Analysis of asymmetrical cold rolling with varying coefficients of friction

In this research, asymmetrical cold rolling was produced by the difference in the coefficient of friction between rolls and sheets rather than the difference of roll radius or rotation speeds. The influence of friction coefficient ratio on the cross shear deformation, rolling pressure and torque was investigated using slab analysis. The results showed that the shear deformation zone length increased with the increase of the friction coefficient ratio. The rolling force decreased only under the condition that the friction coefficient ratio increased while the sum of the friction coefficients was held constant. As the reduction per pass was increased, the shear deformation zone length increased and the rolling force also increased. An increase of the front tension resulted in a decrease of the shear deformation zone length. An increase of back tension, however, led to an increase of the shear deformation zone length. The reduction of rolling torque for the work roll with higher surface roughness was greater than that for the work roll with lower surface roughness. (C) 2002 Elsevier Science B.V. All rights reserved.

Convergence of the auxiliary particle implementation of the PHD 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), a SMC implementation of the PHD filter which employs auxiliary variables to enhance its efficiency was proposed by Whiteley et. al. Numerical examples were presented for two scenarios, including a challenging nonlinear observation model, to support the claim. This paper studies the theoretical properties of this auxiliary particle implementation. $\mathbb{L}_p$ error bounds are established from which almost sure convergence follows.

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.