², but according to the present example, no significant improvement is expected to be found.

With the approach of above equations (23) and (24), the shape of the 3D directivity is allowed to change with the engine setting N1 . As each 1 /3-oct. band is fitted separately, also the spectral content of the total directivity varies with the power of the engines. The initial airframe model, used for the first calculation of the ratio q' for the data separation as laid down above, is identical to above equation (19), but the parameter Proc is omitted, as all data points of the initial model belong to approaches. Also the directivity in above equation (19) is not changed. The initial engine model as in above equation (22) is reduced by the parameter N1². This prevents an increase of the sound emission level for the extrapolation for N1 below 40%. Therefore, also the longitudinal directivity in above equation 23 reduces for N12.

Reduced Model

If no FDR data is available, the models have to be reduced by the parameters which are not known. For example, when for airframe noise the configuration parameters are missing, they have to be removed from the model approach (see below equations (25) and 26)). The effects of the configuration are still implicitly included in the data set. In contrast to the advanced model, the Ma-dependency on L_em now accounts for the mean configuration of all measured flights. Thus, the parameter Proc is retained in the model due to the same reasons as laid down above. The radiation angle terms remain unchanged (see above equation (20)).

For engine noise the parameter originating from FDR data is N1 . This parameter is crucial as it has the strongest effects on L_em. Therefore, in the case of missing FDR data, N1 can be determined based on spectrographic analyses. The engine model of the reduced model is thus the same as of the advanced model (see above equations 21 to 24).

Weighting

During measurements, the polar angle Θ is only changing slowly with an aircraft far away, whereas it changes quickly while the aircraft overflies the microphone. Consequently, only few data points of the equally spaced acoustic samples are available in the most relevant range of Θ and vice versa. Therefore, the data should be weighted to reduce an influence of the inhomogeneous distribution of data points over θ , which is inversely proportional to the time derivative

= d θ /dt. To do so, the model is fitted with a weighted least squares (WLS) algorithm, in analogy of ordinary least square-sine linear regression.

As each flight and receiver combination has a different geometry, θ' is standardized by the maximum value per event and receiver, denoted as w₀ in below equation (27). The standardization prevents a higher weight of measured levels with an aircraft close to a receiver than far away, where

is generally lower. The weights are then normalized by their mean value

to ensure that the sum of all weights w,, which are used for the WLS algorithm, matches the number of observations n involved in the analysis (see equation 28).

Energy Correction As a consequence of the least squares estimation, the model predicts the arithmetic mean of the sound emission level L_em in dB. A correction is needed to predict the energy mean which is equal to the arithmetic mean of the sound emissions in watt. As L_em is normally distributed, which is a requirement for a linear regression, the energy correction can be analytically determined by 0.1 15^■ σ². The variance σ² can be represented by the error variance estimate

applied for each model as in below equations (29) and (30).

Fig. 15 shows a diagram illustrating an exemplary correction factor for energy mean over frequency for the A320 aircraft. From Fig. 15 it becomes apparent that the error variance is considerably higher for microphones in the far range than in the close range, which is mainly caused by a higher variance due to turbulence and uncertainty in back propagation. In general, microphones for departures in the far range are more distant to the source, which supports the interpretation that the variance is distance dependent. The energy correction should only include the variance of the sound emission level and uncertainty of the measurement. Therefore, the correction is applied for the error variance of the data in the close range (total error of approach and departure).

The energetic sum of the fitted final models for airframe (see above equation (29))

and engine noise (see above equation (30)) results in the total predicted emission spectra of the modelled aircraft according to below equation (31 ).

Reference Types In the present example, in total 19 acoustical reference types are established on the basis of the input data presented above. Below Table 1 gives an overview of the reference types with details about the corresponding aircraft and engine types, the data origin, and the number of flights the models are based on. For instance, the A320_CFM56-5B, the data of which is used frequently in the following account for illustrative purposes, is based on FDR data of the CFM56-5B equipped A320-200 with 673 flights in total. The E170 without FDR data is based on 89 flights in total and will be used to prove the feasibility of the reduced model.

Table 1 : Reference types with grouped aircraft and engine types and their data basis (No. of flights). If the input data bases on FDR the advanced model (Adv.) is established, for other types with N1 -determination the reduced model (Red.) is established.

Some aircraft types of the same aircraft family can be grouped when the number of measured flights is low. As a rule, only types with the same engine are grouped as the engines are the main sound source which can lead to considerably different sound emis- sion. For instance, all subtypes of the B737 with the classic engine option CFM56-3 are grouped, while all types of the new generation which are equipped with modern CFM56- 7B are separately grouped. Grouping for an aircraft family is reasonable and improves the model as a wider range of parameters is covered due to different take-off weights and procedures. In particular, different aircraft types use different N1 for departure as different thrust is needed for different take-off weights. Model Performance

Fig. 16 shows two diagrams illustrating exemplary coefficient of determination over frequency. Airframe and engine model are compared to their separated data sets, while the total model is compared to the original data set. Figure 1 1 depicts the coefficient of de- termination R² over frequency for all 1/3-oct. bands. R² _totai represents the model performance of Eq. 24 to reproduce the original data set of back propagated data L_em. Overall, the goodness-of-fit of the total models indicate good explanatory power of the regression fit with values between 0.7 and 0.8 for the A320 (a) but also for the E170 (b). R² _afm and R² _eng describe the goodness of fit of the source models on the separated data set. The engine model shows R² _eng values slightly larger than 0.8 for the most frequency bands. In contrast, the airframe model of the A320 has R² _afm values between 0.2 and 0.6 with much more variation between the different frequency bands. For the E170 the R² _afm mainly varies between 0.4 and 0.7.

A specific aspect of R² is related to the frequency range in which the sound sources radiate. For instance, R² _eng of the A320 in diagram a) of Fig. 16 is high between 50 to 400 Hz where the jet noise is dominant. Similar, R² _eng is high at 2 to 3 kHz, the bands which contain the blade passing frequency (BPF) of the A320 at departure. Airframe sound sources can be identified in the same manner. In accordance to measurements on an A320 full scale wing in the large low-speed facility (DNW-LLF), the slats (included by the parameter Flaps) considerably radiate sound between 100 and 300 Hz. Further, a prominent cavity tone in the wing can be found at 500 and 630 Hz. Finally, excess noise of the flap side edge is prominent between 1 and 1 .6 kHz.

Exactly in those frequency ranges, the R² _afm shows local maxima. On the contrary, there are no explicit sound sources for 50 to 100 Hz and above 1 .6 kHz and consequently R²afm is low. For the E170 no similar measurements in the wind tunnel as for the A320 are known, but the measurements indicate a tone at 100 Hz which also increases the R²afm. In general, the airframe sound sources of the E170 contribute over all frequencies as the R²afm is high.

Model Comparison Exemplary results of spectra and directivity patterns are shown for various flight conditions and compared to measurements.

Fig. 17 shows two diagrams illustrating exemplary spectral directivity patterns of the A320 for departure at high power setting. In Fig. 17, spectral directivity patterns are predicted and compared to mean measured data with similar flight parameter settings as laid down in detail above. A departure with a high power setting of N1 = 93% is shown. The longitudinal directivity in diagram a) of Fig. 17 is presented for an observer on the side at φ = 60°. All frequency bands show a good agreement between predicted and measured data. Low frequencies as 125 and 250 Hz show a typical jet characteristic that is pronounced to the rear. For high frequencies as 2 kHz the characteristic has local maxima to the front and rear given by the fan. Hence, the Fourier series and the interactions with N1 and N1² allow the model to accurately represent longitudinal directivity.

In the same way, the lateral directivity, shown from the rear at Θ = 130° in diagram b) of Fig. 17, agrees well with the measurements. Overall, the lateral radiation is less important and less variable over the frequency bands. Thus, the half range Fourier series with interaction to N1 is a valid approach. Longitudinal and lateral directivity also agree very well for the overall L_em, which supports the chosen model approach for the directivity.

Fig. 18 shows two diagrams illustrating exemplary spectra for final approach (N1 =55%, Ma=0.23) and take-off at high power setting (N1 =93%, Ma=0.24) for the A320 aircraft. In Fig. 17 spectra for typical flight conditions of take-off and final approach are depicted for θ = 90° in diagram a) of Fig. 18 and Θ = 130° in diagram b) of Fig. 18. As expected, the predicted dominant sound source at take-off is the engine. The airframe model is not shown in this case to avoid an overlay with the spectra of the final approach. Next to the strong low-frequency broadband noise of the jet in the rear, also the BPF at 2.5 kHz is represented well. In contrast, the airframe model is relevant for the final approach. At 90° the mid frequencies are still dominated by engine noise, probably turbomachinery noise. At 130° (rear), airframe noise dominates the mid-frequencies. Interestingly, while jet noise is very low for N1 = 55%, the broadband noise of the fan around 2.5 times the BPF (2.5 x 1 .65 kHz = 4.1 kHz) can still be found around 4 kHz in the engine spectra in diagram a) and b) of Fig. 18.

Fig. 19 shows two diagrams illustrating exemplary spectra for final approach (N1 =50%, Ma=0.2) and take-off at high power setting (N1 =86%, Ma=0.24) for the E170 aircraft. The corresponding spectra of the E170 aircraft in Fig. 19 depict a very similar result as shown for the A320 aircraft in Fig. 18. The total spectra are in good agreement with the measurements, and departures are dominated by engine noise. At typical final approach settings engine and airframe noise contribute equally over all frequencies in contrast to the source dependent contributions as seen for the A320. The BPF at departures at 3 kHz is not observed in both diagram a) and diagram b) of Fig. 19 which is in line with the measurements. For the final approach the BPF can be found in diagram a) of Fig. 19 at 1 .7 kHz in the prediction as well as in the measurement.

The fact that each frequency band is fitted on its own allows the model to form different spectral shapes. For instance, the quadratic dependency on N1 allows the engine spectra to change from high jet noise to low power settings, as shown in particular in the rear of the aircraft in Figs. 18 and 19. In addition, also bands with tones emerging out of a smooth broadband spectrum are accounted for. Consequently, according to the present invention, a new sound emission model is presented to overcome the limitations in prediction of aircraft noise models according to the prior art with a moderate number of necessary input parameters. As a major advantage of the present invention in comparison with known models such as Doc. 991 1 or FLULA2, airframe noise, represented by the influence of the Mach number and configuration of the aircraft, can be separately modelled from the engine noise. At the same time, only a minimum of procedural parameters are needed for engine noise that require no detailed knowledge of the engine performance like mass flow or jet speed as in semi-empirical models according to the prior art like ANOPP or PANAM. According to the present invention, jet and fan noise of the engines are considered by N1 as the major parameter, which can be determined acoustically to develop the respective models. A novel according to the present invention allows to separate the total sound emission levels to airframe and engine noise. Hence, no elaborate microphone array measurements are needed to separate the two sound sources. The separation allows to predict airframe and engine noise independently which is an advantage for the assessment of noise abatement procedures. On this basis, new combinations of modelled airframes and engines, for which input data is missing or which are not yet flying in such combination, can be established. A further refinement down to detailed modelling of single sound sources is still challenging, especially with the scope to cover a wide range of aircraft types with different dimensions.

The model parameters chosen for the exemplary embodiments described herein allow to adequately reproduce the directivity and spectra for typical flight conditions. In particular, the A320 aircraft with FDR data and a high number of flights, and the E170 aircraft without FDR data and only 89 flights, show similarly good results. This is the case for all types listed in above Table 1 . Thus, the advanced models as well as the reduced models are comparable and allow to establish models for different input data and aircraft types. Prerequisites to establish the model according to the present invention for further aircraft types are (i) measurements at different locations close and far to the airport, (ii) back propagation to the source, and (iii) spectral analysis to determine N1 or processing FDR data. A limitation of the separation of airframe and engine noise is the assumption, that airframe noise is dominating for the engines in idle. Also, the validity of the separation cannot be proved as no data is available.

As the source model is based on the sound emission level, it can be combined with any sound propagation model to calculate the sound immission at the receiver. However, the propagation model should account for all effects, which were applied in the back propa- gation (e.g. ground effect). By means of a simulation program new procedures as the Continous Descent Approach (CDA) can be optimized acoustically, which could extend current studies on trajectory optimization with noise as cost functional. Thereby, the sound source model allows to calculate various noise metrics, as the effective perceived noise level (EPNL), the event level, and the maximum level with free choice of the spec- tral weighting.

A sound source model for turbofan powered aircraft according to the present invention fills the gap between conventional and high-end models according to the prior art. It provides two separate models for the sound emission of the airframe and the engine. Both were established based on insights of explanatory data analysis, physical knowledge, and statistical modelling. Source models for a wide range of relevant aircraft and engine types were established.

The flight parameters, which connect the sound emission level to the current flight condition, are at best FDR data or alternatively radar data with an additional analysis to determine N1 via the BPF of the fan. When available, it is recommended to use the advanced model for studies on single flights. Nevertheless, the reduced model is similarly applicable, although the effect of flight configuration cannot be represented exactly. At least for airport scenarios and yearly calculations, the reduced model would improve the accuracy of today's noise maps.

The presented exemplary embodiments show the ability of a model according to the present invention to conduct studies to noise abatement procedures. It is possible to provide data from optimizations or full flight simulators, to calculate and compare noise metrics and the affected population. The presented methodology, without a separation of the sources, might also be applied to develop sound emission models for helicopters, propeller-driven airplanes or military jets.

Spectral Three-Dimensional Directivity Patterns in Dependency of Flight Condition

As described above, a semi-empirical sound source model according to the present invention is established by means of multiple linear regression. Therefore, an adequate empirical data set is required to fit the model coefficients for a typical range of flight conditions. In particular, measurements for different flight conditions and a wide range of angle coverage are necessary to establish a model according to the present invention.

Data Processing

The sound pressure levels (SPL) at the measurement locations can be back-propagated to the source to obtain source power distribution levels SPL, using the sophisticated propagation model sonX and accounting for the real atmospheric conditions. Afterwards, the Doppler effect due to the motion of the source should be corrected by applying a frequency shift and an intensity amplification. The resulting acoustical data, directivity angles and the L_w, is to be synchronized and complemented with FDR data, which provides a wealth of parameters such as the trajectory, the rotational speed N1 of the compressor and configuration changes of gears and flaps.

As already mentioned above, a full model can be formulated separately for each one- third octave bands from 25 Hz to 5 kHz, denoted as parameter f in the following account. The directivity is modelled in 3D by using spherical coordinates, consisting of the polar Θ and the azimuth angle φ. Both are defined relative to the flight path axis system as illustrated in Fig. 1 to simplify the requirements of the input data for a prediction, as the real orientation of the aircraft is usually not known. The azimuth φ is additionally cor- rected by the roll angle of the aircraft, which can be calculated from the trajectory.

The sound source model is can be divided into two sub models, one for engine and another for airframe, noise, each accounting for different source mechanisms as explained above. An engine model according to the present invention as described in below Equation (32) includes both directivity angles to account for the longitudinal directivity as well as for the lateral installation effect of the engines. The most important parameter is N1 , which represents the power of the engine and is therefore directly related with the jet velocity and with the rotation of the fan and compressors. With the help of engine runups as described above in detail it can be concluded that L_w also depends on N1². Using interactions between N1 and Θ as well as φ, the directivity may change with the power setting. Additionally, the Mach number Ma of the aircraft, which influences the incoming flow and in particular also the source strength of the jet due to the surrounding flow, is included into the model.

Airframe noise can be modelled with a 2D directivity mainly as the measurement setup for landings where all aircraft approximately follow the same trajectory did not allow to reliably establish any lateral effect. The most important continuous explanatory variables are the Mach number Ma and the density p of the surrounding medium, both transformed by the base-10 logarithm. The transformations are necessary to linearize the variables and are in line with semi-empirical models for airframe noise. Additionally, the model includes several categorical variables to reproduce changes in configuration, i.e. the gear positon, flaps position and speedbrakes SB. The full model also includes interactions e.g. of the gears and the Mach number to account for the difference in the dependency on airspeed with and without extended gears. Finally, the factor procedure (Proc) is included because some effects like the level change of the flaps were found to be different for take-off and landing situations. A different angle of attack and thus lift-coefficients might be the cause, which directly influence the noise generation.

Both models for airframe and engine noise are finally summed up energetically to obtain the total source power distribution level in dependency of the considered parameters. As the model parameters can be obtained with a mean least squares algorithm fit and thus represent the arithmetic mean of L_w, an energetic correction is introduced to correct for the mean source power as described in detail above. The Doppler frequency shift and intensity amplification are applied afterwards to account for the flight effect.

The full model (see above equations (32) to (34)) is established for six exemplary aircraft and engine type combinations of Swiss International Air Lines, for which FDR data was available (see below Table 2). A high amount of flights are measured to establish the present models on a statistically significant basis, but a lower number of flights would also be acceptable. Table 2: Overview of acoustical reference types with FDR and number of flights incorporated into a model according to the present invention.

As also already mentioned above, model approaches according to the present incention allow for reducing the level of detail if the input data lacks of parameter, which is the case if no FDR data is available. Consequently, the number of parameters in the airframe model decreases.

The engine model remains the same as N1 is the most important parameter which should not be removed. If no FDR data are available, it can be determined through a detection of the blade passing frequency with the help of advanced signal analysis. In case of an insufficient coverage of the lateral directivity angle, the model can simply be reduced to 2D by taking out the azimuth angle φ from the engine model.

Comparisons

Three exemplarily cases are presented to show the abilities of source model for three- dimensional directivity patterns according to the present invention and to compare it against exemplary measurements: a) Spectra of airframe and engine noise at final approach, b) Directivity at takeoff, and c) Simulation of approach with extending gears.

The comparisons (a) and (b) an be carried out for the reference type A320_CFM56-5B (A320) on the basis of unweighted L_w at the source to show the influence of the flight condition on spectra and directivity. In (c), the simulated SPL as well as the Us are compared for the A320 and the A333_TRENT7 (A330) to show the strong effects of the gears.

Spectral Comparison

A key property of a model for three-dimensional directivity patterns according to the pre- sent invention is the spectral resolution in one-third octave bands. Furthermore, the source model and thus the spectra are separated into airframe and engine noise. Owing to the dominance of engine noise for departures, spectra for the final approach of the A320 can be predicted to show the interplay of engine and airframe noise with the help of two different flight conditions: Idle power (N1 = 30%) at Ma = 0.26 versus N1 = 50% at final landing speed of Ma = 0.21 . All flight parameters used for the prediction with the full model are listed in below Table 3. At the same time, the empirical dataset, which is also used to fit the model, can be filtered for the same flight conditions with a certain tolerance for the parameters. For each data bin the arithmetic mean L_w can be determined to test how accurate the regression model is able to reproduce the input data.

Table 3: Parameter settings for the final approach prediction and tolerances for the measurement data.

Directivity Comparison

For the comparison of the directivity with measured data, typical parameter settings for a take-off can be chosen as the directivity is most distinct with high engine power. Similar to what is described in the following section, the regression dataset can be filtered within tolerance ranges of the predicted mean values (see below Table 4) to test for reproducibility of a model according to the present invention.

At first, the longitudinal directivity of the full model (3D, see above equation (32) is shown for four exemplary frequencies. Secondly, the integrated L_w over all frequencies is de- picted for three power settings: a high power setting at 93%, a medium power setting at 90% and a low power setting close to cutback power (87%). In addition, the influence of the reduced model (2D, see above equation (36)) is shown. Table 4: Parameter settings for the departure prediction and tolerances for the measurement data.

Simulation of real Approach Situations

Finally, an exemplary approach situation is shown for a receiver beneath the glide path, situated 15 km from threshold of runway 34 of the exemplary airport, i.e. Zurich airport. In this situation, the azimuth angle φ is below 5° and the aircraft flies over the receiver at an altitude of approx. 600 m. Similar situations for the A320 aircraft as well as the A330 aircraft can be selected, to show the influence of the extending gears during overflight.

The level-time-history (LAS) of the full 3D model according to the present invention (aww above Equation (33)) and reduced 3D model (no configuration, see above equation (35)) are compared to the measurement. In addition, the simulated flights are presented as unweighted spectrograms with the change of the SPL in one-third octave bands over time, exactly as an advanced level meter would measure it. Results - Spectral Comparison

Fig. 20 shows two diagrams illustrating exemplary spectra of an approach of an A320 aircraft with full flaps and extended gears at Θ = 130°. Stage 1 (left) in idle power and Ma = 0.26 versus Stage 2 (right) with N1 = 55% and Ma = 0.21 . Each total spectrum is divided into predicted contributions of airframe (dash-dotted, blue) and engine (dashed, magenta). Hence, two spectra of the A320 aircraft in final approach with extended gears are depicted in Figure 20 with the total level and their corresponding contributions from airframe (dash-dotted, blue) and engine (dashed, magenta) noise. In the first stage (left) the engines are in idle and the Mach number is 0.26. In this case, the model indicates that the whole spectrum is dominated by airframe noise. Indeed, due to the model development based on measurements of the overall aircraft it is inevitable that the airframe model still contains the engines in idle. At the second stage (right), the aircraft achieved the landing airspeed of and the engines are driven at 55% to maintain the glide path. Thus, the engine model Ma = 0.21 predicts a spectrum that slightly dominates below 160 Hz due to increased jet broadband noise and above 2 kHz due to increased fan broadband noise. The airframe spectrum still dominates for the mid frequencies although the level decreased by 4 dB compared to stage 1 due to the lower Mach number.

The empirical mean values show good agreement with both stages. Deviations at frequencies below 100 Hz and above 3 kHz can be explained by higher uncertainty of the measurement due to the back propagation with high air absorption. However, especially for frequencies between 125 Hz and 3 kHz, this interval is crucial for A-weighted levels at the receiver, the deviations are below 1 .1 dB. Results - Directivity Comparison

Fig. 21 shows two diagrams illustrating exemplary spectral directivity patterns for a departure at low power setting (N1 = 87%). The longitudinal directivity versus polar angle Θ (left) and for φ = 130° the corresponding lateral directivity versus azimuth angle φ (right) are depicted. For a typical departure, the total L_w mostly stems from engine noise. As expected, the 125 Hz band is very pronounced at the rear with a peak around 140° and corresponds to the typical behaviour of jet noise as shown in Figure 21 . For higher frequency bands the maximum level shifts to 90° and changes it shape. Especially for 2 kHz the shape completely changed and peaks at 40°. It is assumed to be the fan noise, which dominates to the front. The full model reproduces the measured data accurately, with deviations mostly below 2 dB. These deviations are within of the standard deviation of the measurement, which varies between 1 .6 dB to 3 dB, dependent on frequency and Θ.

In Fig. 21 on the right, the lateral directivity is shown for Θ = 130°. Lateral directivity is more pronounced at frequencies above 125 Hz, as only frequencies of small wave length are reflected at the wings surfaces. Maximum levels for higher frequency bands occur at azimuth angles around 30° to 60°, which exceed the level at 0° by approx. 2 dB. The model predicts the measured values accurately, with deviations for φ 60° below 2 dB, while overestimating L_w for φ > 60°. However, these angles are less important for noise calculations because they contribute only in far areas to the side.

Fig. 22 shows two diagrams illustrating exemplary Longitudinal directivity of the overall Lw for three different take-off power settings of the A320 aircraft: below the aircraft at φ = 0° (left) and to the side φ = 50° (right). In Fig. 22, integrated, unweighted L_w for φ = 0° (left) and φ = 50° (right) are illustrated. For relevant polar angles of 60° to 120°, a 3D model according to the present invention predicts measured data well with deviations below 1 dB. For polar angles beyond this range, in contrast, deviations are larger for both models, particularly for φ = 0°. The 2D model shows slightly larger deviations on the left which become considerably large for φ = 50° on the right.

Fig. 23 shows two diagrams illustrating exemplary lateral directivity of the overall Lw for three different takeoff power settings of the A320 aircraft: perpendicular at Θ = 90° (left) and to the rear Θ = 130° (right). Similar results as described above in relation to Fig. 22 are found for the lateral directivity illustrated in Figure 23 for Θ = 90° (left). It turns out, that the predicted levels with a 2D model would systematically overestimate the levels directly below the track and underestimate the level for lateral positions with φ between 20° to 60°. In contrast, for Θ = 130°in Figure 23 (right) the deviations of the 2D and the 3D model can be neglected, at least for φ < 60°. Each 3%-step of N1 leads to an increase in the overall L_w by approx. 1 dB for Θ = 90° and approx. 2 dB for Θ = 130°, which is reproduced well by both models.

Simulation of real Approach Situations Fig. 24 shows six diagrams exemplarily illustrating two approaches in idle power setting and extending gears (dash-dotted vertical lines) and high lift elements at a receiver approx. 15 km in front of the runway threshold. Flight parameters from FDR data and the resulting predicted and measured LAS are shown for the A320 (left) and A330 (right) air- crafts. Hence, two approaches and their flight parameters are depicted in Figure 24. The A320 on the left arrives in idle power, flaps position 2 and extends the gears with short use of the speedbrakes at the marked point. Same procedure applies for the A330 (right), but without use of the speedbrakes. The level-time-histories of the measurement and the 3D model generally agree very well. This is however not the case for the reduced model (3Dred) where the configuration of the aircraft is not modelled. After gear extension, the level of the A320 is only slightly lower, but for the A330 the level is considerably lower from 30s to 50s and does not agree well with the measurement.

Fig. 25 shows two diagrams illustrating exemplary spectra of an approach of an A320 aircraft with idle power approx. 15 km in front of the runway threshold. Predicted (left) versus measured (right) spectrogram in 1/3 octave bands from 25 Hz to 5 kHz at a receiver. The presented model provides many details for a single overflight comparable to a real measurement. Figure 7 shows the simulated (full model, left) and measured (right) spectrograms of the same event as shown in Figure 24 left. The SPL over time is in very good agreement, although low frequencies are overestimated at the rear (A). The air absorption of high frequency bands (B) and the ground effect (C) are well visible and correlate with the measurements. The gear extension at (D) shows a slight increase in level for frequencies below 100 Hz in simulation and measurement. A specific cavity tone of the A320, which can be found at 800 Hz decaying to 400 Hz due to the Doppler shift, is well reproduced although it smears over two frequency bands for the first 15 s (E). Fig. 26 shows two diagrams illustrating exemplary spectra of an approach of an A330 aircraft with idle power approx. 15 km in front of the runway threshold. Predicted (left) versus measured (right) spectrogram in 1/3 octave bands from 25 Hz to 5 kHz at a receiver. In the same way as Fig. 26, Fig. 26 shows the approach of the A330 as shown in Figure 24 right. Again, a very good agreement between simulation (left) and measure- ment (right) is found with a slight overestimation at (A). The propagation effects (B, C) are in correlation with the measurement. The effect of the gear extension at (D) is remarkable over the whole frequency range and shows the importance to include configuration parameters in the airframe model.

Consequently, all comparisons of the flight conditions, namely departure, approach and final approach agree very well with the measured data. In addition, the reduction of the model to a 2D-directivity or neglecting the configuration were found to reduce the accuracy of the model but still are a viable option if these data are not available to establish a model according to the present invention.

Influence of the atmospheric Stratification on the Sound Propagation of single Flights

Sound propagation through the atmosphere is influenced by local conditions of temperature, humidity and wind speed. For aircraft noise the predominant meteorological effect on sound propagation is dissipation. Second order effects include level fluctuations caused by turbulence and on rare occasions with sound paths close to the ground the evolution of acoustical shadow zones and influences on barrier effects as a consequence of temperature and wind gradients with height.

An element of a method according to the present invention is the separation of the source model and the propagation model. The source model is based on a semi-empirical ap- proach and will account for airframe and engine noise of different flight conditions. The sound propagation model sonX is being adapted to the specific issues of aircraft noise calculations. Apart from the detailed propagation, calculation for the prognosis of single flights it is also used to reversely transform measured data at the receiver to the source. Here, the exact atmospheric reproduction is particularly crucial. A sophisticated propa- gation model also requires a higher level of detail and quality of the input data. Appropriate data of the vertical profile of the atmosphere can be obtained from different sources:

From weather balloons or from measurements of the aircraft itself.

From simulation results of numerical weather prediction models such as COSMO for many European countries. Based on measurements of ground stations, in combination with idealized profiles.

According to the present invention, meteorological data from the three different sources are presented and compared and in order to assess their impact on the resulting sound attenuation for different source-receiver-geometries. A method according to the present invention is described to derive idealized profiles from meteorological data of ground stations. Based on these results the benefit of a detailed modelling of the atmosphere is discussed in comparison with the assumption of a homogenous atmosphere.

Propagation model All propagation calculations according to the present invention can be done by the sonX model. The calculation from a point source to a receiver is conducted in two steps. First, the direct sound propagation for a uniform atmosphere with averaged conditions is calculated according to below equation (37). It accounts for geometrical divergence (Adiv) and atmospheric dissipation

in dependence of the frequency f according to ISO 9613-1 . The model also accounts for barrier and ground effects as well as foliage

attenuation which are negligible for the consideration according to the present

invention.

Second, additional meteorological effects like atmospheric dissipation due to

local temperature and humidity conditions are calculated by below equation (38). The attenuations are reported in level differences in comparison to the basic attenuations of equation (37). In addition, changes of shielding effects and the evolution of acoustical shadow zones due to temperature and wind gradients (D_met) are calculated by using a ray tracing algorithm. These effects are not relevant for the current analysis.

Information about the vertical profile of the atmosphere can be supplied as individual profiles (i.e. from prediction models or flight record data) or as idealized profiles (cf. Sec. 2.3). For the latter a classification scheme has been introduced (see below Table 5). The classification is reduced to the three main classes unstable (U), neutral (N) and stable (S). Depending on the wind speed at 10 m height and the current radiation balance a corresponding class can be determined for any specific atmospheric condition.

Table 5: Classification scheme for different weather conditions.

Radiation Balance and Development of idealized Profiles

The measurement of the radiation balance is possible but not always available as several sensors are needed. For example, in Switzerland typically only the incoming short-wave radiation is available, measured by a Pyranometer. Therefore, the determination of the radiation balance follows the VDI-Standard 3789 Part 2. Regarding a horizontal area, the radiation balance is the sum of the solar short-wave and terrestrial long-wave radiation, equation (39). The solar short-wave radiation is the difference of the global radiation (G) and its reflection (R) which depends on the short-wave albedo of the earth's surface. The emitted thermal radiation (E) of the earth can be simplified for natural ground sur- faces as a black body that emits energy with the fourth power to the surface temperature. Atmospheric gases and clouds reflect back to the earth (A).

Fig. 27 shows two diagrams illustrating an exemplary radiation balance for an exemplary day in September 2013 at Zurich airport (top). In combination with the wind speed the meteorological classes represent the different conditions during daytime (bottom) The radiation balance can be calculated for each day of the acoustical measurements to collect source data (Fig. 27, top). Weather data at station height (Station KLO at airport Zurich, 426 m above MSL) in ten minutes resolution was used as input for the radiation balance. The cloud cover N in eights is a visually observed parameter with a resolution of one hour, thus it was interpolated by a piecewise cubic hermite interpolating polynomial to guarantee a smooth curve of the counterradiation. By means of the radiation balance and the wind speed the classification scheme from above Table 5 was implemented as shown in Fig. 27 (bottom).

For each class in Table 5, predefined LinLog-profiles of the temperature, wind and hu- midity have been calculated, which represent idealized profiles for the meteorological class and different ground types. For the application under specific conditions the profiles were shifted towards the current temperature and humidity at the ground. The weather data used here had reference heights of 2 meters for temperature and humidity and 6 meters for wind direction. The profiles show considerable variations close to the ground. However, towards greater heights (more than 100 m) they exhibit a uniform behaviour with constant wind speed and direction, and an adiabatic lapse rate of 9.8 K/km for unsaturated air respectively 6.5 K/km for saturated air. Absolut humidity is assumed to be unchanged and hence relative humidity increases with height up to a maximum of 100%.

Profile Data

Fig. 28 shows two diagrams illustrating exemplary temperature, wind and humidity profiles for an exemplary day at 9 a.m. in September 2013 at Zurich airport. This example shows idealized profiles (blue solid line) in high divergence to profiles from the numerical model COSMO-2 (magenta dashed line) and FDR data (red dash-dotted line). The dashed black line represents a homogenous atmosphere with values measured at station height. Exemplary studies underlying the present invention include flight data records (FDR) for 223 departures at Zurich airport, which are provided by Swiss International Airlines. From this data, the air temperature and the wind speed and its direction were processed to create vertical profiles like in Fig. 28. In a method according to the present invention, as mentioned above, the FDR will further be processed in combination with the acoustical measurements to develop the sound emission model in function of the flight configuration.

All data considered in this paper originate from flights that have been measured within four weeks between August 21 and September 13 in 2013. Most of the departures of the A320-family took place at daytime between 9 a.m. and 4 p.m. While variations of atmospheric conditions are therefore limited, the temperatures still varied between 12°C and 28°C and the humidity between 20% and 80%. In addition, ten flights of the A340-300 aircrafts and three other types were measured at night around 1 1 p.m., where the temperature was still around 17°C to 20°C and the humidity some 65%. As an alternative, profile data of the numerical weather prediction model COSMO-2 was used as input data for the propagation calculation. COSMO is the Consortium for Small- Scale Modelling of the national weather services of Germany, Greece, Italy, Poland, Romania, Russia, and Switzerland. MeteoSwiss, who provided the data, uses the local scale model COSMO-2 with a grid spacing of 2.2 km, which also includes the Alpine arc (17). In fact, the numerical model assimilates atmospheric observation data from radiosonde, aircraft, wind profiler, and surface-level data. The provided hourly profiles include temperature, humidity, and wind speed and direction for the level-surfaces 24 to 60 equaling heights above ground of approx. 10 m to 4900 m. In Fig. 28, the four types of profiles are exemplarily compared with each other. For a comparison with a homogenous atmosphere based on momentary conditions, weather data at Zurich airport was used at a reference height of 2 m and is also plotted over height. Figure 2 shows an unstable situation at 10 a.m., for which all data sources show a similar pattern over the entire range of height up to 800 m. Fig. 29 shows three diagrams illustrating exemplary temperature, wind and humidity profiles for an exemplary day at 10 a.m. in September 2013 at Zurich airport. This example shows idealized profiles (blue solid line) in good agreement with profiles from the numerical model COSMO-2 (magenta dashed line) and FDR data (red dash-dotted line). The dashed black line represents a homogenous atmosphere with values measured at sta- tion height. In contrast to Fig. 28, Fig. 29 depicts a situation where the different profiles deviate considerably. The temperature decreases with increasing height for the COSMO-2 and FDR profiles, indicating an unstable stratification. In contrast the idealized profile already assumes a neutral condition. In the same way the humidity profiles differ strongly. Fig. 30 shows two diagrams illustrating exemplary selected temperature and humidity profiles for an exemplary day between 9 a.m. and 12 noon in September 2013 at Zurich airport. The numerical model COSMO-2 (magenta dashed line) indicates that the stratification from a stable boundary layer at night to a typically unstable layer at a sunny day is still ongoing until noon. The classification scheme already assumes an unstable stratification (blue solid line), the idealized profiles could not always reproduce the temporal transition of a stable boundary layer at night to a typically unstable layer at a sunny day correctly. In Figure 4 the vertical profiles of the idealized profiles and COSMO-2 data are compared for three different times of the day between 9.30 a.m. and noon. For this sunny day (see Fig. 27), the sun rises already at 7.30 a.m. and the radiation balance leads to an unstable stratification already 2 hours later if the classification scheme is applied. In contrast, the data of COSMO-2 indicate that the change of the stratification up to 500 m is still ongoing until noon, the temperature and humidity profiles converge only slowly.

In summary, FDR and COSMO-2 profiles of wind and temperature are generally highly consistent. The extrapolation of temperature from ground conditions to greater heights as performed by the idealized profiles seems to be valid in most cases. However wind and humidity profiles differ significantly compared to the more sophisticated profiles from the COSMO-2 model.

Propagation Calculation

Fig. 31 shows a schematic illustration of a calculation scenario based on a flight path. Although the flight path of the 223 used departures is available, the same generic source points from a virtual flight path can be used for all flights to avoid differences in propagation due to different flight path geometry. The scenario depicted in Figure 31 shows the three different source positions (S), one 500 m above receiver R1 and the others in 45° and 30° angle with respect to the flight direction. A second receiver R2 was set 500 m sidewise. The receivers are set 4 m above a plain grassland terrain. In the following, the results are presented as attenuations A_Meteo (see above equation (38)) of the propagation calculation to show the differences between a homogenous atmosphere based on momentary local conditions (LC) and on averaged conditions for Switzerland. Furthermore, the results of the COSMO-2 data are compared to those of the homogenous atmosphere based on momentary conditions (see below equation (40)). In addition the results of the idealized standard profiles (IP) are compared to those of COMSO-2 profiles (see below equation (41 )). The differences of the attenuations for each one-third octave band up to 5 kHz are discussed more in detail below. In particular, the influence on the A-weighted sound exposure level L_AE is discussed. As FDR data do not provide information on humidity data, this information was taken from COMSO-2 for the sound propagation calculation. However, the results turned out to be very similar to the calculations with COSMO-2 profiles and are therefore not shown and discussed further.

Results

Fig. 32 shows a diagram illustrating an exemplary variation of air absorption of a homogenous atmosphere shifted to momentary conditions at 2 m to a uniform atmosphere with averaged conditions. Results for the propagation S1 to R1 at 500 m distanceDistributions of the calculated differences of air absorption are presented for the 223 exemplary departures respectively their assigned meteorological situations. For each one-third octave band the differences are shown as Box-Whiskers-plots (cf. legend in Fig. 32). Providing the most reliable data COMSO-2 are used as reference for the comparison of results. Differences between homogenous Atmospheres

In a first step, the attenuation of a homogenous atmosphere based on momentary conditions at the ground is compared to the attenuation of homogenous atmosphere with averaged values of 8°C and 76% for Switzerland. The results for the closest point of approach (CPA) in Fig. 32 show only minor variations less than 0.6 dB below 500 Hz. Between 500 Hz and 1 .6 kHz mean values of approx. +0.5 dB resulted with maximum values of +1 .9 dB and positive minima (except for 1 .6 kHz). Hence, the momentary conditions always led to higher attenuations than the averaged atmosphere. For high frequencies the trend changed to negative differences but showed much higher variations in both directions. The mean value of the 5-kHz-band is -4.3 dB with a minimum value of -10.3 dB and a maximum of +15.0 dB.

Fig. 33 shows a diagram illustrating an exemplary Variation of air absorption of a homogenous atmosphere shifted to momentary conditions at 2 m to a uniform atmosphere with averaged conditions. Results for the propagation S3 to R2 at 1 1 18 m distance. Hence, from Fig. 33, the attenuation spectra for the largest propagation distance of 1 1 18 m can be derived. The same trend is observed as for the CPA with a turn to negative values at 2 kHz. The mean values for 500 Hz to 1 .6 kHz ranged from +0.5 dB to +1 .0 dB with maximal values from +2.0 dB to +4.3 dB and also positive minima. The high frequencies showed higher negative mean dissipation for an atmosphere based on momentary con- ditions, again with large deviations between -23 dB to +34 dB.

Differences of the Profile Data Sources

Fig. 34 shows two diagrams illustrating exemplary Differences in air absorption between a homogenous atmosphere at momentary conditions and COSMO-2 profiles. Results for the propagation S1 to R1 (500 m) and S3 to R2 (1 1 18 m). According to the present exemplary embodiments of the present invention, results are presented only for 250 Hz to 5 kHz because the variation of low frequencies is negligible. Fig. 34 (left) shows the variations in air absorption between the homogenous atmosphere at momentary condi- tions and the COSMO-2 profiles for S1 to R1 . Below 2 kHz the mean values were slightly positive. In contrast, above 2 kHz the mean differences increased up to -3.6 dB for 5 kHz with large variations of -17.4 dB to +5.7 dB. Fig. 34 (right) compares the propagation from S3 to R2. The trend is similar, but with larger variations for mid and high frequencies as a consequence of the greater propagation distance. Fig. 35 shows two diagrams illustrating exemplary differences in air absorption between idealized profiles and COSMO-2 profiles. Results for the propagation S1 to R1 (500 m) and S3 to R2 (1 1 18 m). The variance of the idealized profiles compared to the COMSO- 2 profiles is presented in Fig. 35. For both spectra there were no variations higher than 0.5 dB below 1 kHz. For higher frequencies the mean values for Figure 35 (left) de- creased to 4.2 dB at 5 kHz varying from -17.3 dB to 2.3 dB. In Figure 35 (right) the mean values also decreased to 3.4 dB but varied from -15.1 dB to 8.1 dB.

Influence on the resulting Sound Exposure Level

The above discussed results demonstrate considerable variations of air absorption for frequencies above 250 Hz. The question thus arises how relevant these variations are for the resulting LAE. Therefore, sound emission directivities of 35 Airbus A320 can be averaged and the resulting A-weighted spectra as well as the total LAE at receiver R1 were calculated (Figure 10). Then, the differences to the LAE can be determined for the mean difference and minimal and maximal variations as described above. Variations at frequencies above 2.5 kHz have almost no influence on the UE (<0.1 dB(A)), particularly due to the high absolute atmospheric absorption. The same applies for frequencies below 125 Hz that are highly attenuated by the A-weighting. The influence between a homogenous atmosphere at local and average conditions on the LAE for 500 m (S1 R1 ) is -0.2 dB(A) as a mean but varies from -1 .4 dB(A) to 0.3 dB(A) for single flights. At 1000 m (S3R1 ) the mean variation on the LAE is -0.6 dB(A) with a range from -2.6 dB(A) to 0.2 dB(A).

In the same way the influence of the differences in air absorption between a homogenous atmosphere at momentary conditions and COSMO-2 profiles are -0.6 dB(A) to 1 .3 dB(A) at 500 m and -0.9 dB(A) to 0.4 dB(A) at 1000 m. The differences in calculated air absorption of idealized and COSMO-2 profiles change the LAE from -0.2 dB(A) to 1 .5 dB(A) at 500 m and from -0.5 dB(A) to 0.7 dB(A) at 1000 m.

As Fig. 35 shows, the differences between idealized and COSMO-2 profiles at frequencies above 1 kHz are of the same order of magnitude as the variance between the ho- mogenous atmosphere at momentary conditions and COMSO-2. However, for mid-frequencies below 1 kHz, which strongly influence the LAE, the variations are small.

Fig. 36 shows a diagram illustrating an exemplary influence of the variance of dissipation on the A-weighted spectrum at the receiver R1 of the A320 for the incidence from S1 (90°) and from the front at S3 (30°). The indicators represent the minimal and maximal variations between the homogenous atmospheres at momentary resp. averaged conditions.

Consequently, a considerable dependence of the sound level at higher frequencies on varying conditions of temperature and humidity can be found. For the frequency bands considerably effecting the resulting A-weighted level the differences are smaller but still in the range of several decibels. Looking at the mean values it can be seen that the deviations between the different datasets show a clear trend, hence having a systematic influence also on the resulting long-term averages.

Comparing the different sources for meteorological data, prediction models such as COSMO-2 seem most reliable. While FDR data are in good agreement with COSMO-2 for wind and temperature, they provide no humidity data. In addition to the fact that FDR- data cannot be used as sole data source, the availability of FDR data is usually restricted and also the accuracy of input data depends on the type of aircraft. Therefore, FDR data alone is not an appropriate source for meteorological data.

The use of standardized profiles of the atmosphere which are normalized to conditions at the ground as shown above has a beneficial effect on the accuracy of the sound propagation calculation compared to the assumption of a homogenous atmosphere. The advantage of this approach is that profiles can be generated with very few, easily accessible input data.

A variance of air absorption can be expected to be of the same order of magnitude as the results presented here. In contrast, the variations between the homogenous atmosphere at momentary conditions and idealized profiles to the COSMO-2 profiles are not expected to change considerably and the following conclusions can also be regarded as generally applicable.

The use of momentary ground conditions of temperature and humidity is an important improvement compared to a uniform atmosphere with averaged conditions for the calculation of single flights. Additionally, a correct reproduction of the stratification in the propagation calculation has again a beneficial effect on the accuracy of the resulting LAE. In particular, the use of data from weather prediction models such as COSMO-2 is assumed to be the most accurate solution. Specifically for the development of an emission model according to the present invention, in which single flight events are reversely transformed to the source, it is recommended to make use of such detailed input data. Although high frequencies over 2.5 kHz are negligible for the L_AE above 500 m, the large variation of the air absorption could lead to large errors in this band.

It can be assumed that idealized profiles are not able to replace the more detailed profiles from COSMO-2. The assumptions, particularly for the humidity but also for the temperature above 100 m often lead to an extrapolation of the ground conditions, which is not valid for greater heights. Hence, the differences in air absorption compared to the COSMO-2 profiles, which are considerable for frequencies above 1 kHz, change the L_AE and result in a less accurate prognosis for single flights.

Models for Reflections at Forests, Cliffs, Buildings, Walls and other rigid Surfaces

A method according to the present invention may also include models for reflections at buildings, walls and other rigid surfaces as well as diffuse reflections at forest edges and cliffs. For a detailed description as well as references regarding such extensions of a propagation model underlying a method according to the present invention it is being referred to the "Documentation of the sonX model" dated 12 September 2016 as well as scientific papers published in ACTA ACUSTICA UNITED WITH ACUSTICA, namely "An Extended Model to Predict Reflections from Forests" (Jean Marc Wunderii; Vol. 98 (2012) 263 - 278; DO1 10.3813/AAA.918510); "A Model to Predict Sound Reflections from Cliffs" (Reto Pieren, Jean Marc Wunderii ;Vol. 97 (201 1 ) 243 - 253; DO1 10.3813/AAA.918404); "Calculation of Reflections in an Urban Environment" (Kurt Heutschi; Vol. 95 (2009) 644 - 652; DOI 10.3813/AAA.918193); and "An Engineering Model for Sound Pressure in Shadow Zones Based on Numerical Simulations" (Jan Hofmann, Kurt Heutschi; Vol. 91 (2005) 661 - 670), which are incorporated herein by reference. Subspace Concept

Fig. 37 shows a schematic perspective view of a vehicle 1 1 1 , such as an aircraft, in particular an aeroplane for which noise emissions and immissions are to be calculated in line with a method according to the present invention. An air space, within which the vehicle 1 1 1 travels is divided into subspaces 1 12 which constitute cells. Each of the subspaces 1 12 may have a cubic shape such that it provides eight corners 1 13.

Each of the subspaces 1 13 represents a potential source location. From each corner 1 13, of one of the subspaces 1 13, through which the vehicle 1 1 1 travels, to each receiver point, attenuation is stored in a database. During individual flights relation, attenuations from the corners 1 13 are looked up in the database. The resulting attenuation is determined as a linear interpolation of the attenuations of the corners 1 13 in comparison to the effective source position, i.e. the position of the vehicle 1 1 1 .

Fig. 37 shows a schematic perspective view of an air space divided into subspaces 1 12 in line with a method according to the present invention. Source locations 1 14 of a sound source, such as a vehicle 1 1 1 constitute an estimated trajectory 1 15 or defined trajectory 1 16. The air space and thus the subspaces 1 12 extend along a longitudinal direction X, a transverse direction Y, and a height direction Z which together form a Cartesian coordinate system. Preferably, in a projection along the height direction Z, each of the sub- spaces 1 12 has a quadratic shape. However, particularly vertical edges of the subspaces extending in parallel to the height direction Z may have different and/or changing lengths and coordinates along the height direction Z.

By dividing the air space into the subspaces 1 12, significantly less attenuations and therefore corresponding calculations have to be performed then in comparison with this full-size simulation. This enables an efficient calculation of different traffic scenarios in a method according to the present invention. Maximum level calculations and individual flight stimulations as well as real-time simulations of noise pollution are possible. This enables precise calculations with a method according to the present invention, incorporating spectral noise propagation models, considerations of meteor influences, coherent and incoherent reflections at buildings, shielding effects through buildings, and/or con- siderations of ground reflection/noise propagation influences depending on soil types as described above. Furthermore, a precise emission model is enabled which can be incorporated in a method according to the present invention for simulation of low-noise approach and departure procedures of vehicles to and from airports or alike, respectively.

Computing Devices, Systems and Methods

According to at least one aspect of a method and system according to the present invention, interfaces for noise calculations on computing devices operating in parallel to each other can be provided. A central data storage for facilitated administration can be implemented. Flexible configurable interfaces for data import can be made available. Methods and systems according to the present invention can provide functionality for data preparation and homogenisation. Furthermore, modules for evaluating and reporting can be provided for generating reports and standard file formats regarding noise exposure of people, buildings, flats, workspaces, areas, etc.

Fig. 39 shows a schematic diagram illustrating a system 1 17 for performing a method according to the present invention. The system 1 17 comprises an external module 1 18 an internal module 1 19. In the external module 1 18, external data, such as cockpit data, radar data, transponder data, emissions data an evaluation data as well as statistics can be provided and prepared. The statistics particularly comprise certain numbers of flight movements for certain aircraft types and routes. Based on such statistics, trajectories are being superimposed for generating the footprints and deriving and/or computing therefrom overall sound immission values for the at least one receiving point R, or in general a number of receiving points arranged along the trajectories.

In the internal module 1 19, calculations according to models incorporated in a method according to the present invention are conducted, which comprise the generation of flight events and geometries, source locations, receiving locations and a sound propagation based thereon as well as attenuation data derived therefrom and a simulation of single flights, as well as the generation of footprints comprising a bundle of estimated and/or defined trajectories, and finally noise pollution maps. The internal module 1 19 comprises a mainframe computer and/or computer cluster 120 and at least one client device 121 . In the computer cluster 120, the most demanding calculating operations for simulating models as described above according to the present invention are performed. Therefore, the computer cluster 120 preferably comprises a plurality of digital processors for performing the calculations which may be implemented in mainframes, servers or alike. The client device 121 may be a personal computer or alike, where less demanding calcula- tions and operations are performed. The system 1 17 according to the present invention is adapted to perform a method according to the present invention which comprises the following steps:

On the side of the external module 1 18, for example by external data providers and social services, in a first step S1 , localisation data, such as cockpit data, radar data, tran- sponder data and further related data is provided. In a second step S2, the localisation data is prepared in order to be entered into the internal module 1 19.

In the internal module 1 19, in particular the computer cluster 120, flight events including geometries are prepared and a third step S3. Based on the flight events, in a fourth step is for, sound source positions are calculated. In parallel or subsequently to the third step as 3, in a fourth step S4, receiving points are calculated. The source positions and receiving points then leave the computer cluster 120 in order to be displayed at the client device 121 . In the client device 121 , initial actual propagation calculations can be performed in a sixth step S6 in a way that they can be adjusted and alternated by a user of the client device 121 . The propagation calculations are then passed back from the client device 121 to the computer cluster 120. In the computer cluster 120, in a seventh step S7, attenuation data is calculated. The attenuation data is handed back to the client device 121 , where in an eighth step S8, single flight simulations are performed. Results of at least one single flight simulation, preferably a plurality of single flight simulations is passed back to the computer cluster in order to generate footprints containing nice simulation data pertaining to several tra- jectories can be generated while taking into account emissions data provided in a ninth step S9 from the external module 1 18.

Based on the generation of footprints in a tenth step S10, which can be performed by the computer cluster 120 and/or in the client device 121 , in combination with movement statistics regarding a population gained in an eleventh step S1 1 from the external module 1 18, noise pollution maps are generated in a twelfth step S12. Based on the noise pollution maps, a discussion of trajectories, in particular aeroplane routes can be objectified with the help of a method according to the present invention, so that all parties involved, such as operators, carriers, the public as well as politicians can find feasible and acceptable solutions when planning and managing traffic, in particular air traffic.

REFERENCE NUMERALS

1 First microphone location S Source

2 Second microphone location R Receiver

3 Third microphone location

4 Fourth microphone location X longitudinal direction

5 Fifth microphone location Y transverse direction

6 Sixth microphone location Z height direction

7 Seventh microphone location 35

8 Eighth microphone location θ Polar angle

9 Ninth microphone location φ Azimuth angle

10 Tenth microphone location p Density of Medium

16 First runway (starts)

28 First runway (landings)

34 Second runway

1 1 1 Vehicle

1 12 Subspace

1 13 Corner of subspace

1 14 Source location

1 15 Estimated trajectory

1 16 Defined trajectory

1 17 System

1 18 External module

1 19 Internal module

120 Computer cluster / mainframe

121 Client device

Claims

PATENT CLAIMS

1. Method for computing for at least one receiving point (R) a noise level generated by a sound source (S, 1 1 1 ), in particular an aeroplane, moving along a defined trajectory (1 16) with respect to the at least one receiving point (R), the method comprising the steps of: providing a sound propagation model for an airspace extending between the at least one receiving point and at least one estimated trajectory (1 15) along which the sound source is expected to be moving with respect to the receiving point; computing the noise level by entering the defined trajectory (1 16) into the sound propagation model and calculating a sound propagation between the sound source

(S, 1 1 1 ) and the at least one receiving point (R) for each one of a number of different sound source locations (1 14) arranged along the defined trajectory.

2. Method according to claim 1 , wherein the sound propagation is calculated based on at least one sound emission value of the sound source (S, 1 1 1 ).

3. Method according to claim 2, wherein the at least one sound emission value is calculated in dependence of a sound radiation pattern associated with a type of the sound source (S, 1 1 1 ) for each one of a number of different sound source locations (1 14) arranged along the defined trajectory (1 16).

4. Method according to claim 3, wherein the sound radiation pattern is based on a sound power level associated with the type of the sound source (S, 1 1 1 ).

5. Method according to claim 4, wherein the sound power level is estimated based on travel parameters of the sound source (S, 1 1 1 ) derived from the defined trajectory (1 16).

6. Method according to at least one of claims 3 to 5, wherein the sound radiation pattern is based on a directivity pattern associated with the type of the sound source (S, 1 1 1 ).

7. Method according to at least one of claims 1 to 6, wherein the sound propagation model comprises a direct propagation scenario and a complex propagation scenario; wherein for the direct propagation scenario, a direct sound propagation between the sound source (S, 1 1 1 ) and the at least one receiving point (R) is assumed; and wherein for the complex propagation scenario, a complex sound propagation between the sound source (S, 1 1 1 ) and the at least one receiving point (R) is assumed.

8. Method according to claim 7, wherein for each one of the number of different sound source locations (1 14), an angle of sight is determined between the sound source (S, 1 1 1 ) and a horizon; wherein the direct propagation model is applied for angles of sight greater than a negligibility threshold; and wherein it is being assumed that for angles of sight greater than the negligibility threshold, complex sound propagation becomes neglectable.

9. Method according to claim 7 or 8, wherein for the direct propagation scenario, a homogeneous atmosphere within the airspace is assumed.

10. Method according to claim 9, wherein the direct propagation scenario comprises at least one of a geometrical divergence model, a dissipation model, a barrier effects model, a foliage attenuation model, and a ground effects model for the airspace.

11. Method according to claim 10, wherein the ground effects model comprises at least one of a spherical wave propagation determination, an uneven terrain model, a surface property variation, and coherence loss model for modelling a loss of coherence of different sound paths between the sound source (S, 1 1 1 ) and the receiving point (R).

12. Method according to at least one of claims 7 to 1 1 , wherein the complex propagation scenario comprises at least one of a meteorological effects correction model, an obstacle reflection model, and a forest diffusion model for the airspace.

13. Method according to claim 12, wherein the meteorological effects correction model adapts a calculation of sound dissipation within the airspace to local temperature and humidity values of the airspace.

14. Method according to claim 12 or 13, wherein the meteorological effects correction model adapts a calculation of barrier effects within the airspace to vertical gradients of at least one of wind speed values and temperature values of the airspace.

15. Method according to claim 14, wherein the barrier effects include an acoustical shadow zone effect for at least one acoustical shadow area within the airspace where sound rays directly and/or indirectly emitted by the sound source do not directly reach the at least one receiving point due to upwind conditions identified based on the vertical gradients of the at least one wind speed value.

16. Method according to claim 15, wherein a residual sound exposure of the at least one receiving point located within the at least one acoustical shadow area is calculated based on at least one of a diffraction effects model and a scattering effects model applied to a sound ray passing along the at least one acoustical shadow area.

17. Method according to at least one of claims 1 to 16, further comprising the steps of dividing the airspace into subspaces (1 12) adjoining each other; calculating for each of the subspaces (1 12) a subspace model for determining a finite sound propagation within each of the subspaces (1 12); composing the sound propagation model from the subspace models with at least one boarder region between adjacent subspaces (1 12) representing at least one of a virtual sound source and a virtual receiving point for a virtual sound transfer value representing a virtual sound power level transferred between at least two adjacent subspaces (1 12).

18. Method according to claim 17, wherein a transfer of virtual sound power values is calculated for a number of possible combinations of virtual sound sources and virtual receiving points.

19. Method according to claim 17 or 18, wherein a virtual attenuation is calculated for each of the virtual sound sources and/or virtual receiving points, the virtual attenuation representing an attenuation of the virtual sound power value upon transfer between the virtual sound sources and/or virtual receiving points.

20. Method according to claim 19, wherein virtual attenuations are stored in a sub- space database.

21. Method according to claim 20, wherein during calculation of the noise level, the virtual attenuations are read from the subspace database.

22. Method according to at least one of claims 17 to 21 , wherein the propagation model includes an intermediate attenuation interpolated between the defined trajectory (1 16) and the at least one border region.

23. Method according to at least one of claims 17 to 22, wherein the airspace is divided into the subspaces along a homogeneous horizontal grid with constant distances between the subspaces in a lateral direction (X) and a transverse direction (Y) of the airspace.

24. Method according to at least one of claims 17 to 24, wherein the airspace is divided into the subspaces along a heterogenic vertical grid with an increasing height of the subspaces along a height direction (Z) of the airspace.

25. Method according to at least one of claims 17 to 24, wherein the subspaces (1 12) have a cuboid shape.

26. Method according to claim 25, wherein the border regions are constituted by eight corners (1 13) of each one of the cuboid subspaces (1 12).

27. Method according to at least one of claims 1 to 26, wherein sound propagation between the sound source (S, 1 1 1 ) and the at least one receiving point (R) is calculated both in the time domain and in the frequency domain.

28. Method according to claim 27, wherein a frequency spectrum of the sound propagation in the frequency domain is divided into frequency bands and the sound propagation is calculated for each of the frequency bands.

29. Method according to at least one of claims 1 to 28, wherein the sound propagation is calculated with unweighted sound pressure levels and the noise level is displayed with A-weighted sound pressure levels.

30. Method according to at least one of claims 1 to 29, wherein the noise level is weighted with a human population value representing an estimated population of the at least one receiving point with a number of human beings at a predefined time when the sound source (S, 1 1 1 ) moves along the defined trajectory (1 16).

31. Method according to at least one of claims 1 to 30, wherein calculating the sound propagation is distributed between a client device (121 ) providing a number of client FLOPs per cycle and a computer cluster (120) providing a number of cluster FLOPs per cycle, and wherein the number of client FLOPs per cycle is smaller than the number of cluster FLOPs per cycle.

32. Method according to claim 31 , wherein at least one total sound attenuation data set representing an attenuation of sound along at least one sound path established between the sound source (S, 1 1 1 ) and the at least one receiving point (R) is calculated from a number of partial attenuation value datasets generated by the computer cluster and representing different sound attenuation characteristics of the airspace for a respective scenario.

33. Method according to claim 32, wherein the total attenuation value dataset is calculated by the computer cluster (120) and transferred to the client device (121 ) or calculated on the client device (121 ).

34. Method according to at least one of claims 31 to 33, wherein a sound footprint is provided comprising at least one mean noise level at the at least one receiving point; and wherein the at least one mean noise level is associated to a bundle of sound source trajectories.

35. Method according to claim 34, wherein the sound foot print is calculated by the computer cluster (120) and transferred to the client device (121 ).

36. Method according to claim 34, wherein a superposition of at least two foot prints is calculated by the client device (121 ).

37. Method according to at least one of claims 1 to 36, further comprising a data preparation step, wherein a number of source points corresponding to the different sound source locations (1 14) along the defined trajectory (1 15) is defined.

38. Method according to claim 37, wherein the source points (1 14) are derived from at least one of a radar data obtained from a radar system and a transponder data obtained from a transponder system, the radar system and the transponder system adapted for locating and/or tracking the at least one sound source (S, 1 1 1 ).

39. Method according to claim 37 or 39, wherein the sound propagation model is calculated based on at least the number of source points, a number of receiving points, and a geo data set representing a geological environment of the airspace.

40. Method according to at least one of claims 1 to 39, wherein the at least one sound source is an airborne vehicle.

41. Computer-readable medium containing computer readable instructions for enabling a computer system to carry out a method according to at least one of claims 1 to 40.

42. Computer system (1 17) adapted to carry out a method according to at least one of claims 1 to 40.