D. K. Wilson

Forchheimer‐type nonlinearities for high‐intensity propagation of pure tones in air‐saturated porous media

A linear rigid frame, cylindrical capillary theory of sound propagation in porous media is extended to include nonlinear effects of the Forchheimer type, by making a particle velocity‐dependent correction to the complex density. This type of nonlinearity becomes important at incident sound‐pressure levels above approximately 120 dB re: 20 μPa for highly porous fibrous materials. Data from three experiments on air‐saturated porous media and foams, at levels up to 170 dB, are compared to the rigid frame theory with Forchheimer‐type extension. One of the experiments measured a low‐frequency approximation for the complex density directly; the others measured internal attenuation and surface admittance (inverse impedance). The generally good agreement found between predictions based on the Forchheimer‐type nonlinear theory and each of the experiments suggests that this type of nonlinearity is the dominant one for propagation in many types of air‐saturated fibrous porous media. Some interesting surface absorpti...

Acoustic tomographic monitoring of the atmospheric boundary layer

Abstract Acoustic tomography is proposed as a method for monitoring near-surface atmospheric temperature and wind velocity fields. Basic issues relating to the feasibility and implementation of atmospheric tomography are discussed. Among these issues are the causes of fluctuations in acoustic signals propagated through the atmosphere, appropriate spatial dimensions of an array, signal detection and processing techniques, mathematical inverse techniques and their numerical implementation, and whether or not tomography m provide measures of dynamical variables of interest to atmospheric scientists. Surface-layer, horizontal-slice tomography was implemented experimentally, with an array of three sources and seven receivers distributed over a region approximately 200 m square. Travel-time fluctuations at the receivers were used to reconstruct the temperature and wind fields with about 50-m resolution in the horizontal plane.

Sampling-Based Sensitivity Analysis through Proper Orthogonal Decomposition and Cluster-Weighted Models

Numerical estimation of the sensitivity of a spatially distributed process to its governing parameters is an essential preliminary step in uncertainty quantication, but it can be computationally costly. A sensitivity analysis (SA) framework is described which uses an equitable sampling method for exploring the parameter space (e.g., Latin hypercube sampling), proper orthogonal decomposition (POD) for constructing compact representations of the process’ variability from an ensemble of realizations, and cluster-weighted models (CWMs) for quickly forecasting the process given new parameter samples. New process realizations are computed eciently through coupling the POD basis and CWMs to form a

Development of a high-fidelity simulation capability for battlefield acoustics.

Findings are presented from the first year of a joint project between the U.S. Army Engineer Research and Development Center, the U.S. Army Research Laboratory, and the Sandia National Laboratories. The purpose of the project is to develop a finite-difference, time-domain (FDTD) capability for simulating the acoustic signals received by battlefield acoustic sensors. Many important effects, such as scattering from trees and buildings, interactions with dynamic atmospheric wind and temperature fields, and nonstationary target properties, can be accommodated by the simulation. Such a capability has much potential for mitigating the need for costly field data collection and furthering the development of robust identification and tracking algorithms. The FDTD code is based on a carefully derived set of first-order differential equations that is more general and accurate than most current sound propagation formulations. For application to three-dimensional problems of practical interest in battlefield acoustics, the code must be run on massively parallel computers. Some example computations involving sound propagation in a moving atmosphere and propagation in the presence of trees and barriers are presented.

Frequency decorrelation and pulse propagation in a turbulent atmosphere

The impact of atmospheric turbulence on sound propagation is an important consideration for source localization with acoustic sensor arrays, studies of noise pollution, and the development of new remote sensing techniques. This paper takes as a starting point a recently derived, closed-form equation for the spatial-temporal coherence function of a broadband acoustic signal propagating in a refractive, turbulent atmosphere with spatial-temporal fluctuations in temperature and wind velocity. The theory is quite general and enables analysis of many statistical characteristics of the sound field. It has certain advantages in comparison with Monte-Carlo simulations and has already been used to study the spatial-temporal coherence of narrowband signals. In the present paper, this theory is employed to calculate and analyze the frequency decorrelation of broadband acoustic signals for different regimes of the atmospheric surface layer. The results are then used to study the effect of atmospheric turbulence on th...

Waveguide sound propagation in a turbulent atmosphere above randomly rough ground

Waveguide sound propagation in a refractive, turbulent atmosphere above randomly rough ground is considered. The waveguide is formed between ground surface and turning points of sound waves in the downwind direction or in a temperature inversion. Using the Beilis-Tappert transformation, a modal decomposition of the sound field, and the Chernov method, closed-form equations for the coherence function of the sound field are derived. The coherence function is expressed in terms of the effective spectrum, which is a linear combination of the one-dimensional spectra of temperature and wind velocity fluctuations, and a spectrum of the surface roughness. The derived effective spectrum is used to study the relative contributions of atmospheric turbulence and surface roughness to the coherence loss of propagating sound.

Bayesian Regression and Updating for Sampling-Based Sensitivity Analysis

A model’s predictive power in representing an incompletely known environment cannot be assessed without first quantifying its sensitivity throughout the parameter space. If the system is spatially distributed, knowledge of these sensitivities throughout the spatial domain also is essential for effectively investing data-gathering resources to support forecasts. Sensitivity analysis therefore is central to raising the relevance of computational mechanics in practical applications.A sampling-based sensitivity analysis framework was presented recently that computes full-field sensitivities throughout the model’s parameter space and provides estimates of the forecast uncertainty in these sensitivities. A central component of this method is Bayesian regression with cluster-weighted models. Extensions and practical improvements of CWM training and derivative computation are described here; these include (1) a more flexible conditional expected value model that incorporates locally quadratic terms, (2) the ability to compute second-order sensitivities, and (3) k-fold cross-validation for regularizing the underlying regression models. Results from the improved framework were compared with a standard analytical function dominated by several strong minima and maxima. Good reproduction of the training data and first-order derivatives were observed, along with partly satisfactory reproduction of the second-order derivatives. A plan is also described for developing the means to efficiently recompute sensitivities as new training data are obtained.

Correspondence between sound propagation in discrete and continuous random media

Wave propagation in random media is important in many applications such as sound propagation in a turbulent atmosphere and scattering by bubbles and microparticles in the ocean. Formulations for the statistical moments of the sound pressure field in continuous and discrete random media are usually done independently. In this presentation, it is demonstrated that the equations for the first two statistical moments in a continuous random medium have the same form as those for a discrete random medium if the scattering properties of the media are expressed in terms of the differential scattering cross section and total cross section. This analogy enables us to apply methods developed in wave propagation in continuous random media to discrete media, and vice versa. As an example, the existing theory of the interference of the direct and ground reflected waves in a turbulent atmosphere is used to study the effect of trees on the interference of these waves in a forest. The results obtained are compared with experimental data. The correspondence between wave propagation in discrete and continuous random media can also be used in other fields of physics.Wave propagation in random media is important in many applications such as sound propagation in a turbulent atmosphere and scattering by bubbles and microparticles in the ocean. Formulations for the statistical moments of the sound pressure field in continuous and discrete random media are usually done independently. In this presentation, it is demonstrated that the equations for the first two statistical moments in a continuous random medium have the same form as those for a discrete random medium if the scattering properties of the media are expressed in terms of the differential scattering cross section and total cross section. This analogy enables us to apply methods developed in wave propagation in continuous random media to discrete media, and vice versa. As an example, the existing theory of the interference of the direct and ground reflected waves in a turbulent atmosphere is used to study the effect of trees on the interference of these waves in a forest. The results obtained are compared with ex...

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...

Modeling of acoustic pulse propagation and beamforming in forests

Acoustic pulse propagation through forests is important for many applications, including noise attenuation by stands of trees, and localization of sound sources. Due to the highly complicated distribution of trees in natural forests, it is appropriate to consider a forest as a continuous distribution of scatterers of various shapes and sizes. A propagation model based on radiative transfer theory under a modified Born approximation may be developed for this situation to describe both the coherent and diffuse sound propagation . The simple case of an impulse in an infinite homogeneous forest of diffuse scatterers is first considered, and then the effects of successively including non-diffuse scatterers, ground reflections in a forest of finite height, and, finally, a realistic forest model are analyzed. These theoretical findings are then compared with experimental results. Lastly, a numerical example describing the effect of a forest on a simple beamforming array is considered.Acoustic pulse propagation through forests is important for many applications, including noise attenuation by stands of trees, and localization of sound sources. Due to the highly complicated distribution of trees in natural forests, it is appropriate to consider a forest as a continuous distribution of scatterers of various shapes and sizes. A propagation model based on radiative transfer theory under a modified Born approximation may be developed for this situation to describe both the coherent and diffuse sound propagation . The simple case of an impulse in an infinite homogeneous forest of diffuse scatterers is first considered, and then the effects of successively including non-diffuse scatterers, ground reflections in a forest of finite height, and, finally, a realistic forest model are analyzed. These theoretical findings are then compared with experimental results. Lastly, a numerical example describing the effect of a forest on a simple beamforming array is considered.