Paul A. Elmore

An iterative approach for approximating bubble distributions from attenuation measurements

A precise theory exists, based on an integral equation, by which acoustic signal attenuation versus frequency, due to a known bubble-density distribution versus bubble radius, may be calculated. Lacking a simple inversion scheme for the integral equation, an approximation which accounts only for attenuation due to resonant bubbles is available (and often applied) to calculate a bubble distribution. An iterative approach for improving on that resonant bubble approximation is presented here. That new approach is based on alternating calculations and corrections between attenuation data and the bubble distribution presumed to have produced it. This iterative technique is tested, first, on two simulated data sets of bubble distributions. It is then applied to attenuation data measured as a function of frequency from 39 to 244 kHz during the Scripps Pier Experiment [Caruthers et al., Proc. 16th Int. Cong. on Acoust., pp. 697–698 (1998)]. The results of the simulations demonstrate the validity of the method by ...

Acoustic attenuation in very shallow water due to the presence of bubbles in rip currents

An experiment was performed just off the research pier at the Scripps Institute of Oceanography to determine the acoustic effects of small bubbles in very shallow water (∼6 m depth). The distance offshore was ∼300 m. The propagation lengths were 2–10 m, and the frequency range was from 39 to 244 kHz. During the experiment, rip currents passed through the field of measurement instruments. These rip currents were laden with bubbles created in the surf between the instruments and the shore. The effects of these rip currents on the spatial distributions of the resulting acoustic attenuation are discussed. From the attenuation data, the bubble distributions are calculated using a new iterative approach [Caruthers et al., in press, J. Acoust. Soc. Am.] that is based on the well-known resonant bubble approximation. Calculated bubble distributions varied from an essentially uniform lack of bubbles during quiescent periods to highly inhomogeneous and dense bubbly regions within rip events. Such observed distributi...

Soft likelihood functions in combining evidence

Abstract We develop an approach for flexible computation of likelihood functions of probabilistic evidence in the context of forensic crime investigations. An ordered weighted average (OWA) aggregation approach allows a softening of the strong likelihood constraint of requiring all such evidence. Use of the OWA measure known as attitudinal character provides OWA weights allowing optimistic or pessimistic likelihood results. This approach is extended by introducing the reliability of evidence in the computations of likelihood functions. Examples of the basic OWA computation and the likelihood results introducing reliability are provided.

Combining uncertain information of differing modalities

In this paper we consider approaches for combining separately possibilistic uncertainty, probabilistic uncertainty and situations where both forms of uncertainty appear. An approach to probability aggregation using rational consensus with equi-weighting is developed. This aggregation is analyzed with information measures as one way to assess combinations and understand the impact on uncertainty. The analysis is based on combinations of bounding cases of probability distributions. Measures of conflict and the effect on information are developed. Next possibility transformations are used and illustrated by three representative possibility cases. The resultant transformed probabilities are aggregated with general probability distributions and the result evaluated with information measures as before. Finally a general approach to combining possibility distributions directly using quality criteria is described. An example is provided to illustrate the basic possibility distribution aggregation fusion developed.

Mine burial by scour: preliminary results from the Gulf of Mexico

Mine burial experiments were conducted on fine and coarse sandy sediments, in 13 to 15-m water depths, 15 km off Indian Rocks Beach, West-Central Florida. Experimental sites were chosen based on extensive acoustic (side scan, chirp and multibeam) surveys and sediment samples collected by USF. Four acoustic (NRL and OMNI Technologies) and six optical (FWG) cylindrical mines were deployed during January-March 2003. The extensive sediment (USF and NRL) data combined with predictions from NOAA wave buoys operating offshore of Tampa, FL during these experiments is used to predict burial by waveinduced scour (VIMS). Extensive wave and current data collected with bottom mounted tripods is compared to physical oceanographic model predictions. Time-dependent scour measured using the optical and acoustic mines, characterized by sector scan sonar (USF), ROV video (USF), and diver photographs/observations (USF and NRL) is compared to model predictions.

Assessing scour model performance with experimental data

Equations by Soulsby and Whitehouse have been applied to predicting mine burial by scour in tidal estuaries. The main equation, which has the functional form of [1-exp(-t/T)], computes the depth of the scour pit with time under steady state conditions. This theory may be applied to changing conditions by using the RMS values of the frictional stress at the bed and assuming a quasi-steady state of the RMS values over a small time period. From 1999-2002, the Naval Research Laboratory conducted scour burial experiments using instrumented mines that measure mine motion (heading, roll, and pitch) and percent burial (surface area covered with sediment). Using oceanographic and sediment data obtained during these experiments, this study examines how well the predictions match the mine burial measurements.

Geospatial Modeling Using Dempster–Shafer Theory

Uncertainty in spatial geometrical issues is represented using Dempster–Shafer (D–S) theory. Interval approaches are used for D–S uncertainty of spatial locations and the associated arithmetic operations on such intervals described. Categories of uncertainty for points and lines are defined using interval formulations. Based on these, approaches for calculation of geometric areas, line length and line slopes are given. Compatibility of imprecise point locations is discussed and potential aggregations for similar points considered. Finally, topological spatial relationships are described for objects with uncertain boundaries. This will provide a formal framework for the use of a D–S interval approach for uncertainty in spatial geometric issues.

Fuzzy Choquet integration of homogeneous possibility and probability distributions

The fuzzy integral (FI) is an extremely flexible and powerful tool for data and information aggregation. The FI is parametrized by the fuzzy measure (FM), a normal and monotone capacity. Based on the selection of FM, the FI produces different aggregation operators. In recent years, a number of FI extensions have been put forth relative to different types of uncertain information, e.g., real-, interval- and set-valued (under various constraints). Herein, we study the applicability and behavior of different extensions of the fuzzy Choquet integral for fusing homogeneous possibility and probability distributions. This analysis is of great utility in terms of understanding what extensions and under what conditions it is possible to aggregate and maintain homogeneity within uncertain information. We show that two extensions, gFI and NDFI, can aggregate both probability and possibility distributions. While these extensions do not always maintain homogeneity, they do under certain conditions. Last, while we specifically focus on the aggregation of homogeneous uncertain information, the propositions put forth also shed light into heterogeneous information aggregation via the gFI and the NDFI.

Higher order corrections to an iterative approach for approximating bubble distributions from attenuation measurements

A formal theory exists for determining sound attenuation from a known distribution of bubble sizes in the ocean; however, an integral equation must be inverted if attenuation is given and the distribution of bubbles is not. An approximate distribution can be determined based on the resonant bubble approximation (RBA). An iterative approach, for which the RBA represents the zeroth iteration, was proposed and carried out to the first iteration in a previous paper . It was suggested that additional iterations would improve the bubble-distribution results. Here we formulate the procedure to carry the results to a higher order and demonstrate, based on a theoretical distribution of a multiple power law form, the improvements in successive approximations of the bubble distribution to the fourth iteration level. A recursion relation is developed that allows one to carry the iteration out to an arbitrary order. It is shown that regions of the distribution that change in the power-law exponent are places where the higher order corrections improve the results the most.

Binary fuzzy measures and Choquet integration for multi-source fusion

Countless challenges in engineering require the intelligent combining (aka fusion) of data or information from multiple sources. The Choquet integral (ChI), a parametric aggregation function, is a well-known tool for multi-source fusion, where source refers to sensors, humans and/or algorithms. In particular, a selling point of the ChI is its ability to model and subsequently exploit rich interactions between inputs. For a task with N inputs, the ChI has 2N interaction variables. Therefore, the ChI becomes intractable quickly in terms of storage and its data-driven learning. Herein, we study the properties of an efficient to store, compute, and ultimately optimize version of the ChI based on a binary fuzzy measure (BFM). The BFM is further motivated by empirical observations in the areas of multi-sensor fusion and hyperspectral image processing. Herein, we provide a deeper understanding of the inner workings, capabilities and underlying philosophy of a BFM ChI (BChI). We also prove that two fuzzy integrals, the ChI and the Sugeno integral, are equivalent for a BFM. Furthermore, only a small subset of BFM variables need be stored, which reduces the BChI to a relatively simple look up operation.