UNIVERSITY OF SOUTHAMPTON FACULTY OF ENGINEERING AND THE ENVIRONMENT INSTITUTE OF SOUND AND VIBRATION RESEARCH SCAN-BASED SOUND VISUALISATION METHODS USING SOUND PRESSURE AND PARTICLE VELOCITY by Daniel Fern´andezComesa~na Thesis for the degree of Doctor of Philosophy July 2014 UNIVERSITY OF SOUTHAMPTON Faculty of Engineering and the Environment Institute of Sound and Vibration Research Abstract Doctor of Philosophy SCAN-BASED SOUND VISUALISATION METHODS USING SOUND PRESSURE AND PARTICLE VELOCITY by Daniel Fern´andezComesa~na Sound visualisation techniques have played a key role in the development of acoustics throughout history. Progress in measurement apparatus and the techniques used to display sound and vibration phenomena has provided excellent tools for understanding specific acoustic problems. Traditional methods, however, such as step-by-step mea- surements or simultaneous multichannel systems, require a significant trade-off between time requirements, flexibility, and cost. This thesis explores the foundations of a novel sound field mapping procedure. The proposed technique, Scan and Paint, is based on the acquisition of sound pressure and particle velocity by manually moving a p-u probe (pressure-particle velocity sensor) across a sound field, whilst filming the event with a camera. The sensor position is extracted by applying automatic colour tracking to each frame of the recorded video. It is then possible to directly visualise sound variations across the space in terms of sound pressure, particle velocity or acoustic intensity. The high flexibility, high resolution, and low cost characteristics of the proposed mea- surement methodology, along with its short time requirements, define Scan and Paint as an efficient sound visualisation technique for stationary sound fields. A wide range of specialised applications have been studied, proving that the measurement technique is not only suitable for near-field source localisation purposes but also for vibro-acoustic problems, panel noise contribution analysis, source radiation assessment, intensity vector field mapping and far field localisation. Keywords: sound visualisation, sound mapping, sound radiation, scanning methods, p-u intensity probes, panel contribution analysis, sound source ranking, operational deflections shapes, virtual phased arrays. Contents Abstract iii Table of Contents iv List of Figures ix List of Tables xiii Declaration of Authorship xv List of Publications xvi Acknowledgements xxiii Abbreviations xxv Symbols xxvii 1 Introduction 1 1.1 Sound field visualisation . 1 1.2 Sound and vibration transducers . 2 1.3 Measurement procedures . 4 1.4 Applications of acoustic imaging techniques . 6 1.5 Research objective . 6 1.6 Thesis organisation . 7 1.7 Original Contributions . 8 2 Literature review 11 2.1 Introduction . 11 2.2 Early experiments on sound and vibration imaging . 11 2.3 Visualisation of wave propagation . 14 2.4 Novel acoustic methods of the 20th century . 16 2.4.1 Scan-based sound visualisation methods . 17 2.4.2 Cymatics . 17 2.4.3 Holographic interferometry . 18 2.5 Current experimental sound visualisation methods . 19 2.5.1 Acoustic holography . 20 v vi Contents 2.5.2 Acousto-optic mapping . 21 2.5.3 Beamforming . 22 2.5.4 Direct mapping methods . 24 2.5.5 Particle Image Velocimetry . 25 2.5.6 Schlieren and shadowgraph imaging . 26 2.6 Summary . 27 3 Fundamentals of Scan & Paint 29 3.1 Introduction . 29 3.2 Mathematical formulation . 31 3.2.1 Planar grid discretisation method . 31 3.2.2 Point discretisation method . 34 3.3 Sound received by a moving transducer . 35 3.3.1 The Doppler effect . 35 3.3.2 Sound pressure, particle velocity and velocity potential . 36 3.4 Statistical considerations . 38 3.4.1 Mean estimate . 38 3.4.2 Autospectral density estimate . 39 3.4.2.1 Bias of the estimate . 41 3.4.2.2 Variance of the estimate . 43 3.5 Practical considerations . 46 3.5.1 Tracking camera . 46 3.5.2 Video frame rate . 47 3.5.3 Reference sensor . 48 3.5.4 Manual scanning error . 49 3.5.5 Scanning speed . 52 3.6 Summary . 53 4 Sound mapping applications 55 4.1 Introduction . 55 4.2 Near-field source localisation . 55 4.2.1 Influence of background noise on sound mapping . 56 4.2.1.1 Sound emission . 56 4.2.1.2 Sensor directivity . 58 4.2.1.3 Background noise perceived near a rigid boundary . 60 4.2.2 Spatial resolution of direct mapping methods . 62 4.2.3 Experimental examples . 67 4.2.3.1 Small scale problems . 67 4.2.3.2 Vehicle interior noise . 67 4.2.3.3 Leak detection in building acoustics . 69 4.3 Acoustic vector field mapping . 71 4.3.1 Three dimensional sound intensity . 72 4.3.2 Experimental examples . 74 4.3.2.1 Loudspeaker in a room . 74 4.3.2.2 Vehicle exterior noise . 75 4.3.2.3 Unmanned Aerial Vehicles . 77 4.4 Summary . 77 Contents vii 5 Scanning Panel Contribution Analysis 79 5.1 Introduction . 79 5.2 Overview of panel contribution methods . 80 5.2.1 The windowing technique . 81 5.2.2 Surface velocity sampling methods . 82 5.2.3 Airborne Source Quantification (ASQ) . 82 5.2.4 Equivalent source methods (ESM) . 83 5.2.5 Near-field Acoustic Holography (NAH) based methods . 84 5.2.6 Pressure-velocity based reconstruction techniques . 84 5.3 Fundamentals of Panel Noise Contribution Analysis . 85 5.4 The Reference-Related method . 86 5.5 Measurement methodology . 88 5.5.1 Operational measurement . 88 5.5.2 Reciprocal transfer functions . 88 5.5.3 Camera positioning . 89 5.6 Experimental evaluation . 89 5.6.1 Experimental set-up and instrumentation . 90 5.6.2 Measurement process . 90 5.6.3 Measurement validation . 91 5.6.4 Analysis of results . 92 5.7 Comparison of scanning panel contribution analysis with current solutions 95 5.8 Summary . 96 6 Virtual Phased Arrays 97 6.1 Introduction . 97 6.2 Foundations of VPA . 98 6.2.1 Relative phase information . 98 6.2.2 Covariance matrix synthesis . 100 6.3 Source localisation and DOA algorithms . 102 6.3.1 Delay-and-sum beamforming . 102 6.3.2 MUSIC . 103 6.3.3 Least Squares Beamformer . 104 6.4 Deconvolution algorithms for VPA . 105 6.4.1 Fundamentals of iterative algorithms . 105 6.4.2 DAMAS . 106 6.4.3 Non-Negative Least Squares (NNLS) . 107 6.4.4 Iterative Sidelobe Cleaner Algorithm (ISCA) . 108 6.5 Simulations . 109 6.5.1 Relative phase information for DOA estimation . 110 6.5.2 Deconvolution algorithms . 111 6.5.2.1 Convergence of ISCA . 112 6.5.2.2 Localisation of sources with equal strength . 113 6.5.2.3 Localisation of sources with multiple strengths . 114 6.5.2.4 Localisation of sources including noise . 115 6.6 Practical implementation . 117 6.6.1 Measurement methodology and VPA configuration . 117 6.6.2 Instrumentation and experimental setup . 119 viii Contents 6.6.3 Data analysis . 121 6.6.4 Sound localisation maps . 122 6.6.5 DOA estimation . 123 6.6.6 Near-field pressure mapping versus VPA . 124 6.7 Comparison of different beamforming techniques for VPA . 125 6.8 Large multichannel arrays versus VPA . 126 6.9 Summary . 127 7 Conclusions and Recommendations 129 7.1 Summary of the main conclusions . 129 7.2 Recommendations for future work . 131 A Sound power measurements 133 A.1 Introduction . 133 A.2 Sound power estimation . 134 A.2.1 Direct intensity estimation . 135 A.2.2 Indirect intensity estimation . ..