Carl R. Hart

Comparisons between physics-based, engineering, and statistical learning models for outdoor sound propagation.

Many outdoor sound propagation models exist, ranging from highly complex physics-based simulations to simplified engineering calculations, and more recently, highly flexible statistical learning methods. Several engineering and statistical learning models are evaluated by using a particular physics-based model, namely, a Crank-Nicholson parabolic equation (CNPE), as a benchmark. Narrowband transmission loss values predicted with the CNPE, based upon a simulated data set of meteorological, boundary, and source conditions, act as simulated observations. In the simulated data set sound propagation conditions span from downward refracting to upward refracting, for acoustically hard and soft boundaries, and low frequencies. Engineering models used in the comparisons include the ISO 9613-2 method, Harmonoise, and Nord2000 propagation models. Statistical learning methods used in the comparisons include bagged decision tree regression, random forest regression, boosting regression, and artificial neural network models. Computed skill scores are relative to sound propagation in a homogeneous atmosphere over a rigid ground. Overall skill scores for the engineering noise models are 0.6%, -7.1%, and 83.8% for the ISO 9613-2, Harmonoise, and Nord2000 models, respectively. Overall skill scores for the statistical learning models are 99.5%, 99.5%, 99.6%, and 99.6% for bagged decision tree, random forest, boosting, and artificial neural network regression models, respectively.

Utility of machine learning algorithms for natural background photo classification

In support of the Terrain Characterization for Rendering and Field Evaluation effort, the U.S. Army Corps of Engineers, Engineer Research and Development Center (ERDC), Cold Regions Research and Engineering Laboratory (CRREL), assisted the Natick Soldier Research, Development, and Engineering Center (NSRDEC) in evaluating machine learning algorithms to automatically classify three vegetation types (tree, shrub, and herbaceous), and a non-vegetated type in terrestrial images. In a previous partnership between CRREL and NSRDEC, researchers developed the Global Natural Background Image Database (GNBID), a collection of natural background images classified by vegetation attributes to include vegetation type and height, leaf shape, leaf color, and many others. Following deployment, the GNBID successfully improved on-the-ground understanding of natural background environments and quickly revealed the need for a larger database. Manual classification methods proved time intensive and variable, thus CRREL explored the feasibility of automatically identifying features using machine learning algorithms. In this scope-ofwork study, we explore a multitude of computer vision techniques, settling on a supervised deep-learning technique. Here we present the advantages and disadvantages of various techniques, classification results from a subset of images, and recommendations for future research in this area. ERDC/CRREL TR-18-7 iii

A measurement system for the study of nonlinear propagation through arrays of scatterers

Various experimental challenges exist in measuring the spatial and temporal field of a nonlinear acoustic pulse propagating through an array of scatterers. Probe interference and undesirable high-frequency response plague typical approaches with acoustic microphones, which are also limited to resolving the pressure field at a single position. Measurements made with optical methods do not have such drawbacks, and schlieren measurements are particularly well suited to measuring both the spatial and temporal evolution of nonlinear pulse propagation in an array of scatterers. Herein, a measurement system is described based on a z-type schlieren setup, which is suitable for measuring axisymmetric phenomena and visualizing weak shock propagation. In order to reduce directivity and initiate nearly spherically-symmetric propagation, laser induced breakdown serves as the source for the nonlinear pulse. A key component of the schlieren system is a standard schliere, which allows quantitative schlieren measurements ...

Nondimensional analysis of wind noise and atmospheric surface-layer properties

Wind noise is a prominent limitation to the signal to noise ratio of acoustic sensors. Realistic expectations of signal detectability can be generated by predicting the noise floor prior to a sensor deployment; however, a relationship must be established between the wind noise measured by a sensor and atmospheric surface-layer properties. Under conditions of horizontal homogeneity and quasi-steadiness, Monin-Obukhov similarity theory relates friction velocity, temperature scale, and roughness length to the near-surface profiles of mean wind speed and turbulent intensity, which in turn are known to govern wind noise. It is expected that the ratio of one-third octave band root-mean-square sound pressure to the turbulent flux of momentum, Strouhal number, and dimensionless elevation have a nondimensional relationship that collapses wind noise data as a function of Monin-Obukhov parameters. In order to establish such a relationship, we analyze a dataset of wind noise recorded in Spring 2018 within the Army Research Laboratory’s Meteorological Sensing Array on the Jornada Experimental Range, New Mexico. This dataset consists of continuous recordings of ambient noise at several sites on audio microphones up to 20 m above ground level, co-located with a suite of high-fidelity meteorological instruments, including sonic anemometers.

Inferring atmospheric surface-layer properties from wind noise in the nocturnal boundary layer

Uncertainties in the state of the atmosphere, to a large extent, limit the prediction accuracy of outdoor sound propagation. In particular, event sound propagation requires accurate knowledge of wind speed and temperature profiles, spatially averaged over the path of propagation. In a stable quasi-steady nocturnal boundary layer, wind speed and temperature gradients follow a scaling that is asymptotically independent of altitude and depends on Monin-Obukhov similarity parameters. Since these parameters describe the near-surface profiles of wind speed and turbulent intensity, which in turn are known to govern wind noise, it is anticipated that a connection exists between Monin-Obukhov parameters and the statistics of wind noise. It is expected that these parameters may be inferred from wind noise sensed by screened microphones. Ambient noise data collected in the southwest U.S. are analyzed for the purpose of examining whether Monin-Obukov similarity parameters may be inferred from wind noise. We explore the consequences of establishing inferences with a priori distributions for the similarity parameters, and utilizing wind noise data from microphones at one or more altitudes.Uncertainties in the state of the atmosphere, to a large extent, limit the prediction accuracy of outdoor sound propagation. In particular, event sound propagation requires accurate knowledge of wind speed and temperature profiles, spatially averaged over the path of propagation. In a stable quasi-steady nocturnal boundary layer, wind speed and temperature gradients follow a scaling that is asymptotically independent of altitude and depends on Monin-Obukhov similarity parameters. Since these parameters describe the near-surface profiles of wind speed and turbulent intensity, which in turn are known to govern wind noise, it is anticipated that a connection exists between Monin-Obukhov parameters and the statistics of wind noise. It is expected that these parameters may be inferred from wind noise sensed by screened microphones. Ambient noise data collected in the southwest U.S. are analyzed for the purpose of examining whether Monin-Obukov similarity parameters may be inferred from wind noise. We explore t...

A maximum likelihood estimator for spectral models of acoustic noise processes

The power spectral density of time series from many acoustic phenomena can vary rapidly through several decades of magnitude, particularly for noise processes. This property can complicate evaluation of spectral density models with respect to a non-parametric estimate of the spectral density, also known as the periodogram. Typical measures, such as the sum of squares of the residuals, can suffer from bias errors and oversensitivity to large values. A log-likelihood function is here presented for a periodogram derived from a sequence of independent, circularly-symmetric complex normal Fourier components. The bias-corrected Akaike’s information criterion of an expected-value spectral model is shown to be a useful measure for multi-model selection. A maximum-likelihood estimator is formed for spectral model parameters with respect to a known periodogram, along with approximate confidence intervals for the parameter estimates. Results from the maximum-likelihood estimator are compared with weighted and unweig...

Exact wide-angle formulation of the Beilis-Tappert method

The Beilis-Tappert method was originally developed for narrow-angle acoustic propagation under a rough sea surface [A. Beilis and F. D. Tappert, J. Acoust. Soc. Am. 66, 811–826 (1979) ]. The method has also been applied to narrow-angle propagation over irregular terrain for acoustic waves and radar. It is shown here that an exact wide-angle formulation of the Beilis-Tappert method can be derived simply by replacing ∂/∂z with ∂/∂z + ik0 tanφ, where k0 = 2π/λ, λ is the physical wavelength, φ is the slope angle, and i= √-1. The exact formulation makes clear that for large slope angles, much of the acoustic field does not propagate, but decays exponentially with range. Existing finite difference methods and all narrow-angle methods fail to properly account for the exponential decay with a range of the non-propagating components of the acoustic field. The exponential decay with this range is qualitatively explained in terms of rays and quantitatively explained in terms of waves. Properly accounting for the propagating and non-propagating components of the acoustic field is explained.The Beilis-Tappert method was originally developed for narrow-angle acoustic propagation under a rough sea surface [A. Beilis and F. D. Tappert, J. Acoust. Soc. Am. 66, 811–826 (1979) ]. The method has also been applied to narrow-angle propagation over irregular terrain for acoustic waves and radar. It is shown here that an exact wide-angle formulation of the Beilis-Tappert method can be derived simply by replacing ∂/∂z with ∂/∂z + ik0 tanφ, where k0 = 2π/λ, λ is the physical wavelength, φ is the slope angle, and i= √-1. The exact formulation makes clear that for large slope angles, much of the acoustic field does not propagate, but decays exponentially with range. Existing finite difference methods and all narrow-angle methods fail to properly account for the exponential decay with a range of the non-propagating components of the acoustic field. The exponential decay with this range is qualitatively explained in terms of rays and quantitatively explained in terms of waves. Properly accounting for the pro...

Automatic target recognition with uncertain scattered signal distributions

One of the primary challenges for performing robust automated target recognition (ATR) is how to compensate the signatures for environmental propagation effects. ATR algorithms tend to function well only in the specific terrain and atmospheric conditions for which they were trained. This is particularly true for acoustic signals, which undergo strong frequency-dependent scattering and refraction in both outdoor and underwater environments. To address this problem, we formulate a Bayesian sequential updating method, which accounts for realistic signal and noise distributions, and uncertainties in the parameters of these distributions. The formulation utilizes physics-based scattering models for signal fading and the cross coherence between frequencies and transmission paths. We discuss how, in a Bayesian context, the scattering models correspond to likelihood functions, which are conveniently paired with their conjugate priors to efficiently update the uncertain signal parameters (hyperparameters). The ori...

Calculations of low-frequency wind noise along a low two-dimensional hill surface

Measurement of outdoor sound propagation is often limited by wind noise, i.e. pressure fluctuations from atmospheric turbulence, especially for infrasound and low audible frequencies. Over a flat ground surface, the spectral density of wind noise can be predicted by the shear-turbulence mechanism for static pressure fluctuations using a mirror flow atmospheric turbulence model for the inhomogeneous surface-blocking effect. This study moves beyond a flat ground model to consider the effects of flow distortion by weak topography on surface wind noise, specifically, flow over a low two-dimensional hill, free from separation, at large Froude number. The integral solution for the pressure Poisson equation is used as a starting point, with turbulence modeled by the mirror flow in surface-following coordinates. The perturbation analysis of Hunt et al. [Q. J. R. Meteorol. Soc. 114(484), 1435–1470 (1988)] is used to model the mean shear rate as a function of elevation and distance over the hill. For upwind, downwi...

Modeling of signal propagation and sensor performance for infrasound and blast noise

This paper describes a comprehensive modeling approach for infrasonic (sub-audible acoustic) signals, which starts with an accurate representation of the source spectrum and directivity, propagates the signals through the environment, and senses and processes the signals at the receiver. The calculations are implemented within EASEE (Environmental Awareness for Sensor and Emitter Employment), which is a general software framework for modeling the impacts of terrain and weather on target signatures and the performance of a diverse range of battlefield sensing systems, including acoustic, seismic, RF, visible, and infrared. At each stage in the modeling process, the signals are described by realistic statistical distributions. Sensor performance is quantified using statistical metrics such as probability of detection and target location error. To extend EASEE for infrasonic calculations, new feature sets were created including standard octaves and one-third octaves. A library of gunfire and blast noise spectra and directivity functions was added from ERDC’s BNOISE (Blast Noise) and SARNAM (Small Arms Range Noise Assessment Model) software. Infrasonic propagation modeling is supported by extension of several existing propagation algorithms, including a basic ground impedance model, and the Green’s function parabolic equation (GFPE), which provides accurate numerical solutions for wave propagation in a refractive atmosphere. The BNOISE propagation algorithm, which is based on tables generated by a fast-field program (FFP), was also added. Finally, an extensive library of transfer functions for microphones operating in the infrasonic range were added, which interface to EASEE’s sensor performance algorithms. Example calculations illustrate terrain and atmospheric impacts on infrasonic signal propagation and the directivity characteristics of blast noise.