Contributions to discrete-time methods for room acoustic simulation

The sound field distribution in a room is the consequence of the acoustic properties of radiating sources and the position, geometry and absorbing characteristics of the surrounding boundaries in an enclosure (boundary conditions). Despite there existing a consolidated acoustic wave theory, it is very difficult, nearly impossible, to find an analytical expression of the sound variables distribution in a real room, as a function of time and position. This scenario represents as an inhomogeneous boundary value problem, where the complexity of source properties and boundary conditions make that problem extremely hard to solve. Room acoustic simulation, as treated in this thesis, comprises the algebraical approach to solve the wave equation, and the way to define the boundary conditions and source modeling of the scenario under analysis. Numerical methods provide accurate algorithms for this purpose and among the different possibilities, the use of discrete-time methods arises as a suitable solution for solving those partial differential equations, particularized by some specific constrains. Together with the constant growth of computer power, those methods are increasing their suitability for room acoustic simulation. However, there exists an important lack of accuracy in the definition of some of these conditions so far: current frequency-dependent boundary conditions do not comply with any physical model, and directive sources in discrete-time methods have been hardly treated. This thesis discusses about the current state-of-the-art of the boundary conditions and source modeling in discrete-time methods for room acoustic simulation, and it contributes some algorithms to enhance boundary condition formulation, in a locally reacting impedance sense, and source modelling in terms of directive sources under a defined radiation pattern. These algorithms have been particularized to some discrete-time methods such as the Finite Difference Time Domain and the Digital Waveguide Mesh.Escolano Carrasco, J. (2008). Contributions to discrete-time methods for room acoustic simulation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8309Palanci

Physics-based models for the acoustic representation of space in virtual environments

In questo lavoro sono state affrontate alcune questioni inserite nel tema pi\uf9 generale della rappresentazione di scene e ambienti virtuali in contesti d\u2019interazione uomo-macchina, nei quali la modalit\ue0 acustica costituisca parte integrante o prevalente dell\u2019informazione complessiva trasmessa dalla macchina all\u2019utilizzatore attraverso un\u2019interfaccia personale multimodale oppure monomodale acustica. Pi\uf9 precisamente \ue8 stato preso in esame il problema di come presentare il messaggio audio, in modo tale che lo stesso messaggio fornisca all\u2019utilizzatore un\u2019informazione quanto pi\uf9 precisa e utilizzabile relativamente al contesto rappresentato. Il fine di tutto ci\uf2 \ue8 riuscire a integrare all\u2019interno di uno scenario virtuale almeno parte dell\u2019informazione acustica che lo stesso utilizzatore, in un contesto stavolta reale, normalmente utilizza per trarre esperienza dal mondo circostante nel suo complesso. Ci\uf2 \ue8 importante soprattutto quando il focus dell\u2019attenzione, che tipicamente impegna il canale visivo quasi completamente, \ue8 volto a un compito specifico.This work deals with the simulation of virtual acoustic spaces using physics-based models. The acoustic space is what we perceive about space using our auditory system. The physical nature of the models means that they will present spatial attributes (such as, for example, shape and size) as a salient feature of their structure, in a way that space will be directly represented and manipulated by means of them

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Higher-order Finite Difference Time Domain Algorithms for Room Acoustic Modelling

The acoustic qualities of indoor spaces are fundamental to the intelligibility of speech, the quality of musical performances, and perceived noise levels. Computationally heavy wave-based acoustic modelling algorithms have gained momentum in the field of room acoustic modelling, as ever-increasing computational power makes their use more feasible. Most notably the Finite Difference Time Domain (FDTD) method is often employed for rendering the low- and mid-frequency part of room impulse responses (RIRs). However, this algorithm has known disadvantages, most prominently dispersion error, which renders a large part of the simulated RIR invalid. This thesis is concerned with the implementation and analysis of higher-order FDTD stencils as a means to improve the current state-of-art FDTD methods that solve the room acoustic wave equation. A detailed analysis of dispersive properties, stability, and required grid spacing of current and higher-order stencils is presented, and has been verified using a GPU implementation of the different algorithms. It is argued that the 4th-order stencil gives the best result in terms of output quality versus computational effort. In addition, this thesis focusses on the derivation of absorbing boundaries for the 4th-order scheme, its stability analysis, and detailed analysis of absorptive properties compared to established boundary models for 2nd-order schemes. The newly proposed 4th-order scheme and its boundaries are tested in two case studies: a large shoebox model, in order to test the validity against a common benchmark and a complex acoustic space. For the latter study, impulse responses were measured in the National Centre for Early Music in York, UK, and computationally generated using the current state-of-the-art as well as the proposed 4th-order FDTD algorithm and boundaries. It is shown that the 4th-order stencil gives at least as good as, or better results than those achieved using the 2nd-order stencil, at lower computational costs

Finite difference and finite volume methods for wave-based modelling of room acoustics

Wave-based models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional time-stepping grid-based methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequency-dependent wall impedances over non-trivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over non-trivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wave-based room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higher-order and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequency-domain analyses, as well as energy techniques whenever possible, allowing for stable and frequency-dependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of non-Cartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios

Algorithms and architectures for the multirate additive synthesis of musical tones

In classical Additive Synthesis (AS), the output signal is the sum of a large number of independently controllable sinusoidal partials. The advantages of AS for music synthesis are well known as is the high computational cost. This thesis is concerned with the computational optimisation of AS by multirate DSP techniques. In note-based music synthesis, the expected bounds of the frequency trajectory of each partial in a finite lifecycle tone determine critical time-invariant partial-specific sample rates which are lower than the conventional rate (in excess of 40kHz) resulting in computational savings. Scheduling and interpolation (to suppress quantisation noise) for many sample rates is required, leading to the concept of Multirate Additive Synthesis (MAS) where these overheads are minimised by synthesis filterbanks which quantise the set of available sample rates. Alternative AS optimisations are also appraised. It is shown that a hierarchical interpretation of the QMF filterbank preserves AS generality and permits efficient context-specific adaptation of computation to required note dynamics. Practical QMF implementation and the modifications necessary for MAS are discussed. QMF transition widths can be logically excluded from the MAS paradigm, at a cost. Therefore a novel filterbank is evaluated where transition widths are physically excluded. Benchmarking of a hypothetical orchestral synthesis application provides a tentative quantitative analysis of the performance improvement of MAS over AS. The mapping of MAS into VLSI is opened by a review of sine computation techniques. Then the functional specification and high-level design of a conceptual MAS Coprocessor (MASC) is developed which functions with high autonomy in a loosely-coupled master- slave configuration with a Host CPU which executes filterbanks in software. Standard hardware optimisation techniques are used, such as pipelining, based upon the principle of an application-specific memory hierarchy which maximises MASC throughput

Evaluating the graphics processing unit for digital audio synthesis and the development of HyperModels

The extraordinary growth in computation in single processors for almost half a century is becoming increasingly difficult to maintain. Future computational growth is expected from parallel processors, as seen in the increasing number of tightly coupled processors inside the conventional modern heterogeneous system. The graphics processing unit (GPU) is a massively parallel processing unit that can be used to accelerate particular digital audio processes; However, digital audio developers are cautious of adopting the GPU into their designs to avoid any complications the GPU architecture may have. For example, linear systems simulated using finite-difference-based physical model synthesis is highly suited for the GPU, but developers will be reluctant to use it without a complete evaluation of the GPU for digital audio. Previously limited by computation, the audio landscape could see future advancement by providing a comprehensive evaluation of the GPU in digital audio and developing a framework for accelerating particular audio processes. This thesis is separated into two parts; Part one evaluates the utility of the GPU as a hardware accelerator for digital audio processing using bespoke performance benchmarking suites. The results suggest that the GPU is appropriate under particular conditions; For example, the sample buffer size dispatched to the GPU must be within 32 to 512 to meet real-time digital audio requirements. However, despite some constraints, the GPU could support linear finite-difference-based physical models with 4X higher resolution than the equivalent CPU version. These results suggest that the GPU is superior to the CPU for high-resolution physical models. Therefore, the second part of this thesis presents the design of the novel HyperModels framework to facilitate the development of real-time linear physical models for interaction and performance. HyperModels uses vector graphics to describe a model's geometry and a domain-specific language (DSL) to define the physics equations that operate in the physical model. An implementation of the HyperModels framework is then objectively evaluated by comparing the performance with manually written CPU and GPU equivalent versions. The automatically generated GPU programs from HyperModels were shown to outperform the CPU versions for resolutions 64x64 and above whilst maintaining similar performance to the manually written GPU versions. To conclude part 2, the expressibility and usability of HyperModels is demonstrated by presenting two instruments built using the framewor