Sheri Martinelli

Computational modeling of acoustic wavefronts propagating in an underwater environment with uncertain parameters

High frequency simulation of underwater sound propagation is a vital part of modeling and simulation of acoustic systems for evaluation and performance prediction. Existing simulations use deterministic ray tracing to propagate the acoustic field and simulate uncertainty by varying results according to basic distributions (e.g., adding ”jitter” to ray arrival angle). Rather than incorporate randomness as a form of post-processing, this work seeks to model uncertainty where it exists in the underwater environment where it is easier to specify, and then propagate the relevant random quantities through the system applying stochastic collocation to an existing deterministic model. Further, this work addresses the drawbacks of ray tracing by taking the deterministic method to be a model that computes propagation of entire wavefronts rather than rays, thus maintaining error control over the physical domain. To this end, generalized polynomial chaos expansions are applied to a level-sets based wavefront propagat...

A study of underwater propagation model performance in complex environments with inherent uncertainty

A number of computational models have been developed for purposes of modeling and simulation of acoustic wave propagation in underwater environments. Almost all of these models make approximations to the wave equation; furthermore, the method of implementation has a direct impact on the trade-off between accuracy and computational efficiency. Sonar technologies also vary greatly in range and frequency and one model is generally not suited for all applications; there are often subtle differences between them that can be highly dependent on the particulars of the environment. We investigate the performance of various models (ray tracing, level sets, normal modes, parabolic equation, and energy flux) using at-sea data from real world environments to assess their robustness of in the presence of the inherent uncertainty involved in reconstructing an underwater environment. In particular, we focus on the effect of perturbations in the sound speed profile. The sound speed profile, as a model input parameter, is subject to measurement error, as well as to undersampling of what, in many geographical areas of interest, is a complex spatial-temporal process. Ultimately, our objective is to establish some guidelines for practical use of the models in applications. A number of computational models have been developed for purposes of modeling and simulation of acoustic wave propagation in underwater environments. Almost all of these models make approximations to the wave equation; furthermore, the method of implementation has a direct impact on the trade-off between accuracy and computational efficiency. Sonar technologies also vary greatly in range and frequency and one model is generally not suited for all applications; there are often subtle differences between them that can be highly dependent on the particulars of the environment. We investigate the performance of various models (ray tracing, level sets, normal modes, parabolic equation, and energy flux) using at-sea data from real world environments to assess their robustness of in the presence of the inherent uncertainty involved in reconstructing an underwater environment. In particular, we focus on the effect of perturbations in the sound speed profile. The sound speed profile, as a model input parameter, is...

Modal response uncertainty in structural acoustic systems using generalized polynomial chaos expansion

When knowledge of material design parameters is lacking, it is important to understand how this uncertainty effects the system response. Generalized polynomial chaos (gPC) expansions provide a means for quantifying this uncertainty and typically show good agreement with Monte Carlo techniques at a much reduced cost [K. Sepahvand et al. / Applied Acoustics 87 (2015) 23-29]. In this work, we apply gPC expansions to study the effects of design parameter uncertainty on a structure’s modal characteristics—both eigenvalues and eigenfunctions. The gPC expansions permit the propagation of uncertainty from the design parameters to the modes and natural frequencies, which then characterize the vibration response of the system as a function of the random parameters. The response uncertainty can then be described using the solutions of the deterministic system sampled carefully over the parameter space. Uncertainty in the forcing function can also be included in this formulation. Numerical calculations demonstrate th...

Effects of depth-dependent sound speed on Lloyd mirror patterns

The classical Lloyd mirror describes the interference pattern in pressure magnitude between direct and reflected propagation paths arising from a point source at depth d in the water column at a receiver located at range R, R >> d. In a homogeneous medium, the magnitude of acoustic pressure has a simple expression in terms of (approximate) propagation angle: |p|=(2/R0)|sin kd cos Θ0. For fast calculation of reverberation strength, we can apply this pattern to capture the effects of reflections from an idealized flat sea surface. However since we are interested in long range calculations, it is expected that the existence of sound speed gradients will affect the shape of this pattern, but how significant are these effects? To study this question, we derive a generalized Lloyd mirror for a linear-in-depth sound speed profile. We present results and discuss the implications. [Work supported by ONR through a STTR partnership with OASIS.]

Efficient sequential Monte Carlo estimation of range-dependent seabed properties

Seabed geoacoustic properties play a crucial role in shallow-water sonar applications, including the detection of unexploded ordnance. Our goal is improved efficiency of Bayesian seabed parameter and uncertainty estimation for large data volumes. While Bayesian uncertainty estimation provides important information for sonar applications, the approach is computationally expensive which limits utility for large surveys, where an abundance of range-dependent data can be collected. This work considers the efficiency of a particle filter to quantify information content of multiple data sets along the survey track by considering results from previous data along the track to inform the importance sampling at the current point. Efficiency is improved by tempering the likelihood function of particle subsets and including exchange moves (parallel tempering), and by adapting the proposal distribution for the Markov-chain steps. In particular, perturbations are proposed in principal-component space, with the rotation...

Effects of seabed curvature on the scattered acoustic field

Knowledge of the acoustic properties of the sea bottom provides valuable input into the development and performance of information processing algorithms designed to detect and identify, e.g., man-made objects near to, or embedded in, the seabed. This information is also useful for improving modeling and simulation results in reverberation-limited environments. A critical challenge in this area is in allowing for range dependent bathymetry as it can affect the propagating acoustic field in ways that are difficult to predict. Typical approaches to modeling variable bathymetry assume either piecewise flat or tilted (linear) geometry; however, this only serves as a discrete approximation to reality. This study investigates the effects of mild curvature on the 3D acoustic field in frequency and angle space via finite difference time domain simulations. We present results and discuss the implications on forward modeling of the acoustic interaction with the seabed. [Work supported by the Strategic Environmental ...

Newtonian and weighted essentially non-oscillatory models to describe the generation and propagation of the Cicada mating calls

Experiments and analyses of Hughes et al., JASA, 2009 are the origins of this research where we study the in-air waveform generation and propagation of the acoustic signals generated by cicadas. The sound generation is studied in a Newtonian model and the sound propagation is analysis by a numerical solver for viscous Burgers’ equation. The time histories from the tymbal surface velocities recorded by a laser Doppler vibrometer to the microphones positioned near the cicadas provide the test data. The Newtonian model describes the sound production systems process to generate the mating call signal structure. The numerical solver employs weighted essentially non-oscillatory (WENO) reconstruction to approximate the first and second derivatives of the semi-discrete operator. The WENO is utilizes due to the non-smooth structure of the cicada propagating waveform. Principally, the cicada mating signal in question has sharp transitions, since spectral methods tend to produce spurious oscillations as a result of attempting to represent a discontinuous function by a Fourier basis expansion. Thus, these analytical models are computationally tested to determine if the results capture the sound production and the transmission of the cicada mating calls. To verify the models are meaningful, the simulations are verified with real experimental data.

Optimizing eigenray generation for real time simulations

Real time simulation is a critical supplement to in-water testing for the assessment of naval system performance. Limitations exist on the number of independent runs, on geographical locations in which in-water tests can be performed, and on the amount of control experimenters possess over the test environment. Many systems have critical time-sensitive functionality (e.g., acoustic homing) which constrains the ability to produce realistic time series for injection; but a reduced fidelity solution can still be of use. Graphics hardware (GPU) has become a significant computing platform in its own right. Its application requires a mapping of the propagation algorithm to the GPU computing paradigm and careful tweaking to squeeze out maximum performance. We will look at taking from theory just what we need to hand-tune code for a GPU + CPU computing platform, and the limitations of a high speed, range dependent, eigenray code. We also consider a related approach that uses the resulting eigenrays to initialize ...

A method for numerical representation of arbitrary boundaries in acoustic wavefront propagation.

An enhancement to the application of a wavefront propagation algorithm for underwater acoustics based on the level set method is presented. The presence of discontinuities in the phase space at reflecting boundaries requires the use of specialized differencing techniques to prevent oscillations in the computed solutions of the acoustic phase. A weighted essentially non‐oscillatory method is applied for this purpose, necessitating the use of uniformly spaced grids over the computational domain. In order to represent arbitrary boundaries in this implementation, one has to either modify the grid to include the boundary (reduces the convergence rate) or develop an appropriate boundary condition to apply within the region of interest. Earlier versions of this work approximated the actual boundary location by the location of the nearest grid point. This resulted in a stair‐step effect in the solutions, which resolves with finer grid resolution. However, the phase space is high‐dimensional; a highly resolved gri...

Range dependence in the level set method for underwater acoustics.

The level set method due to Osher and Sethian [J. Comput. Phys. 79, 12–49 (1988)] provides a way to obtain fixed grid solutions to the high‐frequency wave equation. Instead of tracing rays from the source, the level set method embeds the wavefront implicitly in the phase space and propagates it according to the velocity field determined by the local ray direction, thus avoiding the complications involved in the spatial reconstruction of wavefronts from diverging rays. A level set method has been developed and implemented as a fixed‐grid alternative to ray tracing to solve for the acoustic phase. One of the issues that arises with the increased dimensionality of posing the propagation problem in the level set framework is that the presence of reflecting boundaries produces a discontinuity in the phase space corresponding to a sudden change in propagation direction. When a reflecting boundary is range‐dependent, further complications arise. To improve algorithm performance, specialized methods are applied t...