Localization of sound sources plays an important role in our everyday lives. The shape of the human head, the torso and especially the shape of the outer ear (pinna) have a filtering effect on incoming sounds and thus play an important role for sound localization. This filtering effect can be described using the so called head related transfer functions (HRTFs). By calculating the distribution of the sound pressure around the head with numerical methods like the boundary element method (BEM), these HRTFs can be calculated numerically.

In BIOTOP the numerical calculations shall be made more efficient by using adaptive wavelet- and frame techniques. Compared to commonly used BEM basis functions, wavelets have the advantage that wavelets can adapt better to a given distribution of the acoustic field on the head. As a generalization of wavelets, frames allow for an even more flexible construction method and thus for a better adaption to the problem at hand.

BIOTOP combines abstract theoretical mathematics with numerical and applied mathematics. It is an international DACH (DFG-FWF-SFG) project between the Philipps-Universität Marburg (Stephan Dahlke), the University Basel (Helmut Harbrecht) and the ARI. The expertise of all three research groups shall be combined to develop new strategies and numerical methods. The project is funded by the FWF: Pr. Nr. I-1018-N25

Read more: BIOTOP: Adaptive Wavelet and Frame techniques for acoustic BEM. FWF Project I-1018-N25

SysBahnLärm was a joint project of the ARI with the TU Vienna the Austrian Railways and industrial partners funded by the FFG as well as the ÖBB. Aim of the project was to create a handbook on the systemic reduction of railway noise. The ARI was responsible for the psychoacoustic evaluation of the effects of noise from wheels with different roughness and of different noise reduction systems e.g. rail damping systems. Further, the ARI investigated the emission pattern of the rail-wheel contact using our 64-channel microphone array.

Using measured train pass-by signals, a psychoacoustic testing procedure was developed and stimuli for this test were selected. Subjects had to rate the relative annoyance of different trains or different noise reduction systems with respect to each other.

For investigating the rail-wheel contact, a beamforming technique was used in order to determine the point of the maximal emission relative to the top of the rail.

The handbook should act as a guideline for the different noise reduction measures and their respective advantages and problems.

The Acoustic Research Institute was mandated to do measurements with the acoustic 64-channel microphone array using the beam forming method to derive a source model for high speed trains according to the new guideline CNOSSOS-EU.

The beam forming method was used, because the train is a fast moving vehicle and therefore a transient acoustic source. Five heights were used in the evaluation based on the CNOSSOS-EU and additionally five heights were evaluated that fit to the geometry of the trains.

Speeds from 200 km/h up to 330 km/h were tested for the ICEs and from 200 km/h up to 250 km/h for the Railjet. At the same speed both trains had the same acoustic level.

Standard noise mapping software use geometrical approaches to determine insertion loss for a noise barrier. These methods are not well suited for evaluating complex geometries e.g. curved noise barriers or noise barriers with multiple refracting edges. Here, we aim at deriving frequency and source- as well as receiver-position dependent adjustments using the boundary element method. Further, the effect of absorbing layers will be investigated as a function of the geometry. Results will be incorporated into a standard noise mapping software.

The cross-sections of different geometries are first parameterized and discretized and then evaluated using two-dimensional boundary element simulations. The BEM code was developed at our institute. Different parameter sets are evaluated in order to derive the adjustments for the specific geometries compared to a straight noise barrier. To make the simulations more realistic, a grassland impedance model is used instead of a fully reflecting half plane. Simulations will also be evaluated using measurements from actual noise barriers.

- TAS Schreiner (measurements)
- Soundplan (implementation in sound mapping software)

This project is funded from the VIF2011 call of the FFG (BMVIT, ASFINAG, ÖBB)

The boundary element method (BEM) is an often used tool for numerically solving acoustic radiation and reflection problems. Most of the time, a formulation in the frequency domain can be used, however, for short impulses or when the acoustic simulation is coupled with a non-linear behaviour caused by structure deformation, a formulation in the time domain is necessary.

The boundary integral equations and the fundamental solution necessary for the BEM in the time domain are derived by inverse Fourier transformation of the corresponding formulations in the frequency domain. These equations are then discretized using the Galerkin method in the spatial dimensions and the collocation method in the time dimension. The MOT (Marching-On-in-Time) method is used to solve the resulting system of equations. The well known stability problem of the MOT-method is handled by using the Burton-Miller approach in combination with the Galerkin method in the spatial discretization and high order temporal interpolations. It is well known that these measures enhance the stability of MOT.

Additionally it is planned to enhance the efficiency of the method by using a modified plane wave time decomposition (PWTD) algorithm.

Acoustic holography is a mathematical tool for the localization of sources in a coherent sound field.

Using the information of the sound pressure in one plane, the whole three-dimensional sound field is reconstructed. The sound field must be coherent and the half-space in which the sources are situated must be known.

Acoustic holography is used to calculate the sound field in planes parallel to the measured plane. Normally, a plane near the hull of the structure is chosen. Concentrations in the plane are assumed to be the noise source.

The usual transformation in acoustics is the Fourier-Transformation. A fast and simple implementation is the windowed Fast Fourier Transformation. A disadvantage of the FFT is that all frequencies are equally spaced in the time frequency plane. A logarithmic spacing that allows keeps the relative resolution in the frequency plane constant is the Wavelet Transformation. This gives the possibility of a higher temporal resolution in the high frequency plane. Several types are implemented in STX and PAK.

A higher temporal resolution is possible, if quadratic transformations defined in the Cohen Class are used. The Windowed Pseudo Wigner Ville Distribution and a discrete version of the Choi-Williams Distribution are implemented in STX and PAK. Disadvantages of these transformations are the cross products that are reduced by smoothing in the different transformations of the Cohen class.

A handbook is written for or the practical use of the difficult transformations. The Handbook documents the possibilities and the limits of the transformations

If measurements are possible only at the hull of a machine, a tool is needed to separate the dominating near-field components from the far-field components. This, in turn, allows the far-field levels to be estimated. The separation is often not possible using spectral methods, because both components have nearly the same frequency. Using a limited number of microphones, a modal separation is also impossible. Instead of a modal analysis, a principal component analysis is applied.

The narrow-band Fourier transform method is used, and a separate analysis is conducted for each frequency. The cross-power matrix spanning all microphone positions is used. The components are then calculated using the PCA. As long as the modes at the microphone positions have different relative values, PCA can be used to separate them. In an initial test, the far field is observed and the transfer function for every component from the near field to the far field is estimated. These transfer functions are assumed to be constant in time. They are used for the estimation of the overall far-field level.

Observation of the far-field level of machines.

This project aims to develop an independent modulus for the wavelet analysis that contains a simple program interface and can be used flexibly.

The implementation was in C++ in the form of a wavelet analysis class and a signal queue. Features:

- The Input/Output data format can be chosen at run time. The Input and the Output are separately configurable.
- There are several possibilities for choosing the array and distribution of the frequency bin. The frequency bin vector can also be transferred.
- Seven wavelets are implemented.
- A down-sampling method can be used for the acceleration (factor: 1.2 convert frequency bins are chosen automatically).
- Because of the disjunction in signal queue and analysis, an asynchrony Input/Output is possible.
- Compiling an optimized numerical library can be achieved. Currently, the application of the "Intel® Signal Processing Library" (SPL) or of the "Intel® Integrated Performance Primitives" (IPP) is possible.
- The signal queue class can be used independently of the analysis class. It also implements the down-sampling function.

The developed classes are used as a modulus in the acoustic measurement and analysis system PAK. The analysis class was also integrated as a signal processing atom WLLIB in ST^{x}.

The Spatial Transform of Sound Fields (STSF) is an extension of the acoustic holography that enables the handling of incoherent sound sources.

The Karhunen Loeve Expansion or Principal Component Analysis (PCA) method is used to separate the random field recorded at different microphone positions into coherent components. Again, acoustic holography is used to transform every component from the measurement plane into a plane in arbitrary depth. If needed, the total incoherent sound field in the chosen depth can be reconstructed.

Localization of incoherent sound sources near the hull of the structure.

In Cooperation with National Instruments an implementation of MPEG4 features in the software package DIADEM is planned.

The application of MPEG4 features to noise is proven. Now the implementation of MPEG4 features into DIADEM is planned. In preparation of the project additional features were implemented into STX. The implementation into DIADEM is projected in the future.

DIADEM is a database that allows for a rapid search of measurement recordings. New search indexes can be generated based on the MPEG4 features of the recordings.

Upon first investigation, the design of new outward-curved noise barriers has an improved noise-shielding effect if absorbing material is applied. Further investigation shall prove this ability. Numeric simulations and measurements are being processed.

Advanced boundary element methods (BEM) in two dimensions will prove the noise-shielding ability of the sound barrier. Different curvy and straight designs are compared to each other with respect to their shielding effect in the spectrum. Measurements at existing walls are processed and compared. Measurements are conducted without a noise barrier. A simulated softening affect of the noise barrier walls is used to simulate the noise signal behind the new barriers.

Calma Tec has patented the designs and will offer new designs in practice.

01. Traffic Noise Recording Plan. 02. Sound Data Storage, Retrieval and Spectrographic Description. 03. Descriptive Noise Statistics. 04. Pricipal Component Analysis. 05. Sound Barrier Mesh Models. 06. Simulation, Transfer Functions & Clustering. 07. Visualization. 08. Psychoacoustic Irrelevance. 09 Modulation Effects. 10. Subjective Preference Tests. 11. Conclusions

In certain measurement setups, such as the measurement of gear mechanism behavior undergoing load reversal, the fine structure of the rotation speed function within a single rotation is interesting. In these situations, measurement errors caused by irregular cog intervals or by other failures of cogwheels are disturbing and must be corrected.

From a reference signal, the distribution parameter of the rotation angle for each cog of the cogwheel is assigned as a cogwheel model. This cogwheel model can minimize the measurement failures caused by the cogwheel if its cog is implemented in synch with the measurement signal. If the reference signal and the measurement signal come from different measurements, the synchronicity has to be established first. The calculation of the shift between the two signals is determined by the cog index, which has the maximum correlation of the rotation angle allocation between the reference signal and the measurement signal.

The developed method will be used as a module in the acoustic measurement and analysis system PAK.

In the boundary element method for infinite exterior spaces occur spurious modes that belong to the interior problem. The resonances are caused by a singularity of the matrix. As compensation additional equations are used that belong to chief points in the interior space.

A new method that does not depend on the appropriate selection of chief points is the Burton Miller Method. It assures good results but increases the numerical calculation and gives unsymmetrical matrices. In combination with the Fast Multipole Method (FMM) a fast calculation of non symmetric matrices is possible.

An important difficulty of ray-tracing and boundary element method is the fine grid, which is needed in the high frequency region.

By means of new alternating shape functions e.g. wavelets at the boundary it could be possible to define a grid on the boundary that is independent from the wave number.

Beside the Fast Multipole Method wavelet based approaches are of increasing interest for the fast calculation of large matrices.

The first part of the project is the implementation of the wavelet method for the compression of the data. Next step is the investigation whether wavelet and FMM approaches can be used together and whether an additional speed up is possible.

The aim of the project is the development of an algorithm that allows for a fast calculation of large matrices. The final aim is the possibilities to handle large acoustic problems numerically.

The Multilevel Fast Multipole Method, when used in combination with the Boundary Element Method (BEM), is a tool to significantly speed up the simulation of large objects almost without loss in accuracy.

The Fast Multipole Method subdivides the Boundary Element mesh into different clusters. If two clusters are sufficiently far away from each other (i.e. they are in each other's far field), all calculations that would have to be made for every pair of nodes can be reduced to the midpoints of the clusters with almost no loss of accuracy. For clusters not in the far field, the traditional BEM has to be applied. The Multilevel Fast Multipole Method introduces different levels of clustering (clusters made out of smaller clusters) to additionally enhance computation speed.

The MLFFM is used for the simulation of head related transfer functions. The diagram above compares the result of a classical BEM with the MLFMM.

In order to numerically calculate individual head-related transfer functions (HRTFs), a boundary element model (BEM) was developed. This model makes it possible to calculate the sound pressure at the head that is caused by different external sound sources with frequencies up to 20,000 Hz.

In engineering, the traditional BEM is widely used for solving problems. However, the computational effort of the BEM grows quadratically with the number of unknowns. This is one reason why the traditional BEM cannot be used for large models, even on highly advanced computers. In order to calculate the sound pressure at the head at high frequencies, very fine meshes need to be used. These meshes result in large systems of equations. Nevertheless, to be able to use the BEM, the equations must be combined with the Fast Multipole Method (FMM). With the FMM, the resulting matrices can be kept smaller, thus allowing the numeric solving of the Helmholtz equation with feasible effort and almost no accuracy loss as compared to the traditional BEM.

The geometry of the head (especially the form of the outer ear or pinna) acts as a kind of filter. This geometry is very important in localizing sound in the vertical direction and distinguishing between sounds coming from the front or the back. The BEM model can be used to numerically calculate these filter functions, which are dependent on the position and the frequency of the sound source.

FWF (Austrian Science Fund): Project #P18401-B15

- Kreuzer, W., Majdak, P., Chen, Z. (2009): Fast multipole boundary element method to calculate head-related transfer functions for a wide frequency range, in: J. Acoust .Soc. Am. 126, 1280-1290.
- Kreuzer, W. and Chen, Z. S. (2008). "A Fast Multipole Boundary Element Method for calculating HRTFs," AES preprint 7020, AES Convention, Vienna.