Peak Probability Density Function Research Articles

Volume scattering: Echo peak PDF

The probability density function (PDF) of the maximum echo value achieved in a depth gate has been analytically derived, computer simulated, and measured in the field—all in cases where clouds of scatterers are involved. The clouds of interest are plankton, nekton, bubbles, etc. or a combination and are sufficiently dense so that echoes from the individual scatterers overlap. We show that this echo peak PDF is quite different than the Rayleigh PDF of the envelope, even for gate lengths smaller than one transmission pulse length. We have employed measured PDFs by (1) estimating the abundance of occasional large scatterers that are within the clouds (for example large fish feeding on plankton) since their occurrence is differentiable from the rest of the cloud in the PDF, and (2) clearly differentiating between conditions where the echoes overlap and do not overlap. Once it is determined whether or not they overlap, lower or upper bounds in scatterer density (number per unit volume) may be calculated. We have utilized both of these techniques in situ at the Gulf Stream Boundary near Cape Hatteras, NC where we observed continuous distributions of plankton and nekton. [Work supported by the ONR.]

Life Expectancy of Highway Bridges to Vehicle Loads

Life expectancy of highway bridges to vehicle loads is studied. Vehicular traffic is represented by the Poisson process and response of bridges is considered as a filtered Poisson process. A method is developed to obtain, numerically, peak probability density function and expected total number of peaks per unit time of stress response of bridges. These quantities are used in conjunction with Palmgren-Miner's theory of cumulative damage to predict the fatigue life of a particular bridge.