Acoustic Array Systems E-Book

Mingsian R. Bai

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley - IEEE
• Sprache: Englisch

Seitenzahl: 694

Veröffentlichungsjahr: 2013

Beschreibung

Presents a unified framework of far-field and near-field array techniques for noise source identification and sound field visualization, from theory to application. Acoustic Array Systems: Theory, Implementation, and Application provides an overview of microphone array technology with applications in noise source identification and sound field visualization. In the comprehensive treatment of microphone arrays, the topics covered include an introduction to the theory, far-field and near-field array signal processing algorithms, practical implementations, and common applications: vehicles, computing and communications equipment, compressors, fans, and household appliances, and hands-free speech. The author concludes with other emerging techniques and innovative algorithms. * Encompasses theoretical background, implementation considerations and application know-how * Shows how to tackle broader problems in signal processing, control, and transudcers * Covers both farfield and nearfield techniques in a balanced way * Introduces innovative algorithms including equivalent source imaging (NESI) and high-resolution nearfield arrays * Selected code examples available for download for readers to practice on their own * Presentation slides available for instructor use A valuable resource for Postgraduates and researchers in acoustics, noise control engineering, audio engineering, and signal processing.

Leseprobe

Contents

Cover

Title Page

Copyright

Preface

Acknowledgments

Glossary: Symbols and Abbreviations

Chapter 1: Introduction

1.1 Background and Motivation

1.2 Review of Prior Approaches for Noise Identification Problems

1.3 Organization of the Book

References

Chapter 2: Theoretical Preliminaries of Acoustics

2.1 Fundamentals of Acoustics

2.2 Sound Field Representation Using Basis Function Expansion

2.3 Sound Field Representation Using Helmholtz Integral Equation

2.4 Inverse Problems and Ill-Posedness

References

Chapter 3: Theoretical Preliminaries of Array Signal Processing

3.1 Linear Algebra Basics

3.2 Digital Signal Processing Basics

3.3 Array Signal Processing Basics

3.4 Optimization Algorithms

3.5 Inverse Filtering from a Model Matching Perspective

3.6 Parameter Estimation Theory

References

Chapter 4: Farfield Array Signal Processing Algorithms

4.1 Low-Resolution Algorithms

4.2 High-Resolution Algorithms

4.3 Comparison of the Farfield Algorithms

References

Chapter 5: Nearfield Array Signal Processing Algorithms

5.1 Fourier NAH

5.2 Basis Function Model (BFM)-based NAH

5.3 BEM-based NAH (IBEM): Direct and Indirect Formulations

5.4 Equivalent Source Model (ESM)-based NAH

5.5 Comparison of the Nearfield Algorithms

References

Chapter 6: Practical Implementation

6.1 Inverse Filter Design

6.2 Multi-Channel Fast Filtering

6.3 Post-Processing

6.4 Choice of Distance of Reconstruction and Lattice Spacing

6.5 Virtual Microphone Technique: Field Interpolation and Extrapolation

6.6 Choice of Retreat Distance

6.7 Optimization of Sensor Deployment: Uniform vs. Random Array

6.8 System Integration and Experimental Arrangement

References

Chapter 7: Time-Domain MVDR Array Filter for Speech Enhancement

7.1 Signal Model and Problem Formulation

7.2 Linear Array Model

7.3 Performance Measures

7.4 MVDR Filter

7.5 Link With Other Filters

7.6 Further Results

References

Chapter 8: Frequency-Domain Array Beamformers for Noise Reduction

8.1 Signal Model and Problem Formulation

8.2 Linear Array Model

8.3 Performance Measures

8.4 Optimal Beamformers

8.5 Particular Case: Single Microphone

References

Chapter 9: Application Examples

9.1 Scooter: Transient Sources

9.2 Compressor

9.3 Vacuum Cleaner

9.4 Automotive Internal Combustion Engine

9.5 Transient Wave Propagation Over an Impacted Thin Plate

9.6 IT Equipment

9.7 Wooden Box

9.8 Non-contact Modal Analysis

9.9 Speech Enhancement in Reverberant Environments

9.10 Impact Localization and Haptic Feedback for a Touch Panel

9.11 Intelligent Stethoscope: Blind Beamforming

9.12 Rendering and Control of Sound Field by Array Speakers

9.13 Sound Field Reconstruction Using ESM and BFM

References

Chapter 10: Concluding Remarks and Future Perspectives

10.1 Concluding Remarks

10.2 Future Perspectives

References

Appendix: Acoustic Boundary Element Method

A.1 Introduction

A.2 Kirchhoff–Helmholtz Integral Equation

A.3 Discretization

A.4 Solution Strategy of Acoustic Boundary Element Method

A.5 Nonuniqueness Problem

References

Index

This edition first published 2013

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Library of Congress Cataloging-in-Publication Data

Bai, R. Mingsian.

Acoustic array systems : theory, implementation, and application / Mingsian R. Bai, Jeong-Guon Ih, Jacob Benesty.

pages cm

Includes bibliographical references and index.

ISBN 978-0-470-82723-9 (cloth)

1. Noise generators (Electronics) 2. Microphone arrays 3. Sound analyzers. 4. Noise–Measurement. 5. Noise control. I. Ih, Jeong-Guon. II. Benesty, Jacob. III. Title.

TK7872.N6B35 2013

620.2′3–dc23

2012038776

Preface

This monograph provides an overview on the theory and implementation of farfield and nearfield acoustic array technologies aimed primarily at sound source identification, sound field visualization, speech enhancement, sound field reconstruction, and sound field rendering. Considering that the intended audience is postgraduate students and academic or industrial researchers, this book is self-contained and comprehensive in that it provides not only the theoretical background required in the microphone or loudspeaker array systems but also the technical ingredients necessary for implementing array systems to meet real-world applications.

As for the motivation, this monograph can be regarded as the documentation of the acoustics education and research on acoustic array systems by the first author's 21-year career in National Chiao-Tung University (NCTU) and 2-year career in National Tsing Hua University (NTHU) in Taiwan. The first author also feels privileged to ask the other two prominent experts, Professor Ih (specializing in inverse vibro-acoustics and sound field rendering) at KAIST, Korea, and Professor Benesty (specializing in audio signal processing), to join this great endeavor. The paradigm of acoustic array has great promise in addressing the needs of the industries in Computers, Communications, Consumer electronics and Cars, the so-called 4C industries, with emphasis placed on telecom acoustics, eletroacoustics, audio signal processing, and noise control involved in 4C products. To meet the ever changing challenges, an interdisciplinary approach including signal processing and control systems is exploited in addition to acoustics. It is hoped by the authors that, with these new perspectives, acoustic array techniques can be treated within a unified framework.

This book is distinct from the others of seemingly similar nature in two respects. First, this work aims at sound field visualization, manipulation, and auralization, while other books in the signal processing and telecommunications community deal with conventional issues such as direction of arrival and beamforming. Second, this book is a bold attempt to treat the acoustic imaging and synthesis problem from a perspective of control systems and signal processing, which differentiates itself from the conventional methodology embraced by the acoustics community. Admittedly, the signal processing methodology applied in this text is to a great extent influenced by the farfield array signal processing predecessors in radio waves. Despite the commonality shared by radio wave and acoustic arrays, there are still fundamental differences between these two. While radio wave arrays deal with mainly narrowband and farfield sources, acoustic arrays are concerned with broadband and both farfield and nearfield sources. Without appropriate adaptations, direct transplants from radio wave technology could prove ineffective in acoustic problems, in particular at audible frequencies. This monograph serves to bridge this gap.

Acoustic array technology has a long history of development in various disciplines such as geophysics, ultrasonics, telecommunications, underwater acoustics, noise control, architectural acoustics, and so on. In line with this development, it is logical to deal first with farfield arrays followed by nearfield array. These two serve different purposes. Farfield arrays are intended for imaging large sources in long distance, while nearfield arrays are intended for small sources near the array. By assuming the spherical wave model, a number of farfield imaging algorithms are described in this book, including the conventional delay-and-sum (DAS) algorithm, the time reversal (TR) algorithm, the single-input–multiple-output equivalent source inverse filtering (SIMO–ESIF) algorithm, the minimum variance distortionless response (MVDR) algorithm and the multiple signal classification (MUSIC) algorithm are employed to localize the sources.

In addition to the farfield algorithms, another main focus of this book is nearfield arrays. A nearfield equivalence source imaging (NESI) technique is described to identify locations and strengths of sources in the nearfield. The processing of the NESI algorithm can be conducted in either the time domain or the frequency domain, which enables the identification of not only stationary but also transient sources. In the formulation stage, multichannel inverse filters are designed, based on the least-squares optimization, while regularization is required to mitigate the ill-posedness inherent in the model-matching problem.

Many implementation issues are discussed in depth in this monograph. In practical applications in which only patch array with sparse sensor layout is possible, a virtual microphone approach is developed in order to ameliorate edge effects using extrapolation and to improve imaging resolution using interpolation. Several resolution-enhancing strategies are compared and discussed in the text. The price of the multichannel processing methods is obviously the heavy, if not intractable, computational burden. To tackle the problem, we use the state-space minimal realization or the frequency-domain block convolution to considerably enhance the processing efficiency of multichannel inverse filters. For nearfield arrays, we also investigated the sensor deployment issue as we did for farfield imaging. As indicated by the simulations and experiments, the microphone array acoustic imaging techniques prove effective in identifying sources of numerous kinds, including broadband, narrowband, stationary, and transient sources.

Although some of the work presented in this monograph is mainly academic at present, there is considerable potential for commercial or industrial application of the resulting technology. Admittedly, there remain many difficult problems to be resolved during this pursuit. More efforts are required before this wildest dream, but fondest hope, is fulfilled.

This book is organized as follows. The first part, Chapters 1–5, deals with the theoretical background required in array technology. Chapter 1 is an introductory chapter, giving the background and motivation of the book, followed by a review of prior research and developments. Chapter 2 addresses the physics, or acoustics, relevant to the book. Chapter 3 reviews theoretical background necessary for comprehending the book, which is a blend of multiple disciplines in linear algebra, array signal processing, optimization theory, and so on. Chapters 4 and 5 deal with farfield and nearfield acoustic array formulations and processing algorithms. The second part, Chapter 6, addresses how to apply the preceding theories to implement an array system. Issues encountered in the implementation phase are discussed in depth. Fast inverse filters, array parameters, field interpolation, sensor deployment, among many practical issues, are examined. The third part, Chapters 7–10, gives several application examples of acoustic arrays. Chapters 7 and 8, mainly contributed by the third author, Benesty, focus on speech enhancement using microphone arrays. Chapter 9 presents numerous application examples, including scooter noise, compressor noise, internal combustion engine noise, vacuum cleaner, and so forth. Chapter 10 in particular concludes the book and suggests several future perspectives for acoustic array technology.

Acknowledgments

The first author would like acknowledge the contributions of many of his current and former graduate students, in particular Jia-Hong Lin and Ching-Cheng Chen, whose research work has comprised the main content of the monograph. A debt of gratitude is owed to the help and support of the institute of Sound and Music Innovative Technology (SMIT), NCTU and the Telecom Acoustics, Eletroacoustics and Audio Signal Processing (TEA) Laboratory, NTHU in Taiwan. The second author, J.-G. Ih, would like to mention the effort of former graduate students in the Acoustics Laboratory at KAIST, of which the results of coworks with them are reflected in this book: Dr. Bong-Ki Kim, Dr. Seung-Chon Kang, Dr. In-Youl Jeon, Dr. Wan-Ho Cho, and Dr. Agustinus Oey. The second author greatly appreciates their contributions.

We feel extremely fortunate to have worked with James Murphy and Shelley Chow of John Wiley for the past three years. Their help and professional suggestions have enhanced tremendously the enjoyment of writing and completing this book.

Special thanks are due to Dr. Jorgen Hald of Brüel and Kjæl, Dr. Jesper Gomes of the University of Southern Denmark, Professor Yang-Hann Kim of Korea Advanced Institute of Science and Technology (KAIST), and Professor Ning Xiang of Rensselaer Polytechnic Institute (RPI) who have provided stimulating discussions. The first author would also like to thank Professor Gary Koopmann of Penn State University, Professor Steve Elliott of ISVR, University of Southampton, and Colin Hansen of the University of Adelaide for hosting him during sabbatical leaves, which were indeed fruitful academic visits. The first author would like to express his sincere gratitude to the late Professor Anna Pate and Professor David Holger of Iowa State University who had led him to the realm of acoustics.

The third author would like to thank Professor Jingdong Chen from Northwestern Polytechnical University, Xi'an, China for a wonderful collaboration and great discussions that have led us to a better understanding of microphone array signal processing.

However, this acknowledgment is not at all exhaustive. The first author would like to thank his wife, Chun-May Yang, his daughter Irene, and his son Albert for their loving support and encouragement and those, too many to name, who have been inspiring the development of the book.

Glossary: Symbols and Abbreviations

Abbreviations

2D FFTTwo-dimensional fast Fourier transformAICAkaike information criterionAGArray GainANCActive Noise ControlAWFSAdaptive wave field synthesisBEMBoundary element methodBFMBasis function modelBMBlocking matrixCBWConstant beamwidthCGConjugate GradientCHIEFCombined Helmholtz integral equation formulationDASDelay-and-sumDBEMDirect boundary element methodDCDirect convolutionDIDirectivity IndexDMADifferential microphone arrayDOADirection of arrivalDORDistance of reconstructionDTFTDiscrete time Fourier transformsEfIEffective independence methodERAEigensystem realization algorithmESMEquivalent source methodEVDEigenvalue decompositionFBFFixed beamformerFBRFront-to-back ratioFDMFinite difference methodFDOAFrequency-domain-overlap-addFEAFinite element analysisFEADFront-end accessory driveFEMFinite element methodFFTFast Fourier transformFIRFinite impulse responseFRFFrequency response functionGCCGeneralized cross-correlationGSSGolden section searchHELSHelmholtz equation least squaresHRTFHead-related transfer functionsIBIntra-blockIBEMInverse boundary element methodIBMCIntra-block Monte CarloIFFTInverse fast Fourier transformIIRInfinite impulse responseIRFImpulse response functionITInformation technologyKHIEKirchhoff–Helmholtz integral equationLAFLeaky adaptive filterL-CL-curve criterionLMSLeast mean squaresMCMonte CarloMCMultiple-input cancelerMCBWMaximum for constant beamwidthMDIMaximum for directive indexMFBRMaximum for front-to-back ratioMMSEMinimized Mean Square ErrorMSEMean square errorMSLMaximum side-lobe levelMUSICMultiple signal classificationMVDRMinimum variance distortionless responseNAHNear-field acoustical holographyNESINear-field equivalence source imagingNSINoise source identificationOADOverlap-add methodOASOverlap-save methodOPSOperations per samplePCHHIPressure-based conformal holography with a hologram and a source interior couplingPCHHSPressure-based conformal holography with a hologram and a source surface couplingPCMParameter choice methodsPDFProbability density functionPSDPower spectral densitiesRDRetreat distanceSASimulated annealingSDISpeech-distortion indexSFVSound field visualizationSIMO–ESIFSingle input multiple output equivalent source inverse filteringSNRSignal-to-noise ratioSNRGSignal-to-noise ratio gainSONAHStatistically optimal NAHSOSWESingle Origin Spherical Wave ExpansionSRPSteered response powerSRP–PHATSteered response power-phase transformSTFTShort time Fourier transformSTSFSpatial transformation of sound fieldSVDSingular value decompositionTDOATime Difference Of ArrivalTFTransfer functionTRTime reversalTRMTime reversal mirrorTSVDTruncated singular value decompositionULAUniform linear arraysURAUniform rectangular arraysVCHHIVelocity-based conformal holography with a hologram and a source interior couplingVCHHSVelocity-based conformal holography with a hologram and a source surface couplingWFSWave Field SynthesisWNGWhite Noise Gain

Symbols

Vector 2-normFrobenius norm*Commutative convolution operation(*)Circular convolutionGradient operatorDivergence operatorStochastic noise gradientADOA matrixA*Complex conjugate of AA+Pseudo-inverse of A matrixAAmplitudeaArray manifold vectorbBeam patternset of complex numberscSpeed of soundSource model of dipoledMicrophone spacingFocal point spacingWeighting factor normalized to areafextExternal force acting on the control volumefsForce acting on the surface S of the control volumefFrequencyBandwidth of interestfsSampling rateGPropagation matrixGHHermitian transpose of GG(θ,ϕ)Array response function expressed in the spherical coordinates andFree-space Green's function (field point and source point )Green's function (field point and source point )Hankel function of the first/second kind of order nhImpulse response vectorIIdentity matrixImaginary partActive intensityJCost functionjkWave vectorkWave numberLLinear momentumlmnDistance between sensors m and nthe set of functions that have bounded infinity normSource model of monopoleMaxima of the main-lobenOutward unit vector normalnDiscrete-time indexAssociated Legendre function of order m and degree npSound pressure vectorphasor of pressureMeasured sound pressure vector on the microphone hologram surfacePressure vector on the source surfacepSound pressureQCost functionqSource strength vectorqSource strengthRCorrelation matrixRPropagation distance from the source to the receiverrange spaceAutocorrelation function of Cross-correlation function of and Source-pointsurfaceField-point surfaceSpatial power spectrumMicrophone surfaceMUSIC spatial power spectrumMVDR spatial power spectrumReconstruction surfaceSource surfaceVirtual source surfacesSource signal vectorMaxima of side-lobesTPeriodtTime variableULeft singular matrixuParticle velocityVRight singular matrixwarray weight vectorMVDR array weight vector and Position vectors of the field and source pointsPseudo-coherence matrixSpecific heat ratioCoherence function between signals x and yDirac's delta functionunit pulse sequenceθparameter vectorκUnit wave vector at the look directionWavelengthμStep sizeSignal-to-Noise Ratio (SNR) at the frequency fξAverage square error, Noise/speech reduction factorsΠPower flowInstantaneous densityAir densitythe unit vector pointing from the array reference to the sourceA diagonal matrix composed of singular values of the matrixThe ith singular valueTime delayFractional delayDelay of the Wiener filterPoisson's ratioSpeech distortion indexThe ith basis functionΨSpherical function matrixΩAnalog frequencyAngular frequencyDigital center frequencyLLinear momentumfextExternal forcefsForce acting on the surface S of the control volume.The ith eigenfunctionspherical coordinate systemcolumn space of matrix unit basis vectors of the Cartesian coordinate system

1

Introduction

An acoustic array system refers to a collection of acoustic transducers operating concurrently for certain acoustic signal process purposes. Acoustic transducers operating in audible range and air medium are predominantly loudspeakers and microphones. In particular, microphone array technologies have received considerable research interest as a means of enhancing voice quality and, more recently, visualizing sound fields, and identifying noise sources. Despite the fact that the sensors being discussed in this book are microphones, the signal processing methodology is to a great extent influenced by the farfield array signal processing predecessors in radio waves. Not limited to the radio wave applications, array signal processing technologies [1–8] has found their way into many application areas nowadays, such as non-destructive evaluation [9, 10], underwater imaging [11, 12], machine diagnosis [13, 14], and so forth. For a number of reasons, arrays serve as an appealing solution for these application scenarios. First, by properly using the array, the signal-to-noise ratio (SNR) of noise-corrupted signals can usually be increased. Second, arrays per se are spatial filters, which enables manipulation of array directivity (also referred to as beamforming). This feature is appealing in that it allows us to focus on the primary source of interest while rejecting noise and reverberation in the background. Third, the beam can be “electronically steered” by incorporating appropriate time delays or phase shift into the signals in each channel, without having to point the array physically. With these three features, arrays are widely used in the context of estimating direction of arrival (DOA) and enhancing speech quality in telecommunication applications. Apart from the prior farfield array technologies, acousticians also developed nearfield arrays in the 1980s. These nearfield array techniques were given the name “nearfield acoustical holography” (NAH) when they were first introduced. Since then, numerous NAH techniques have been suggested based on different principles. Microphone signal processing techniques using farfield and nearfield arrays, as detailed in this book, have a different purpose than the aforementioned speech enhancement in telecommunications. Instead, we are primarily aiming at noise source identification (NSI) and sound field visualization (SFV) for noise analysis and control engineering.

1.1 Background and Motivation

Noise source identification (NSI) is one of the crucial steps in noise analysis and diagnostic phase before a noise control program can be successfully implemented. Noise sources can be categorized into two kinds: vibration-induced noise and flow-induced noise. Examples of the first category include noises resulting from imbalance in rotating machines, impact and collision, structural resonance, braking squeal, and so on. Examples of the second category include fan noise, pump and compressor noise, jet noise, and so on. There are many tools available for NSI purposes, for example, sound level meters, sound intensity probes, accelerometers, laser vibrometers, and so on. These conventional tools are “local” in nature and often-times may require prior knowledge of the number and locations of noise sources. For example, accelerometers can access only the “problematic” points and require mounting fixtures. The laser vibrometer can be used in a non-contact fashion, but can be quite time consuming and costly if a global measurement is desired. The other more recently introduced approaches, sound field visualization (SFV) techniques, can have operational and interpretational advantages over the conventional techniques in providing the information of source positions as well as source strengths (). SFV techniques can be useful in the context of non-destructive evaluation [9, 10], underwater imaging [11, 12], machine diagnosis [13, 14], and so forth. SFV techniques fall into two categories: beamforming and nearfield acoustical holography (NAH). These two classes of techniques enable farfield and nearfield imaging of noise sources, using microphone arrays. In general, beamforming relies upon the farfield assumption that the sources are far away and the waves become spherical or planar at the array position. The aim is to determine the direction of arrival (DOA) or even the location of the sources from the array output by a single shot of measurement with the microphones. Hence, farfield arrays are considered multiple-input–single-output systems. Apart from this, however, beamforming does not really provide information on acoustical variables of the noise sources and their radiated sound field. In contrast, NAH requires deploying microphones in the vicinity of the source surface. The sound pressures picked up by the microphones are processed by an imaging algorithm of some type to reconstruct a map of the surface motion and the sound field with a high spatial resolution. In this context, farfield arrays are considered to be multiple-input–multiple-output systems. As an early development, Fourier NAH techniques were suggested to reconstruct regularly shaped sources with planar, spherical, and cylindrical geometries. Arbitrary distributions of sound and vibration fields are decomposed by means of a spatial Fourier transform into generalized wavenumber spectra. Inverse reconstruction is accomplished in the wavenumber domain, with proper regularization of the ill-posedness inherent in the reconstruction process. In addition to the Fourier NAH, discrete models can be constructed and used for inverse reconstruction of the acoustical field, as will be detailed next. NAH differs from the preceding farfield techniques in that it can provide acoustical quantities such as sound pressure, velocity, intensity, sound power, and the like.