Holger Waubke

A FORMULATION OF THE FAST MULTIPOLE BOUNDARY ELEMENT METHOD (FMBEM) FOR ACOUSTIC RADIATION AND SCATTERING FROM THREE-DIMENSIONAL STRUCTURES

Compared to the traditional boundary element method (BEM), the single level fast multipole boundary element method (SLFMBEM) or the multilevel fast multipole boundary element method (MLFMBEM) reduces the computational complexity of a job from O(n2) to O(n3/2) or O(n log2n), respectively with n being the number of unknowns; this means a dramatical reduction in terms of CPU-time and storage requirement. Large scale problems, unsolvable with the traditional BEM, can be solved by using the FMBEM. In this paper, the traditional BEM, SLFMBEM, and MLFMBEM are formulated within the framework of the Burton–Miller Collocation BEM for acoustic radiation and scattering from 3D structures. Attention is especially paid to the practical aspects of the method in order to get a reliable and efficient computation code. The performance of the method is tested with practical examples, including one for computing the head-related transfer function (HRTF) between 1000 and 18 000 Hz.

Effect of train type on annoyance and acoustic features of the rolling noise

This study investigated the annoyance associated with the rolling noise of different railway stock. Passbys of nine train types (passenger and freight trains) equipped with different braking systems were recorded. Acoustic features showed a clear distinction of the braking system with the A-weighted energy equivalent sound level (LAeq) showing a difference in the range of 10 dB between cast-iron braked trains and trains with disk or K-block brakes. Further, annoyance was evaluated in a psychoacoustic experiment where listeners rated the relative annoyance of the rolling noise for the different train types. Stimuli with and without the original LAeq differences were tested. For the original LAeq differences, the braking system significantly affected the annoyance with cast-iron brakes being most annoying, most likely as a consequence of the increased wheel roughness causing an increased LAeq. Contribution of the acoustic features to the annoyance was investigated revealing that the LAeq explained up to 94% of the variance. For the stimuli without differences in the LAeq, cast-iron braked train types were significantly less annoying and the spectral features explained up to 60% of the variance in the annoyance. The effect of these spectral features on the annoyance of the rolling noise is discussed.

A STOCHASTIC 2D-MODEL FOR CALCULATING VIBRATIONS IN RANDOM LAYERS

Vibrations induced by machinery and traffic have become of increasing concern in the last years, for example, when constructing buildings near railway lines. In this paper we will present a model designed to predict the vibration level in the ground. Since in practice it is nearly impossible to determine exact material parameters for soil layers, we use a model with a stochastic shear modulus G. Under moderate assumptions G can be split with the Karhunen–Loeve expansion into a mean value G0 and a stochastic part Gstoch. Using a combination method of finite elements, Fourier transformation and Polynomial Chaos, it is possible to transform the partial differential equation describing the system into a matrix-vector formulation Kx = b which can be split into a deterministic and a stochastic part (K0 + Ks) x = b analog to the shear modulus. To keep the dimensions of the matrices involved with this system small, we use a Neumann-like iteration to solve it. Finally, results for a small example are presented.

A 3D MODEL TO SIMULATE VIBRATIONS IN A LAYERED MEDIUM WITH STOCHASTIC MATERIAL PARAMETERS

A major problem for the simulation of the propagation of vibrations in ground layers is the fact that it is almost impossible to determine the material parameters needed for a numerical model exactly. In this work, we present a 3D model for layered soil, where in each layer the shear modulus is modeled as a stochastic process. Using the Karhunen Loeve expansion, the polynomial chaos expansion, and the Fourier transform, the stochastic system can be transformed into a linear system of equations in the wavenumber frequency domain. Unfortunately, the size of this system becomes very large and — contrary to a deterministic system — the stochastic system can no longer be decoupled for every wavenumber in the spatial Fourier domain. To solve this system efficiently, we propose an iteration procedure where the system is split into a deterministic and a stochastic part. As an external load on top of the ground, we use a vibrating box load moving along the x-axis. We discuss implementational details and present simulation results.

BOUNDARY ELEMENT METHOD FOR ISOTROPIC MEDIA WITH RANDOM SHEAR MODULI

Greens functions for elastic solids with random properties are usually derived by means of the perturbation method. This paper deals with a new approach that has the potential to deal with a large variability of random shear modulus based on the transformation of a polynomial chaos. The deterministic Greens functions for stresses and displacements and the principal values in the boundary integrals caused by a pressure load on the surface are nonlinear transformations of the random variables. A series of transformations of the polynomial chaos is used to transform significant parts of the equation. The first operation is a projection of the log normal distributed shear modulus to a series of Hermites polynomials based on a Gaussian variable. The second operation is the determination of an arbitrary potential of the wave velocity. The last operation, similar to the first one, consists in the determination of an exponential function depending on the inverse of the wave velocity. These operations, together with multiplications and summations, transform the complete relation from the random shear modulus to Greens functions and principal values. The inversion of the system matrix is already derived for the random finite element approach. The operations are independent of the specific problem and can be applied to almost all acoustic media and similar nonlinear problems.

The relation between psychoacoustical factors and annoyance under different noise reduction conditions for railway noise

The A-weighted sound pressure level (SPL) is commonly used to assess the effect of noise reduction measures on noise-induced annoyance. While for road traffic noise loudness seems to be a better descriptor of annoyance, for railway noise a systematic investigation seems to be lacking. Thus, in this study, the relation between annoyance and perceptually motivated descriptors was investigated for various conditions of binaural recordings of pass-bys of cargo and passenger trains. The conditions included free field and spectral mitigations caused by a 4 m high noise barrier, a 1 m high noise barrier close to the track, and rail dampers. Forty listeners performed a free magnitude estimation of annoyance for different presentation levels and the ratings were fit to various models. Further, level changes required to evoke a noticeable change in annoyance (annoyance thresholds) were acquired. The models based on the A-weighted SPL explained the ratings and thresholds better when the reduction measure was explicitly provided as a parameter. However, the optimal models were loudness-level-based models, which were able to better describe the annoyance, even independently of the reduction measure. Both experiments underline the effectiveness of loudness when describing the annoyance in the area of railway noise reduction.

Gaussian closure technique for Bouc's hysteretic model under white noise excitation

Bouc developed a hysteretic model for materials like rubber under dynamic excitation. The response of a hysteretic system under white noise excitation is normally estimated by means of the statistical linearization or a related method. Disadvantages of this method are the assumption of a Gaussian nature of the random distributions, the high computational efforts caused by the iterations needed and the instability of the iteration in certain parameter regions. Using the assumption of Gaussian random distributions, the Gaussian closure technique can be applied. Analytic solutions of the integrals occurring in this approximation were found and are presented. This solution allows for an explicit time step procedure for the random moments in the transient case. For the stationary case a fast and stable iteration about a set of non linear equations is needed. Both procedures allow to calculate the moments in a fast manner and allow to solve problems with more than one degree of freedom with limited computationa...

NOIDESc: A novel traffic noise description scheme

A novel framework for the acoustic and psychoacoustic description of noise signals (railway and road) has been proposed in order to extend and improve traditional noise classification schemes. In addition to measures of averaged sound‐pressure level and noise exposure duration, the description scheme includes psychoacoustic parameters such as spectral centroid, spectral spread, modulation spectrum, and further dynamic aspects of the sound events corresponding in part to the MPEG‐7/4 standard. The dynamic changes between foreground and background are addressed in the model. The approach assumes the evaluation of several low‐level acoustic parameters of the noise, to be integrated into few high‐level features by means of statistical methods, such as Gaussian mixture models and cluster analysis. As the usage of noise monitoring systems is expected to increase in the near future, the cumulative collection of calibrated sound recordings will provide comprehensive regional and supraregional sound databases to serve as input for automated noise classification. [The work in progress is performed in cooperation with the division of Acoustics of the TGM Vienna and is supported by the Austrian FFG.]