FIRST PASSAGE APPROXIMATION FOR NORMAL STATIONARY RANDOM PROCESSES.

A new approximate solution for the first passage probability of a stationary Gaussian random process is presented which is based on the estimation of the mean clump size. A simple expression for the mean clump size is derived in terms of the cumulative normal distribution function, which avoids the lengthy numerical integrations which are required by similar existing techniques. The method is applied to a linear oscillator and an ideal bandpass process and good agreement with published results is obtained. By making a slight modification to an existing analysis it is shown that a widely used empirical result for the asymptotic form of the first passage probability can be deduced theoretically.

Normal shock boundary layer control with various vortex generator geometries

Various vortex generators which include ramp, split-ramp and a new hybrid concept "ramped-vane" are investigated under normal shock conditions with a diffuser at Mach number of 1.3. The dimensions of the computational domain were designed using Reynolds Average Navier-Stokes studies to be representative of the flow in an external-compression supersonic inlet. Using this flow geometry, various vortex generator concepts were studied with Implicit Large Eddy Simulation. In general, the ramped-vane provided increased vorticity compared to the other devices and reduced the separation length downstream of the device centerline. In addition, the size, edge gap and streamwise position respect to the shock were studied for the ramped-vane and it was found that a height of about half the boundary thickness and a large trailing edge gap yielded a fully attached flow downstream of the device. This ramped-vane also provided the largest reduction in the turbulent kinetic energy and pressure fluctuations. Additional benefits include negligible drag while the reductions in boundary layer displacement thickness and shape factor were seen compared to other devices. © 2010 by Sang Lee.

Normal shock boundary layer control with various vortex generator geometries

Various vortex generators which include ramp, split-ramp and a new hybrid concept "ramped-vane" are investigated under normal shock conditions with a diffuser at Mach number of 1.3. The dimensions of the computational domain were designed using Reynolds Average Navier-Stokes studies to be representative of the flow in an external-compression supersonic inlet. Using this flow geometry, various vortex generator concepts were studied with Implicit Large Eddy Simulation. In general, the ramped-vane provided increased vorticity compared to the other devices and reduced the separation length downstream of the device centerline. In addition, the size, edge gap and streamwise position respect to the shock were studied for the ramped-vane and it was found that a height of about half the boundary thickness and a large trailing edge gap yielded a fully attached flow downstream of the device. This ramped-vane also provided the largest reduction in the turbulent kinetic energy and pressure fluctuations. Additional benefits include negligible drag while the reductions in boundary layer displacement thickness and shape factor were seen compared to other devices. © 2011 Elsevier Ltd.

Auxiliary particle implementation of the probability hypothesis density filter

Optimal Bayesian multi-target filtering is, in general, computationally impractical owing to the high dimensionality of the multi-target state. The Probability Hypothesis Density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed Sequential Monte Carlo (SMC) implementations of the PHD filter. However, these implementations are the equivalent of the Bootstrap Particle Filter, and the latter is well known to be inefficient. Drawing on ideas from the Auxiliary Particle Filter (APF), we present a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency. Numerical examples are presented for two scenarios, including a challenging nonlinear observation model.