David R. Dowling

Source localization is an important structural health monitoring task, yet traditional localization techniques struggle due to complex geometries, dispersive wave propagation, and structure-medium coupling. This study applied matched field processing (MFP), a source localization technique developed for underwater acoustics, to localize impact sources on metal plates using remote acoustic measurements of airborne sound in conjunction with a physics-based acoustic-wave propagation model. A linear array of 14 microphones recorded radiated sound from a stainless-steel ball bearing dropped onto a 0.64 cm-thick, 91.4 cm-diameter aluminum plate in the nominal 5-20 kHz bandwidth. Physics-based finite element models were developed for both infinite and finite plates. The infinite plate model emphasized generic sound radiation with proper time-windowing, while the finite plate model included edge reflections specific to the plate studied. Both models achieved localization errors within 0.5 cm when data were temporally trimmed to accommodate model constraints. In environments with additive Gaussian noise, the finite plate model maintained greater than 80% localization accuracy down to a signal-to-noise ratio of -7.5 dB. Results further showed that MFP is robust to moderate mismatches in source characterization, but deviations in sensor location approaching a half-wavelength and deviations in plate thickness approaching 10% can reduce localization accuracy.

Traditional source localization techniques like matched field processing (MFP) rely on physics-based models of known acoustic environments, which can be impractical for complex systems in structural acoustics. In contrast, machine learning (ML) methods are “model-free,” leveraging patterns in data to predict source locations. This presentation compares MFP and neural network-based ML approaches for localizing impact sources on a 6.4-mm thick circular aluminum plate with diameter 914 mm. The plate was excited by a 12.7-mm-diameter stainless-steel ball bearing dropped from 76 mm above the surface. A linear array of 14 microphones, spaced 51 mm apart and located 92 mm above the plate, recorded the acoustic response of the impact. Because experimental data can be time- and resource-intensive to collect, finite element simulations generated acoustic responses for 8640 source locations in the 5–20 kHz bandwidth. This simulated data was used to train and validate two neural networks: a feedforward neural network using cross-correlation lags and a convolutional neural network using spectrograms. Both models were tested, achieving localization errors down to 0.3 cm (simulated) and 1.0 cm (experimental). ML approaches are also evaluated in terms of data efficiency, computational speed, and robustness to noise and signal variability. [Sponsored by a SMART Scholarship.]

Acoustic remote sensing and source localization are fundamental topics in underwater acoustics, with applications in navigation, environmental monitoring, and surveillance. Traditional signal-processing methods typically rely on frequencies within a recording’s bandwidth. Recent advances have shown that environmental and source information can also be extracted at frequencies outside this bandwidth using frequency-difference and frequency-sum autoproducts [Worthmann and Dowling (2017), J. Acoust. Soc. Am., 141, 4579–4590]. Previous autoproduct studies have primarily examined two-dimensional sound fields. This work presents simulation and experimental autoproduct-based source localization using both vertical-array and horizontal-array recordings, with the horizontal array aligned parallel to an added vertical reflecting surface. Varying array orientation enables comparison across geometries, improving understanding of complex three-dimensional acoustic environments and supporting the experimental work. Recordings were collected in a fully three-dimensional four-ray-path acoustic field generated in a Lloyd’s mirror environment augmented with a vertical reflector. Experiments were conducted in a 1.07-m diameter freshwater tank using short Gaussian-enveloped pulses with a 40–150-kHz nominal bandwidth. Time gating suppressed sidewall and bottom reflections. Simulated and experimental localization results are compared. [Work sponsored by ONR.]

This article introduces the electromagnetic frequency-difference autoproduct, the outer product of the harmonic electric field vector with itself at nearby frequencies, and describes its capacity to improve target localization in random scattering media. The electromagnetic frequency-difference autoproduct is a dyadic quantity that synthetically estimates electric field content at the difference frequency of two constituent electric fields. It is a generalization of the acoustic (scalar) frequency-difference autoproduct. Derivation of the autoproduct governing equation precedes numerical examination of plane wave propagation and scattering from perfectly conducting infinite cylinders. Using linearly-polarized antennas in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vv</i>- (TM) configuration, 3-5 GHz target localization experiments were conducted in wooded areas where randomly-located tree trunks were the primary scatterers. Beamformed outputs demonstrate the advantages of autoproduct processing for active target localization of a metallic reflector at 12 m transmitter-to-target distance. While the lower effective frequency reduces resolution, robustness against scattering and other random media effects is increased.

Acoustics is a wonderful elective subject to teach because interested students arrive on the first day of class with two or more decades of experience operating an acoustic source (their voice) and utilizing multiple acoustic receivers (their ears). Thus, their curiosity and intuition are ripe for exploitation and can even be used to motivate the development of mathematical skills. My path to research and instruction in acoustics does not include any formal training in the subject. Instead, I encountered and learned acoustics at a pace and in manner of my choosing through research, consulting, and teaching. Thus, this lecture begins with a graphical retrospective of my career path punctuated by relevant dates and numbers. This career summary is followed by the statement and description of three main concepts that have guided my 30 + years of engineering science instruction: (i) let the truth be your only story, (ii) know your students and what motivates them, and (iii) engage in student-centric teaching. Descriptions, explanations, and examples related to these three concepts are presented and include: setting the tone of the course on the first day, surveying the students to determine their interests, and review of a few of my favorite homework problems.

Acoustic waves can be ideal for remote sensing and structural health monitoring because they carry source information and can be measured without contact. However, traditional time-of-flight array methods for source localization are ill-suited for structural engineering applications. Specifically, for a plate suspended at an air–water interface, the coupling between the vibrating structure and the surrounding mediums complicates localization efforts. Thus, source localization experiments were conducted using Matched Field Processing (MFP) for a 0.91-m diameter round aluminum plate suspended at an air–water interface and excited by the impact of a 1.3-cm diameter stainless-steel ball bearing dropped from 11.4-cm. A remote linear seven-microphone array placed 10.5-cm above the plate in the air and a remote linear seven-hydrophone array placed 13.5-cm below the plate in the water measured the sound radiated by the 0.64-cm-thick plate at frequencies up to 20 kHz. MFP array signal processing localization techniques were used along with a physics-based finite element acoustic model to localize the impact excitation on the structure. Source localization results using each set of acoustic pressure measurements independently are compared to results using both sets of acoustic pressure data. Localization success rates in a noisy environment are also presented. [Work sponsored by a SMART Scholarship.]

Acoustic waves are well-suited for remote sensing applications and structural health monitoring because they convey information about their source and can be recorded using non-contacting methods. An important structural health monitoring task is localization of an impact excitation. However, traditional array signal processing techniques for source localization are ill-suited for many structural engineering applications because of geometrical complexity, dispersive acoustic wave propagation in structures, and the coupling of the vibrating structure and the surrounding medium. Plus, many traditional methods use contacting sensors, which can permanently alter the structure. This study utilizes Bartlett matched field processing (MFP), a localization technique initially developed for underwater acoustics, to localize an impact source on a metal plate. A 14-microphone array recorded the sound radiated by a 0.64-cm-thick 91.4-cm-diameter round aluminum plate after the impact of a 1.3-cm-diameter stainless-steel ball bearing. MFP and a physics-based finite-element acoustic environment model were used to localize the impact on the plate. Results are presented as ambiguity surfaces where the predicted source location was typically found to be within 1.1 cm of the true source location. Localization performance was also assessed in a noisy environment, with success down to a signal-to-noise ratio of -7.5 dB.

Kinematics is the study of motion without reference to the forces or stresses that produce the motion. In fluid mechanics, the Eulerian description of fluid motion is most common. Here, the fluid velocity field is considered in a fixed region of space through which the fluid moves so there are as many as four independent variables – three spatial coordinates and time. In the Eulerian formulation, fluid acceleration is not determined for individual fluid particles. Instead it is determined as a function of all four independent variables and therefore involves both temporal and spatial differentiation of the fluid velocity field . Streamlines, path lines, and streak lines may be used to describe flow field kinematics within the region of interest. Strain-rate and rotation tensors describe the deformation and rotation of infinitesimal fluid particles. For arbitrary but finite regions of space, commonly called control volumes, time derivatives of volume integrals must include the possibility of fluid and/or volume motion through use of the Reynolds Transport Theorem .

Turbulence is an enigmatic state of fluid flow that includes unpredictable fluctuations even when the flow's boundary conditions are steady and smooth. These fluctuations typically occur over a wide range of length and time scales. For analysis, a turbulent flow is decomposed into average (or mean) and fluctuating fields. The field equations governing the average flow field contain derivatives of the correlation tensor of the fluctuating flow field, and therefore do not represent a closed system of equations. However, when the turbulence is homogeneous and isotropic some relationships between the average and fluctuating flow fields can be deduced. In particular, the kinetic energy that sustains the turbulence is extracted from the average flow and is eventually dissipated by the viscous motions of the smallest turbulent fluctuations. Spectral measurements from a variety of turbulent flows suggest this process is universal. Scaling laws for turbulent shear flows that develop near or away from solid boundaries can be deduced from dimensional analysis, similarity analyses, and geometric considerations. Turbulent mean-flow predictions commonly rely on approximate models that close the system of average-flow equations. Turbulence may be modified in stratified media like the earth's ocean and atmosphere.

Only stable steady solutions to the equations of fluid motion are observed in experiments. Unstable solutions may exist briefly but they will spontaneously develop oscillations in space or time that grow and eventually change the character of the flow. Temporal instability analysis presumes an undisturbed background flow into which a disturbance having infinitesimal amplitude is introduced. The equations governing the disturbance are linear and commonly lead to exponential solutions. If the disturbance amplitude decreases, remains the same, or grows in time after its introduction, the flow is said to be stable, neutrally stable, or unstable, respectively. Common flow instabilities may take the form of traveling waves or spatially stationary oscillations in time or space. Depending on the flow's geometry , instability may be induced by the effects of fluid inertia, gravity, rotation, thermal expansion, differential diffusion, fluid viscosity , etc. Once a flow becomes unstable, the instability may grow to be become a new steady-state solution, or it may trigger additional instabilities that also grow. When growing instabilities reach levels where nonlinear interactions occur between them, the flow may be chaotic or even turbulent.

Laminar boundary-layer flows occur when a moving viscous fluid comes in contact with a solid surface and a layer of rotational fluid, the boundary layer, forms in response to the action of viscosity and the no-slip boundary condition on the surface. When the surface is flat or mildly curved and the boundary layer that develops on it is thin and remains adjacent to it, the flow within this layer may be determined by simplifying the Navier-Stokes equations to account for the flow's geometry and then solving the simplified equations. Unfortunately, when the pressure increases in the downstream direction or when the surface is highly curved, the boundary layer may leave the surface, a phenomenon known as separation, and the simplified form of the Navier-Stokes equations no longer applies. In addition, at sufficiently high Reynolds number , boundary-layer flows may spontaneously become unsteady and then transition to turbulence. In combination, these phenomena provide explanations for the fluid dynamic forces felt as fluid moves past a cylinder or sphere at different Reynolds numbers .

Fluids, materials that deform continuously under an applied shear stress , are omnipresent in the world around us, and beyond. Fluid mechanics is the branch of science concerned with stationary and moving fluids. Here fluids are treated as being continuous even though they are composed of discrete molecules. At the macroscopic level, the molecular character of fluids is manifested as diffusive transport of species, heat, and momentum. With the continuum approximation, dependent flow-field variables (velocity, pressure, density, temperature, etc.) are presumed well defined at every point in space and classical equilibrium thermodynamics is presumed valid. In static situations, gravity and thermodynamic gradients determine the stability of the fluid configuration to small perturbations. When fluids move, they obey Newton's second law but there is no restriction on the system of units used to describe the relevant forces and accelerations. This fact and the requirement for dimensional homogeneity in physically meaningful equations allows potentially useful scaling laws to be developed from considerations of the dimensions of relevant parameters, fluid properties, and fundamental constants.

The dependent field variables used to characterize moving and stationary fluids are scalars, vectors, and second-order tensors. In three spatial dimensions, scalars (like density) can be described by a single number; vectors (like velocity) can be described by three components, one for each orthogonal spatial direction; and second-order tensors (like stress) can be described by nine components, one for each pair of spatial directions. Although the meanings of vectors and second-order tensors that represent physical quantities are independent of the orientation of the coordinate system in which they are resolved, their components do change when coordinate axes are rotated. The equations for fluid motion include a variety of algebraic and differential relationships involving scalars, vectors, and second-order tensors. Index notation is a convenient means for specifying these relationships and operations, especially when the gradient operator (vector derivative) is involved. In addition, integrals of flow-field quantities along curves, on surfaces, and within volumes in two and three dimensions must follow certain relationships.

The laws governing fluid motion are based on conservation of mass , momentum, and energy. For the Eulerian description of fluid motion, these three conservation laws are coupled nonlinear partial differential equations . However, to produce a potentially solvable set of equations, a constitutive relationship must be specified. For many commonly encountered fluids, the simplest possible Newtonian viscosity law – a linear relationship between the stress and strain-rate tensors involving only two material constants – is appropriate. When supplemented by two thermodynamic relationships , such as caloric and thermal equations of state , the number of equations matches the number of unknown dependent field quantities. Thus, with the specification of appropriate boundary conditions, the overall system of equations can in principle be solved even in noninertial coordinate systems. When the equations of fluid motion are cast in dimensionless form , the dimensionless parameters (or numbers) commonly used to specify fluid flow conditions appear as coefficients in the equations. Although analytical solutions to the full set of equations are uncommon, the equations of fluid motion can be simplified, and are easier to solve, under certain circumstances. Examples of such principles, equations, boundary conditions, and dimensionless parameters are provided in this chapter.

Aerodynamics is the branch of fluid mechanics that deals with the fluid dynamic forces and moments that act on moving objects. Lift and drag, the aerodynamic force components perpendicular and parallel to the oncoming fluid velocity, are both the result of viscous effects within a fluid flow. For two-dimensional (infinite span) airfoils at low or moderate angles of attack (up to ∼ 15 ∘ ), lift may be predicted by ideal flow analysis when the effect of viscosity is represented by choosing the foil's circulation so that the aft flow-separation point occurs at the foil's trailing edge . For finite-span wings, trailing vortices aligned with the oncoming flow develop downstream of each wing tip and induce a downward vertical velocity at the wing. This induced velocity locally changes the angle of attack along the wing in a manner that rotates the lift force backward to produce a drag force known as induced drag. Fish, birds, and sailboats use aerodynamic lift forces for propulsion and maneuvering.

When a constant-density fluid flows without rotation and pressure is measured with respect to its local hydrostatic value, the field equation for fluid motion is linear and pressure can be determined from a nonlinear algebraic (Bernoulli) equation. Under these ideal-flow conditions, a single scalar stream function or velocity potential may be used to describe the flow. Ideal flows around corners, near walls, and past simple obstacles may be constructed by superimposing fundamental solutions. In two dimensions these functions are naturally combined into a complex potential that satisfies the Cauchy-Riemann equations for a complex analytic function. The complex potential allows two important ideal-flow theorems to be proved, and it allows complicated flows to be analyzed via complex-variable mapping techniques. For axisymmetric and three-dimensional ideal flows, the fundamental equations are still linear but the extension to complex functions is lost. In particular, unsteady three-dimensional potential flow can be used to determine the apparent (or added) mass of a fully submerged, arbitrarily moving sphere.

The vorticity field – defined as the curl of the velocity field , and twice the rotation rate of fluid particles – is a fundamental quantity in fluid mechanics. Similar to how streamlines were obtained from the velocity field , vortex lines may be determined from a tangency condition of the vorticity vector. However, vortex lines have several special properties and their presence or absence within a region of interest may allow certain simplifications of the field equations for fluid motion. In particular, vortex lines are carried by the flow and cannot end within the fluid, which constrains their possible topology. Vorticity is typically present at solid boundaries and may diffuse into the flow via the action of viscosity . Vorticity may be generated within a flow wherever there is an unbalanced torque on fluid elements, such as when pressure and density gradients are misaligned. The characteristics and geometry of a thin vortex allow the velocity it induces at a distant location to be determined. Thus, multiple vortex lines that are free to move within a fluid may interact with each other. In a rotating coordinate frame, the observed vorticity depends or the frame's rotation rate . This chapter introduces basic concepts and phenomena associated with fluid vorticity and derives useful theorems and transport equations in inertial and rotating frames of reference.

Viscous flows occur when the effects of fluid viscosity are balanced by those arising from fluid inertia, body forces, and/or pressure gradients. In such flows, scaling analyses do not allow a priori neglect of any terms in the equations of fluid motion. However, under certain ideal geometrical circumstances involving locally parallel walls that confine the flow, relatively simple steady and unsteady exact solutions to the Navier-Stokes equations are possible because the nonlinear advective acceleration is identically zero. Interestingly, the character of these exact solutions persists when the flow's geometry deviates mildly from ideal, a fact exploited in lubrication theory. When the flow's boundary and initial conditions do not impose a length or time scale, exact solutions may sometimes be determined in terms of a special combination of two independent variables known as a similarity variable. At sufficiently low Reynolds numbers, the influence of fluid inertia may be neglected (the creeping flow approximation) and this allows the low-Reynolds number viscous flow past a sphere to be determined.

A flow is considered compressible when changes in fluid momentum produce important variations in fluid pressure and density, and the fluid's thermodynamic characteristics play a direct role in the flow's development. When the pressure variations are small enough, linear acoustic theory may apply. However, larger finite-amplitude pressure disturbances produce nonlinear effects . Compressible flows in ducts and nozzles may reach limiting mass-flow-rate values that cannot be exceeded even when the downstream pressure is decreased. Here friction and heat addition or extraction may have unexpected consequences. Supersonic flows (Mach number >1) may also contain shock waves that induce nearly discontinuous changes in the flow's state. In supersonic flow, downstream pressure disturbances cannot propagate upstream and oblique expansion or compression waves emanate from locations where the flow changes direction. Thus, supersonic flows are often easier to analyze than subsonic flows because the various influences of geometric features of the flow's boundaries need not be assessed simultaneously as would be the case in subsonic flow.

Geophysical fluid dynamics deals with flows of air and water in the atmosphere and ocean. Here fluid velocities are subsonic, the medium is stratified, and the rotation rate of the earth is important. The latter two phenomena suppress vertical motions so horizontal velocities predominate, especially at large scales, even when the flow is turbulent. In fact, the length scales of the motion are often so large that the advective acceleration is small compared to the Coriolis acceleration (small Rossby number), and the fluid's horizontal velocity is perpendicular (not parallel) to the horizontal pressure gradient . Near surfaces where friction is important, the direction of the flow in a boundary layer depends on the distance from the surface. Coriolis effects also cause surface-wave motions to include particle deflections in both horizontal directions, and for surface waves to be trapped near vertical boundaries. Coriolis effects modify internal waves, too. At even larger scales where the curvature of the earth leads to nontrivial variations in the Coriolis frequency, Rossby waves spanning a significant range of latitude may be subject to barotropic and/or baroclinic instabilities .

Waves may occur at fluid interfaces when gravity or surface tension provides a restoring force that pushes a deformed surface back toward its equilibrium position . The general formulation of the surface wave problem is nonlinear, even when the flow is inviscid. An appropriate linearization for small surface slope leads to traveling-wave solutions that are dispersive in deep water and nondispersive in shallow water . In particular, the phase and group speeds of deep-water gravity waves are different and both depend on wavelength with longer waves traveling faster. In shallow water , gravity-wave phase and group speeds are equal and depend on the depth of the water in which they travel. The complexity of the situation increases when the waves are nonlinear, when they occur between fluid layers of differing density, and when they occur on density gradients within a stratified fluid . In the latter case, the phase and group velocities are not even in the same direction.

Autoproducts are quadratic or higher products of frequency-domain acoustic fields that can mimic genuine fields at frequencies within or outside the original field's bandwidth. Past studies have found a variety of interesting autoproduct properties but have been limited to quadratic autoproducts. This paper presents cubic autoproduct theory and documents how noise suppression may be attained with the cubic frequency-difference autoproduct, a product of three frequency-domain acoustic fields. The cubic autoproduct's field equations, developed from the inhomogeneous Helmholtz equation, and analytical results in single- and two-path environments justify interpretating the cubic autoproduct as a pseudofield and underscore its similarities to the quadratic autoproducts. For nonzero field bandwidth, many frequency triplets satisfy the relationship for a single cubic autoproduct frequency. Thus, bandwidth averaging can lead to serendipitous noise suppression and is shown herein to facilitate field-phase-structure recovery from ideal free space fields corrupted by Gaussian noise. Cubic-autoproduct-based direction of arrival (DOA) estimation using signal and noise recordings collected in the ocean are found to be more accurate than conventional DOA estimates from the same data. In particular, cubic autoproduct results showed a 3-5 dB noise suppression advantage for 4- and 6-kHz direct- and reflected-path sounds broadcast 200 m to a four-element receiving array.

The prevalence of random scattering from a rough ocean surface increases with increasing χ=kh cos θ, where k is the acoustic wavenumber, h is the root-mean-square surface height, and θ is the incidence angle. Generally, when χ≫1, coherence between incident and surface-scattered fields is lost. However, such coherence may be recovered when χ≫1 by considering the frequency-difference autoproduct of the surface-scattered field, a quadratic product of complex fields at nearby frequencies. Herein, the autoproduct's coherent reflection coefficient for χ> 20 is determined from surface-scattered sound fields obtained from 50 independent realizations of the rough ocean surface measured in pelagic waters off the coast of California in January 1992. The recordings were made with a source at a depth of 147 m that broadcasted 30 and 40 kHz signals to a single receiver 576 m away at depth of 66 m. An analytic formula for the coherent reflection coefficient of the frequency-difference autoproduct, based on the Kirchhoff approximation and a Gaussian surface autocorrelation function, compares favorably with measurements. Improved agreement with the single-receiver measurements is possible via a minor adjustment to the surface autocorrelation length. The adjustment identified here matches that determined previously from horizontal spatial coherence estimates utilizing the experiment's eight-element receiving array.

The coherence of rough sea-surface-scattered acoustic fields decreases with increasing frequency. The frequency-difference autoproduct, a quadratic product of acoustic fields at nearby frequencies, mimics a genuine field at the difference frequency. In rough-surface scattering, the autoproduct's lower effective frequency decreases the apparent surface roughness, restoring coherent reflection. Herein, the recovery of coherent reflection in sea surface scattering via the frequency-difference autoproduct is examined for data collected off the coast of New Jersey during the Shallow Water '06 (SW06) experiment. An acoustic source at depth 40 m and receiver at depth 24.3 m and range 200 m interrogated 160 independent realizations of the ocean surface. The root mean square surface height h was 0.167 m, and broadcast frequencies were 14-20 kHz, so that 2.5 ≤kh cos θ≤ 3.7 for acoustic wavenumber k and incidence angle θ. Measured autoproducts, constructed from scattered constituent fields, show significant coherent reflection at sufficiently low difference frequencies. Theoretical results, using the Kirchhoff approximation and a non-analytic surface autocorrelation function, agree with experimental findings. The match is improved using a numerical strategy, exploiting the relationship between autoproduct-based coherence recovery, the ocean-surface autocorrelation function, and the ocean-surface height spectrum. Error bars computed from Monte Carlo scattering simulations support the validity of the measured coherence recovery.

Acoustic waves are well-suited for remote sensing applications and structural health monitoring purposes because they convey information about their source and can be measured using non-contacting methods. Source localization is an important structural health monitoring task; however, traditional time-of-flight array signal processing techniques used to localize acoustic sources are ill-suited for many structural engineering applications due to the potential for complicated propagation paths, the dispersive propagation of acoustic waves in structures, and the coupling of the vibrating structure and the surrounding medium. Thus, source localization experiments were conducted using matched field processing (MFP) for a 0.9-m diameter round aluminum plate excited by the impact of a 1.3-cm stainless-steel ball bearing dropped from 7.6-cm. A 14-sensor linear remote acoustic array placed 8.9-cm above the plate measured the sound radiated by the 0.64-cm thick plate. MFP array signal processing localization techniques were used along with a physics-based finite element acoustic model to localize the excitation on the structure. Source localization results in both a quiet environment and environment with additive white Gaussian noise are discussed, and these results are compared to those from an acoustic model where plate edge reflections are neglected. [Work was sponsored by a SMART Scholarship and the NEEC.]

Beamforming the signals recorded by an array enables the determination of sound source location(s) or the arrival directions of ray paths between a sound source and the receiving array. Frequency-difference and frequency-sum beamforming are beamforming techniques that provide out-of-band information from in-band signal frequencies. Interestingly, the out-of-band frequencies can be chosen by the user, within limits set by the signal recordings, to achieve desired properties of the beamformed output, such as: increased resolution, reduced sidelobes, or greater robustness to random scattering. Both techniques are general and are not limited to any particular acoustic environment, frequency range, or array geometry. Frequency-sum beamforming, generates higher-frequency information from lower frequency signal components, enhancing beamforming results in scenarios with random scattering between the source and the receivers. However, it is limited by artifacts arising from cross-terms when multiple source signals are present in the same bandwidth. Conversely, frequency-difference beamforming manufactures lower-frequency information from higher frequency signal components, effectively mitigating the impact of spatial aliasing in situations where the receiving array is sparse. This presentation delves into the origins of frequency-difference and frequency-sum beamforming, presents the fundamental mathematics underlying their algorithms, and showcases their performance via simulations and experimental results. [Work supported by ONR.]

Frequency-difference beamforming (Abadi et al., 2012, JASA, 132, 3018–3029) is an array signal processing technique that overcomes the limitations of the spatial Nyquist criterion by utilizing the acoustic autoproduct to shift the processing to below-band frequencies. This is accomplished using a quadratic product of complex signal amplitudes at different frequencies, resulting in wave propagation information at the out-of-band difference-frequency. The resulting field is capable of mitigating many of the in-band challenges often associated with high frequency acoustic signal processing, including sparse receiver arrays and features of the physical environment that are on a scale significant for the in-band wavelength. This presentation uses both laboratory and ocean-based experiments to demonstrate capabilities of the method. The mitigation of sparse array aliasing effects on beamforming (caused by elements that are spaced by many wavelengths) in both a laboratory water tank and an ocean environment utilizing data collected during the KAM11 experiment are considered. Additionally, the method is used to localize a high frequency source in the presence of strong, random scatterers in a water tank experiment. [Work sponsored by NAVSEA and ONR.]

One of the two aims of the Australian Learning and Teaching Council (ALTC) funded Define Your Discipline (DYD) project is to develop an efficient, inclusive, simple and systematic stakeholder consultation process that can be used by discipline stakeholders to define their discipline. During 2010 the DYD stakeholder consultation process was developed and then trialled nationally to develop a draft set of Graduate Outcomes for the environmental engineering discipline. The first part of the paper describes the DYD stakeholder consultation process which uses both divergent and convergent strategies to ensure that the individual voices of the participants are captured, as well as group perspectives. Data was gathered on the tasks undertaken by graduates during their first two or three years of practice. Once the 2010 stakeholder consultation workshops had been completed the data were synthesised to define a draft set of Graduate Outcomes for the discipline. Two different types of workshop are being used during 2011 to refine the draft set of Graduate Outcomes. Throughout this process each outcome remains linked to all of the identified tasks from which it was derived, and the people who submitted those tasks. Thus, the project team can review the importance of the contributions from the various groups of participants (such as academics, graduates and practitioners) as well as some of the characteristics of those groups such as location, and gender. The second part of the paper discusses the feedback received from members of the stakeholder groups who participated in the DYD stakeholder consultation process: 50 of the 110 workshop participants; the project team; and the client---the Environmental Engineering College Board. Overall, the feedback from all parties was very positive. The feedback from the 2010 workshops was used to fine-tune the DYD consultation process for the 2011 workshops.

The disciplines of Science, Technology, Engineering and Mathematics (STEM) are critical for national productivity and global competitiveness. Demand for tertiary graduates with cross-disciplinary STEM skills will continue to exponentially exceed supply in Australia in the next 25 years (McLaughlin &amp; Reid, 2012). Leadership in the promotion of STEM cross-disciplinary learning and teaching is critical to the development of future graduates. With these identified skills shortages across the STEM professions, there is a growing need for academic staff to impart knowledge from their own disciplines across new STEM learning boundaries and build skills in providing cross-disciplinary STEM opportunities for future graduates. This project, through the connection of industry, STEM academics and students created these opportunities and demonstrated the emerging potential in cross-disciplinary learning and teaching. The project also forged new patterns of learning opportunities in STEM tertiary education across Australia and crossed discipline and Australian Qualifications Framework (AQF) boundaries.

The parabolic-equation (PE) method is a popular technique in underwater acoustics for obtaining 2D and 3D acoustic-field predictions in spatially-dependent environments. Tangent linear models for these PE solutions relate perturbations in the environmental properties (inputs) to corresponding changes in the acoustic field-solutions (outputs), enabling efficient schemes for approximately transferring parametric uncertainties through to acoustic-field uncertainty or computing the sensitivity of the acoustic-field to these parameters for adjoint-based acoustic inversions. Previously, first-order and higher-order tangent linear models have been developed with respective square-root operator splitting schemes for use with finite-difference and split-step Fourier PE solutions. This presentation describes the findings of an investigation into using these previously developed tangent linear models with the popular split-step Padé method in 2D problems. Additionally, two new tangent linear models are proposed based on directly perturbing: (1) the combined exponential operator in the analytical solution of the one-way wave equation and (2) the split-step Padé solution itself. The forward errors of these tangent linear models are compared analytically and across a variety of computational examples. The numerical stability of each approach is also important and of interest. Finally, the computational savings (if any) from using each approximation over the original split-step Padé model are discussed.

Acoustic waves provide a wealth of information about their source and the environment in which they propagate. For large structures, it is sometimes desirable to use acoustic remote sensing methods to collect structure-borne sound because the microphone array and structure can then be maintained separately. Traditional time-of-flight array signal processing techniques used to localize acoustic sources are ill-suited for structures due to the potential for complicated propagation paths, the dispersive propagation of acoustic waves in structures, and the coupling of the vibrating structure and surrounding medium. Thus, source localization experiments were conducted using Matched Field Processing for a 6.4-mm thick circular aluminum plate excited by the impact of a 12.7-mm-diameter stainless-steel ball bearing dropped from 76-mm above the plate. This impulsive excitation of the plate contained frequencies between 0 and 5 kHz, resulting in wave speeds in the plate up to approximately 550 m/s. A linear array of 14 microphones with 51-mm spacing located 90-mm above the plate was placed in a random location such that it was not centered over the plate. Source localization results in both a quiet environment and an environment with additive white Gaussian noise are presented. [Sponsored by a SMART Scholarship, and the NEEC.]

Acoustic remote sensing tasks, such as remote unknown source localization, are commonly completed via signal processing schemes that are implemented in the bandwidth of the acoustic recordings. Interestingly, many such schemes can also be implemented at frequencies outside of the bandwidth of the recorded field—despite their absence from the recordings—by using the frequency-difference and frequency-sum autoproducts [Worthmann and Dowling, J. Acoust. Soc. Am., 141 (2017) 4579–4590]. Recent acoustic-field autoproduct studies have involved beamforming and source localization in shallow- and deep-ocean environments, and have addressed the impacts of refraction, shadow zones, rough surface scattering, and noise. These previous efforts primarily explored the properties of the autoproducts when the sound field primarily varies in two spatial dimensions. This presentation provides the results of a study of the autoproducts formed from the simple but fully three-dimensional acoustic fields arising from an isolated source placed in a uniform-sound-speed environment bounded by reflecting surfaces that are not parallel. This study indicates the extent to which the autoproduct properties associated with two dimensional acoustic-field variations extend to three dimensional acoustic-field variations. The results from theory and simulations are presented, and from laboratory water-tank measurements if time allows.

Frequency-difference source localization (FDSL) is a newer method for locating sources emitting acoustic or electromagnetic waves from recorded data. Estimates of location are produced by matching a nonlinear function of the received data with the same nonlinear function of modeled data. This matched-field approach depends on the accuracy of the modeled field. FDSL exhibits less sensitivity to model errors in some cases. Fluctuations of the speed of sound in the ocean are affected by a wide variety of phenomena and internal gravity waves is one where their spectrum is usually well known. There is no analytical theory for predicting how these fluctuations of sound speed affect the accuracy of FDSL, leaving a numerical evaluation as the alternative. Experimental application of FDSL was previously made for an acoustic source of 100 Hz bandwidth surrounding 250 Hz for a 129-km section in the Philippine Sea with data recorded on a long vertical array [Geroski and Dowling, Long-range frequency-difference source localization in the Philippine Sea, J. Acoust. Soc. Am. 146 (2019) 4727–4739.]. The role of internal waves is quantified with a realistic FDSL simulation using models based on the parabolic and ray approximations of the acoustic wave equation. The modeled vertical variation of FDSL error is similar to observed while the modeled horizontal error is too small. The complicated software model is automatic but is computationally intensive, with our version needing about 1.5 mo to compute on a PC with 16 cpu cores.

Long-range passive source localization is possible in the deep ocean using phase-only matched autoproduct processing (POMAP) [Geroski and Dowling (2021). J. Acoust. Soc. Am. 150, 171-182], an algorithm based on matched field processing that is more robust to environmental mismatch. This paper extends these prior POMAP results by analyzing the localization performance of this algorithm in the presence of environmental noise. The noise rejection performance of POMAP is assessed using both simulated and measured signal data, with noise data based on environmental noise measurements. Herein, signal and noise measurements are from the nominally one-year-long PhilSea10 ocean acoustic propagation experiment. All signals were recorded from a single moored source, placed near the ocean sound channel 129.4 km away from a nearly water-column-spanning distributed vertical line array. The source transmitted linear frequency modulated chirps with nominal bandwidth from 200 to 300 Hz. The noise measurements used in this study were collected in the months after this source stopped transmitting, and synthetic samples of noise are calculated based on the characteristics of this measured noise. The effect that noise rejection algorithms have on the source localization performance of POMAP is also evaluated, but only 1 dB of performance improvement is achieved using these.

Story-driven games are growing in popularity across a wide range of genres. However, the narrative potential of video games is still being debated, particularly in light of the so-called tension between gameplay and storytelling. This study proposes that rules and game mechanics perform narrative semiotic functions, offering a ludic grammar of interactive storytelling. Case studies of four representative games show through exploratory player action shaped by rules, the medium of video games can generate meanings that traditional media cannot, thereby better achieving their narrative goals.