Combined wave and ray based room acoustic simulations of small rooms : [challenges and limitations on the way to realistic simulation results]

Classical room acoustic simulation methods based on the principles of geometrical acoustics (GA) have nowadays become an accepted and highly developed tool for acoustic practitioners and researchers in predicting the acoustic characteristics of large rooms like concert halls, theatres or open-space offices. However, when it comes to small rooms, even the most advanced geometrically based methods appear to be flawed due to the inherent negligence of important low frequency wave effects, such as standing waves, diffraction and interference. In order to overcome this limitation the present thesis investigates the potential benefits of the application of the Finite Element Method (FEM) to the modally dominated part of the sound field. However, despite the fact that the FEM is a wellestablished tool in engineering sciences, which fully captures all relevant wave effects, its application to room acoustics introduces far-reaching and yet unresolved questions regarding the realistic source, boundary and receiver representation. The present thesis therefore establishes a complete framework for the combination of FEand GA-based room acoustic simulation results and discusses the inherent challenges and limitations including all aspects of sound generation, sound reflection and sound reception. Moreover, the thesis establishes detailed guidelines for the best-possible determination of all necessary input data for both simulation domains. The investigations conducted in the course of this thesis aim at two different goals. On the one hand the thesis investigates the influence of selected isolated aspects regarding their influence on the simulation accuracy. In particular, these topics include a study on the potential of the image source method to predict the modal characteristics of the low frequency Room Transfer Function (RTF), a study on the efficient modelling of porous absorbers in the FE domain and finally a study on the possible low frequency coupling of the excitation velocity of a loudspeaker to the sound field at the loudspeaker membrane. On the other hand the thesis investigates the overall potential of the presented combined approach by conducting extensive objective and subjective comparisons of measurement and simulation results for three types of acoustically relevant small spaces (a scale-model reverberation room, a recording studio and two different car passenger compartments). For each room considerable efforts have been made to obtain a best-possible a-priori assessment of all necessary material and source data for the simulations. However, especially with regard to the determination of the acoustic surface impedances at the room boundaries certain inevitable inaccuracies have to be accepted. While the presented results reveal an overall good agreement regarding the energy distribution in time and frequency domain for all considered rooms, the results clearly show that as expected the simulation accuracy considerably degrades with increasing complexity of the room geometry and boundary conditions. Moreover, it is important to mention that even with the FEM a precise prediction of the fine structure of the RTF appears

[1]  Finn Jacobsen,et al.  A comparison of two different sound intensity measurement principles , 2005 .

[2]  Toru Otsuru,et al.  In situ measurements of surface impedance and absorption coefficients of porous materials using two microphones and ambient noise , 2005 .

[3]  E. T. Paris,et al.  On the reflexion of sound from a porous surface , 1927 .

[4]  M. Biot.  Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range , 1956 .

[5]  Michael Vorländer,et al.  Beugungssimulation ohne Rechenzeitexplosion: Die Methode der quantisierten Pyramidenstrahlen : ein neues Berechnungsverfahren für Raumakustik und Lärmimmissionsprognose ; Vergleiche, Ansätze, Lösungen , 2004 .

[6]  Heinrich Kuttruff,et al.  Sound Fields in Small Rooms , 1998 .

[7]  Wolfgang Ahnert,et al.  First Approach to Combine Particle Model Algorithms with Modal Analysis using FEM , 2005 .

[8]  Alan V. Oppenheim,et al.  Discrete-time signal processing (2nd ed.) , 1999 .

[9]  Neville Thiele,et al.  Loudspeakers in Vented Boxes: Part 1 , 1971 .

[10]  C. Zwikker,et al.  Sound Absorbing Materials , 1949 .

[11]  R. Heinz.  BINAURALE RAUMSIMULATION MIT HILFE EINES KOMBINIERTEN VERFAHRENS. GETRENNTE SIMULATION DER GEOMETRISCHEN UND DIFFUSEN SCHALLANTEILE , 1993 .

[12]  Richard H. Small.  Vented-Box Loudspeaker Systems-Part 2: Large-Signal Analysis , 1973 .

[13]  J. Borish.  Extension of the image model to arbitrary polyhedra , 1984 .

[14]  Marc Aretz,et al.  Perceptual Comparison of Measured and Simulated Sound Fields in Small Rooms , 2010 .

[15]  Jont B. Allen,et al.  Image method for efficiently simulating small‐room acoustics , 1976 .

[16]  Jean Nicolas,et al.  Measurement of acoustic impedance in a free field at low frequencies , 1988 .

[17]  Yasushi Shimizu,et al.  Assessing the accuracy of auralizations computed using a hybrid geometrical‐acoustics and wave‐acoustics method , 2004 .

[18]  Wim Desmet,et al.  A Hybrid Wave Based - Modally Reduced Finite Element Method for the Efficient Analysis of Low- and Mid-frequency Car Cavity Acoustics , 2009 .

[19]  Paul Funk.  Variationsrechnung und ihre Anwendung in Physik und Technik , 1962 .

[20]  John S. Bradley,et al.  Subjective evaluation of new room acoustic measures , 1995 .

[21]  M. R. Schroeder,et al.  Digital simulation of sound transmission in reverberant spaces (part 1) , 1969 .

[22]  Richard H. Small.  Closed-Box Loudspeaker Systems-Part 2: Synthesis , 1973 .

[23]  Michael Vorländer,et al.  About just noticeable differences for aspects of spatial impressions in concert halls , 2005 .

[24]  H. Dekker,et al.  EDGE effect measurements in a reverberation room , 1974 .

[25]  Wim Desmet,et al.  A Coupled Finite Element–Wave Based Approach for the Steady-State Dynamic Analysis of Acoustic Systems , 2001 .

[26]  Wj Davies,et al.  The sensitivity of listeners to early sound field changes in auditoriums , 1993 .

[27]  Diemer de Vries,et al.  Determining acoustical parameters using cochlear modeling and auditory masking , 2008 .

[28]  T. J. Schultz.  Diffusion in reverberation rooms , 1971 .

[29]  Carl F. Eyring,et al.  Reverberation Time in “Dead” Rooms , 1930 .

[30]  Gerrit Vermeir,et al.  Measuring the free field acoustic impedance and absorption coefficient of sound absorbing materials with a combined particle velocity-pressure sensor , 2006 .

[31]  R. H. Bolt,et al.  Frequency Response Fluctuations in Rooms , 1950 .

[32]  Timothy M. Barry.  Measurement of the absorption spectrum using correlation/spectral density techniques , 1974 .

[33]  G. M. L. Gladwell,et al.  A variational formulation of damped acousto structural vibration problems , 1966 .

[34]  W. Desmet.  A wave based prediction technique for coupled vibro-acoustic analysis , 1998 .

[35]  Renate Heinz.  Entwicklung und Beurteilung von computergestützten Methoden zur binauralen Raumsimulation , 1994 .

[36]  P. Pinsky,et al.  Complex wavenumber Fourier analysis of the p-version finite element method , 1994 .

[37]  Michael Vorländer,et al.  Quality assessment of room acoustic simulation tools by comparing binaural measurements and simulations in an optimized test scenario , 2011 .

[38]  Manfred R. Schroeder,et al.  Computer simulation of sound transmission in rooms , 1963 .

[39]  Richard H. Small.  Vented-Box Loudspeaker Systems-Part 3: Synthesis , 1973 .

[40]  M. Schroeder.  The ‘‘Schroeder frequency’’ revisited , 1996 .

[41]  François Santon.  Numerical prediction of echograms and of the intelligibility of speech in rooms , 1976 .

[42]  Michael Vorländer,et al.  Calculation of head-related transfer functions for arbitrary field points using spherical harmonics decomposition , 2012 .

[43]  Marc Aretz.  Specification of Realistic Boundary Conditions for the FE Simulation of Low Frequency Sound Fields in Recording Studios , 2009 .

[44]  A. Krokstad,et al.  Calculating the acoustical room response by the use of a ray tracing technique , 1968 .

[45]  H. Nélisse,et al.  Characterization of a diffuse field in a reverberant room , 1997 .

[46]  Richard H. Small.  Vented-Box Loudspeaker Systems-Part 4: Appendices , 1973 .

[47]  M. Vorländer.  Simulation of the transient and steady‐state sound propagation in rooms using a new combined ray‐tracing/image‐source algorithm , 1989 .

[48]  J. Blauert.  Spatial Hearing: The Psychophysics of Human Sound Localization , 1983 .

[49]  M. Schroeder,et al.  On Frequency Response Curves in Rooms. Comparison of Experimental, Theoretical, and Monte Carlo Results for the Average Frequency Spacing between Maxima , 1962 .

[50]  H. Kuttruff.  ON THE AUDIBILITY OF PHASE DISTORTIONS IN ROOMS AND ITS SIGNIFICANCE FOR SOUND REPRODUCTION AND DIGITAL SIMULATION IN ROOM ACOUSTICS , 1991 .

[51]  Jean François Allard,et al.  Measurements of acoustic impedance in a free field with two microphones and a spectrum analyzer , 1985 .

[52]  J. S. Bolton,et al.  The application of cepstral techniques to the measurement of transfer functions and acoustical reflection coefficients , 1984 .

[53]  R. Spagnolo,et al.  The effect of stationary diffusers in the measurement of sound absorption coefficients in a reverberation room: An experimental study , 1981 .

[54]  Takeshi Komatsu,et al.  Improvement of the Delany-Bazley and Miki models for fibrous sound-absorbing materials , 2008 .

[55]  Michael Vorländer,et al.  Efficient Modelling of Absorbing Boundaries in Room Acoustic FE Simulations , 2010 .

[56]  Mendel Kleiner,et al.  Experimental auralization of car audio installations , 1996 .

[57]  Cheol-Ho Jeong,et al.  An approximate treatment of reflection coefficient in the phased beam tracing method for the simulation of enclosed sound fields at medium frequencies , 2008 .

[58]  Richard H. Small,et al.  Vented-Box Loudspeaker Systems--Part 1: Small-Signal Analysis , 1973 .

[59]  Finn Jacobsenb,et al.  An Iterative Method for Determining the Surface Impedance of Acoustic Materials In Situ , 2008 .

[60]  Michael Vorländer,et al.  Open Measurements of Edge Diffraction from a Noise Barrier Scale Model , 2011 .

[61]  K. Heinrich Kuttruff.  Sound decay in reverberation chambers with diffusing elements , 1981 .

[62]  R. H. Bolt,et al.  Normal frequency Spacing Statistics , 1947 .

[63]  Smarajit Ghosh.  Network theory : analysis and synthesis , 2005 .

[64]  Michael Vorländer,et al.  Finite-Elemente-Methoden, Lösungsalgorithmen und Werkzeuge für die akustische Simulationstechnik , 2009 .

[65]  W. A. Davern.  Measurement of low frequency absorption , 1987 .

[66]  E. N. Bazley,et al.  Acoustical properties of fibrous absorbent materials , 1970 .

[67]  A. Cops,et al.  Sound absorption in a reverberation room: Causes of discrepancies on measurement results , 1995 .

[68]  J. M. Berman.  The Behavior of Sound in a Bounded Space , 1973 .

[69]  H. Kuttruff.  A simple iteration scheme for the computation of decay constants in enclosures with diffusely reflecting boundaries , 1995 .

[70]  Janina Fels,et al.  From Children to Adults: How Binaural Cues and Ear Canal Impedances Grow , 2008 .

[71]  J. Z. Zhu,et al.  The finite element method , 1977 .

[72]  Richard V. Waterhouse,et al.  Interference Patterns in Reverberant Sound Fields. II , 1955 .

[73]  Manfred R. Schroeder,et al.  Natural Sounding Artificial Reverberation , 1962 .

[74]  Michael Vorländer,et al.  Frequency- and Time-dependent Geometry for Real-time Auralizations , 2010 .

[75]  H. A. Schenck.  Improved Integral Formulation for Acoustic Radiation Problems , 1968 .

[76]  Marc Aretz.  Different approaches for efficient finite element modelling of absorbers in small rooms , 2008 .

[77]  U. Svensson,et al.  An analytic secondary source model of edge diffraction impulse responses , 1999 .

[78]  P. Nelson,et al.  Measurement of transient response of rooms and comparison with geometrical acoustic models , 1999 .

[79]  Walter Lauriks,et al.  The acoustic sound field above a porous layer and the estimation of the acoustic surface impedance from free‐field measurements , 1992 .

[80]  Robert B. Newman,et al.  Collected Papers on Acoustics , 1927 .

[81]  de Bree.  The Microflown, an acoustic particle velocity sensor , 2003 .

[82]  Twan Korthorst,et al.  A NOVEL DEVICE MEASURING ACOUSTICAL FLOWS , 2004 .

[83]  Densil Cabrera,et al.  Basic Considerations for Loudness-Based Analysis of Room Impulse Responses , 2009 .

[84]  Michael Vorländer.  Performance of computer simulations for architectural acoustics , 2010 .

[85]  Cheol-Ho Jeong,et al.  Room acoustic transition time based on reflection overlap. , 2013, The Journal of the Acoustical Society of America.

[86]  Yvan Champoux,et al.  Pressure variation above a layer of absorbing material and impedance measurement at oblique incidence and low frequencies , 1989 .

[87]  C. Molloy.  Propagation of Sound in Porous Materials , 1964 .

[88]  Sylvio R. Bistafa,et al.  Numerical solutions of the acoustic eigenvalue equation in the rectangular room with arbitrary (uniform) wall impedances , 2003 .

[89]  Michael Vorländer,et al.  Sound field simulations in a car passenger compartment using combined wave- and ray-based simulation methods , 2009 .

[90]  Richard H. Small.  Closed-Box Loudspeaker Systems-Part 1: Analysis , 1972 .

[91]  Dirk Schröder,et al.  Physically based real-time auralization of interactive virtual environments , 2011 .