Optimal control with stochastic PDE constraints and uncertain controls

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with the control function possibly decomposed into an unknown deterministic component and a known zero-mean stochastic component. The extra freedom provided by the stochastic dimension in defining cost functionals is explored, demonstrating the scope for controlling statistical aspects of the system response. One-shot stochastic finite element methods are used to find approximate solutions to control problems. It is shown that applying the stochastic collocation finite element method to the formulated problem leads to a coupling between stochastic collocation points when a deterministic optimal control is considered or when moments are included in the cost functional, thereby forgoing the primary advantage of the collocation method over the stochastic Galerkin method for the considered problem. The application of the presented methods is demonstrated through a number of numerical examples. The presented framework is sufficiently general to also consider a class of inverse problems, and numerical examples of this type are also presented. © 2011 Elsevier B.V.

Modelling the vibration of tyre sidewalls

The dynamical behaviour of the sidewall has an important influence on tyre vibration characteristics. Nonetheless, it remains crudely represented in many existing models. The current work considers a geometrically accurate, two-dimensional, sidewall description, with a view to identifying potential shortcomings in the approximate formulations and identifying the physical characteristics that must be accounted for. First, the mean stress state under pressurisation and centrifugal loading is investigated. Finite-Element calculations show that, while the loaded sidewall shape remains close to a toroid, its in-plane tensions differ appreciably from the associated analytical solution. This is largely due to the inability of the anisotropic sidewall material to sustain significant azimuthal stress. An approximate analysis, based on the meridional tension alone, is therefore developed, and shown to yield accurate predictions. In conjunction with a set of formulae for the 'engineering constants' of the sidewall material, the approximate solutions provide a straightforward and efficient means of determining the base state for the vibration analysis. The latter is implemented via a 'waveguide' discretisation of a variational formulation. Its results show that, while the full geometrical description is necessary for a complete and reliable characterisation of the sidewall's vibrational properties, a one-dimensional approximation will often be satisfactory in practice. Meridional thickness variations only become important at higher frequencies (above 500 Hz for the example considered here), and rotational inertia effects appear to be minor at practical vehicle speeds. © 2013 Elsevier Ltd. All rights reserved.

Fertile-free fuels in pressurized water reactors: Design challenges and solutions

This paper investigates the basic feasibility of using reactor-grade Pu in fertile-free fuel (FFF) matrix in pressurized water reactors (PWRs). Several important issues were investigated in this work: the Pu loading required to achieve a specific interrefueling interval, the impact of inert matrix composition on reactivity constrained length of cycle, and the potential of utilizing burnable poisons (BPs) to alleviate degradation of the reactivity control mechanism and temperature coefficients. Although the subject was addressed in the past, no systematic approach for assessment of BP utilization in FFF cores was published. In this work, we examine all commercially available BP materials in all geometrical arrangements currently used by the nuclear industry with regards to their potential to alleviate the problems associated with the use of FFF in PWRs. The recently proposed MgO-ZrO2 solid-state solution fuel matrix, which appears to be very promising in terms of thermal properties and radiation damage resistance, was used as a reference matrix material in this work. The neutronic impact of the relative amounts of MgO and ZrO2 in the matrix were also studied. The analysis was performed with a neutron transport and fuel assembly burnup code BOXER. A modified linear reactivity model was applied to the two-dimensional single fuel assembly results to approximate the full core characteristics. Based on the results of the performed analyses, the Pu-loaded FFF core demonstrated potential feasibility to be used in existing PWRs. Major FFF core design problems may be significantly mitigated through the correct choice of BP design. It was found that a combination of BP materials and geometries may be required to meet all FFF design goals. The use of enriched (in most effective isotope) BPs, such as 167Er and 157Gd, may further improve the BP effectiveness and reduce the fuel cycle length penalty associated with their use.

Image deconvolution using a Gaussian scale mixtures model to approximate the wavelet sparseness constraint

This paper proposes to use an extended Gaussian Scale Mixtures (GSM) model instead of the conventional ℓ1 norm to approximate the sparseness constraint in the wavelet domain. We combine this new constraint with subband-dependent minimization to formulate an iterative algorithm on two shift-invariant wavelet transforms, the Shannon wavelet transform and dual-tree complex wavelet transform (DTCWT). This extented GSM model introduces spatially varying information into the deconvolution process and thus enables the algorithm to achieve better results with fewer iterations in our experiments. ©2009 IEEE.

Asymptotic behaviour of approximate Bayesian estimators

Although approximate Bayesian computation (ABC) has become a popular technique for performing parameter estimation when the likelihood functions are analytically intractable there has not as yet been a complete investigation of the theoretical properties of the resulting estimators. In this paper we give a theoretical analysis of the asymptotic properties of ABC based parameter estimators for hidden Markov models and show that ABC based estimators satisfy asymptotically biased versions of the standard results in the statistical literature.

Filtering via approximate Bayesian computation

Approximate Bayesian computation (ABC) has become a popular technique to facilitate Bayesian inference from complex models. In this article we present an ABC approximation designed to perform biased filtering for a Hidden Markov Model when the likelihood function is intractable. We use a sequential Monte Carlo (SMC) algorithm to both fit and sample from our ABC approximation of the target probability density. This approach is shown to, empirically, be more accurate w.r.t.~the original filter than competing methods. The theoretical bias of our method is investigated; it is shown that the bias goes to zero at the expense of increased computational effort. Our approach is illustrated on a constrained sequential lasso for portfolio allocation to 15 constituents of the FTSE 100 share index.