Rao-Blackwellized particle smoothers for mixed linear/nonlinear state-space models

We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction. © 2013 IEEE.

Bayesian inference and learning in Gaussian process state-space models with Particle MCMC

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and, instead, infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

The role of the catalytic particle in the growth of carbon nanotubes by plasma enhanced chemical vapor deposition

Vertically aligned carbon nanotubes were synthesized by plasma enhanced chemical vapor deposition using nickel as a metal catalyst. High resolution transmission electron microscopy analysis of the particle found at the tip of the tubes reveals the presence of a metastable carbide Ni3C. Since the carbide is found to decompose upon annealing at 600 degreesC, we suggest that Ni3C is formed after the growth is stopped due to the rapid cooling of the Ni-C interstitial solid solution. A detailed description of the tip growth mechanism is given, that accounts for the composite structure of the tube walls. The shape and size of the catalytic particle determine the concentration gradient that drives the diffusion of C atoms across and though the metal. (C) 2004 American Institute of Physics.

Comparative study of the slurry erosion and free-fall particle erosion of aluminum

A study has been performed of the erosion of aluminium by silica sand particles at a velocity of 4.5 m s-1, both air-borne and in the form of a water-borne slurry. Measurements made under similar experimental conditions show that slurry erosion proceeds at a rate several times that of air-borne erosion, the ratio of the two rates depending strongly on the angle of impact. Sand particles become embedded into the metal surface during air-borne particle erosion, forming a composite layer of metal and silica, and provide the major cause of the difference in wear rate. The embedded particles giving rise to surface hardening and a significant reduction in the erosion rate. Embedment of erodent particles was not observed during slurry erosion. Lubrication of the impacting interfaces by water appears to have minimal effect on the wear of aluminium by slurry erosion.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

A backward particle interpretation of Feynman-Kac formulae

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results with respect to the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. Our results have important consequences for online parameter estimation for non-linear non-Gaussian state-space models. We show how the forward filtering backward smoothing estimates of additive functionals can be computed using a forward only recursion.

An overview of sequential Monte Carlo methods for parameter estimation in general state-space models

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, are numerical techniques based on Importance Sampling for solving the optimal state estimation problem. The task of calibrating the state-space model is an important problem frequently faced by practitioners and the observed data may be used to estimate the parameters of the model. The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed for this task accompanied with a discussion of their advantages and limitations.

Poroviscoelastic characterization of particle-reinforced gelatin gels using indentation and homogenization.

Hydrogels are promising materials for bioengineering applications, and are good model materials for the study of hydrated biological tissues. As these materials often have a structural function, the measurement of their mechanical properties is of fundamental importance. In the present study gelatin gels reinforced with ceramic microspheres are produced and their poroviscoelastic response in spherical indentation is studied. The constitutive responses of unreinforced gels are determined using inverse finite element modeling in combination with analytical estimates of material parameters. The behavior of composite gels is assessed by both analytical and numerical homogenization. The results of the identification of the constitutive parameters of unreinforced gels show that it is possible to obtain representative poroviscoelastic parameters by spherical indentation without the need for additional mechanical tests. The agreement between experimental results on composite gelatin and the predictions from homogenization modeling show that the adopted modeling tools are capable of providing estimates of the poroviscoelastic response of particle-reinforced hydrogels.

Failure mechanisms and toughness of Al2O3 ductile-particle toughened ceramics and SiC fibre-ceramic composites

The development of high performance ceramics and ceramic composites often relies on assumptions about their behaviour during loading and at failure. A crucial influence on the mechanical properties of these materials is the degree of sub-critical cracking, which post mortem investigations cannot adequately reveal. Hence a clear picture of the dynamic micromechanisms of cracking is required if applications of fracture and damage mechanics to theoretical models is to be meaningful.

Video tracking using dual-treewavelet polar matching and particle filtering

In this paper, we describe a video tracking application using the dual-tree polar matching algorithm. The models are specified in a probabilistic setting, and a particle ilter is used to perform the sequential inference. Computer simulations demonstrate the ability of the algorithm to track a simulated video moving target in an urban environment with complete and partial occlusions. © The Institution of Engineering and Technology.