Richard A. Katz

Nonlinear analysis of environmental distortions of continuous wave signals in the ocean

Data from an underwater continuous wave signal are analyzed using methods derived from the study of chaotic systems. Distortions by the environment effectively add three degrees of freedom (dimensions) to the signal. The dimension required to reconstruct and analyze the received data is five in contrast to a pure tonal or sine wave that only requires two dimensions. The data are examined with a chaotic data analysis toolkit that includes determination of degrees of freedom using local and global false‐nearest‐neighbor statistics, average mutual information, correlation dimension, and local Lyapunov exponents. These results are important for the development of methods for correction of propagation distortions and nonlinear noise reduction algorithms. Application of this knowledge should lead to improvements in the detection and classification of underwater signals.

Nonlinear acoustics in cicada mating calls enhance sound propagation

An analysis of cicada mating calls, measured in field experiments, indicates that the very high levels of acoustic energy radiated by this relatively small insect are mainly attributed to the nonlinear characteristics of the signal. The cicada emits one of the loudest sounds in all of the insect population with a sound production system occupying a physical space typically less than 3 cc. The sounds made by tymbals are amplified by the hollow abdomen, functioning as a tuned resonator, but models of the signal based solely on linear techniques do not fully account for a sound radiation capability that is so disproportionate to the insects size. The nonlinear behavior of the cicada signal is demonstrated by combining the mutual information and surrogate data techniques; the results obtained indicate decorrelation when the phase-randomized and non-phase-randomized data separate. The Volterra expansion technique is used to fit the nonlinearity in the insects call. The second-order Volterra estimate provides further evidence that the cicada mating calls are dominated by nonlinear characteristics and also suggests that the medium contributes to the cicadas efficient sound propagation. Application of the same principles has the potential to improve radiated sound levels for sonar applications.

Measurements of turbulent pressure fluctuations using a buoyant vehicle coated with a thin elastomer layer

Turbulent pressure fluctuations were measured with piezoelectric pressure transducers which were covered with a 0.125‐in.‐thick elastomer window on a buoyant vehicle. Model predictions (i.e., corrections) were made to account for the turbulent pressure attenuation through the elastomeric coating and spatial averaging effects of a finite transducer. The corrected results were compared with classic turbulent spectral densities measured by others and found to be in good agreement.

Attenuation of turbulent pressure fluctuations through an elastomeric coating.

Turbulent pressure fluctuations were measured with piezoelectric pressure transducers that were covered with a 0.125‐in. elastomer window. Corrections for turbulence attenuation through the elastomer and for spatial averaging effects were made, based on the work of Ko and Schloemer and Corcos. Results are compared to classic turbulent spectral density measurements (Bakewell) and to previous measurements for flush‐mounted transducers (Galib and Zadina). The agreement among the results is very encouraging.

Data requirements for modeling, analysis, and improved understanding of laser beam propagation in a marine boundary layer

In this paper, we draw attention to the requirements for obtaining measurement data essential to accurate modeling and prediction of atmospheric laser beam propagation at heights 10 meters or less above the ocean surface. This is an atmospheric zone we call the marine boundary layer. There are numerous models and applications for optical beam propagation in the upper atmosphere that based on the Kolmogorov Theory of Turbulence. However, close to the ocean surface standard procedures for measuring and modeling the effects of boundary layer turbulence may no longer apply. In addition to classical measurement procedures, we suggest a new methodology and measurement procedures for exploration of beam propagation and the ensuing dynamics within the marine boundary layer.[1,2]

Characterizing nonlinear systems with memory while combating and reducing the curse of dimensionality using new volterra expansion technique

A generalized model for characterizing nonlinear systems was originally proposed by Italian mathematician and physicist Vito Volterra (1860-1940). A further development by American mathematician and MIT Professor Norbert Wiener (1894-1964) was published in 1958. After direct involvement with Norbert Wiener publication, Albert H. Nuttall has recently made new inroads along with his coauthors in applying the Wiener-Volterra model. A general description of a nonlinear system to the third order is termed the Nuttall-Wiener-Volterra model (NWV) after its co-founders. In this formulation, two measurement waveforms on the system are required in order to characterize a specified nonlinear system under consideration: an excitation input, x(t) (the transmitted signal) and a response output, z(t) (the received signal). Given these two measurement waveforms for a given system, a kernel response, h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel...

Characterization of nonlinear systems with memory: combatting the curse of dimensionality

This study investigates laser beam propagation through an atmospheric boundary layer near the ocean surface. Objectives of this research are to ascertain feasibility limits for achieving maximum energy efficiency at extended ranges in the face of atmospheric and other distortions as the laser beam penetrates through transitional (anisotropic) and turbulent (isotropic) boundary layer regimes. Various aspects of turbulence modeling of laser beam propagation near the ocean surface are discussed including: Kolmogorov’s model of atmospheric turbulence, parameterized structure functions (e.g., velocity and temperature gradients, gradients in refractive index) and other important factors affecting near surface propagation such as humidity, aerosols, and wave slap. Various preliminary modeled propagation results are shown, and a new methodology is proposed for improving existing model estimates with new time domain measurement procedures.

Laser beam propagation through an atmospheric transitional and turbulent boundary layer

This study investigates laser beam propagation through an atmospheric boundary layer near the ocean surface. Objectives of this research are to ascertain feasibility limits for achieving maximum energy efficiency at extended ranges in the face of atmospheric and other distortions as the laser beam penetrates through transitional (anisotropic) and turbulent (isotropic) boundary layer regimes. Various aspects of turbulence modeling of laser beam propagation near the ocean surface are discussed including: Kolmogorovs model of atmospheric turbulence, parameterized structure functions (e.g., velocity and temperature gradients, gradients in refractive index) and other important factors affecting near surface propagation such as humidity, aerosols, and wave slap. Various preliminary modeled propagation results are shown, and a new methodology is proposed for improving existing model estimates with new time domain measurement procedures.

Challenges of laser beam propagation near/within marine boundary layer

Marine atmospheric condition plays a critical role on imaging, laser beam propagation, and optical communication of the commercial and military platform. In Military platforms, ships and sailors must be able to defend and communicate with other maritime platform in sometimes volatile and hostile regions around the globe. Naval combatants need defensive and offensive capabilities against a variety of potential threats – many coming at low altitude, UAV, USV etc. High energy lasers (HELs) are currently in development, which have sufficient power levels (~100 kW) to destroy/disable most types of threats. Though target engagement and energy delivery are challenging, a HEL weapon can engage targets at the speed of light, does not require physical ammunition, and is able to run for hours at a time.

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.