Efficient low-frequency room acoustic modelling.

Boris Jean-Francois Mondet

Research output: Book/ReportPh.D. thesis

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Room acoustic simulations are widely used in the design and renovation of various spaces, ranging from offices to theatres or even churches. Nevertheless, small volumes remain a challenge with currently available techniques. These include spaces such as meeting rooms and classrooms, where acoustic conditions are critical. This limitation is due to two main factors. Firstly, surface materials are commonly characterized with simplified parameters which neglect valuable information for low frequencies. It thus leads to an approximate modelling of reflections that is not valid in small rooms. Secondly, research on room acoustic simulations has not been able to find a method that offers accurate results in a timely manner. Indeed, the methods available either favor efficiency by means of approximations or inversely are accurate at the expense of a large computational load. The present PhD thesis thus pursues accurate and efficient acoustic simulations in small rooms by tackling these two limiting factors. The boundary conditions representing surfaces in a room are generally expressed in terms of absorption and scattering coefficients, two energy parameters lacking phase information. The latter is most often estimated from the roughness of a surface, while the former is the only parameter with widely available measured data for the materials found in room acoustics. On the contrary, surface impedance is a complex-valued parameter from which all the information needed to describe a boundary can be derived. Consequently, a method to calculate surface impedances from measured absorption coefficients is introduced in this study. The method is based on a novel impedance model making use of fractional calculus. The information missing in absorption coefficients is then retrieved by solving an inverse problem through constrained optimization. The vast majority of commercial solutions for room acoustic simulations are based on geometrical acoustics. They therefore rely on high frequency assumptions that do not account accurately for interference and diffraction effects. On the other hand, the numerical methods for differential equations, often called wave-based methods in room acoustics, are too heavy computationally for practical application. A compromise method that combines accuracy and efficiency thus has to be found. To this end, the Equivalent Source Method in the time domain is investigated. This method draws its efficiency from assuming a solution to the wave equation and approximately solving the boundary condition equation. A combination of image and equivalent sources is then introduced in order to improve the accuracy of the method at a low computational cost. Accurate acoustic simulations of small rooms are brought closer to practical reality thanks to the contributions of this project. The impedance retrieval method introduced is a tool that can benefit all simulation methods, and hence improve the overall accuracy of room acoustic modelling. The study of the Equivalent Source Method also provides valuable insight on its application to room acoustics. Moreover, the combination of image and equivalent sources presented shows an interesting potential and could lead to further research on the topic.
Original languageEnglish
PublisherTechnical University of Denmark
Number of pages116
Publication statusPublished - 2020

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