The inverse problem in magnetic force microscopy--inferring sample magnetization from MFM images.

Nanomagnetic structures have the potential to surpass silicon's scaling limitations both as elements in hybrid CMOS logic and as novel computational elements. Magnetic force microscopy (MFM) offers a convenient characterization technique for use in the design of such nanomagnetic structures. MFM measures the magnetic field and not the sample's magnetization. As such the question of the uniqueness of the relationship between an external magnetic field and a magnetization distribution is a relevant one. To study this problem we present a simple algorithm which searches for magnetization distributions consistent with an external magnetic field and solutions to the micromagnetic equations' qualitative features. The algorithm is not computationally intensive and is found to be effective for our test cases. On the basis of our results we propose a systematic approach for interpreting MFM measurements.

Erosion-corrosion of mild steel in a temperature gradient

Thinning of heat-exchanger tubes by erosion-corrosion has been a problem in fluidized bed combustors (FBCs), particularly at lower metal temperatures where thicker, mechanically protective oxide scales are unable to form. Many laboratory-scale tests have shown a decrease in material loss at higher temperatures, in a similar manner to FBC boilers, but also show a decrease in wastage at low temperatures (e.g. 200°C) which has not been detected in boilers. It has been suggested that this difference is due to laboratory tests being carried out isothermally whereas in a FBC boiler the fluidized bed is considerably hotter than the metal heat exchanger tubing. In this laboratory study the simulation was therefore improved by internally cooling one of the two low carbon steel specimens. These were rotated in a horizontal plane within a lightly fluidized bed with relative particle velocities of 1.3-2.5 m s-1. Tests were carried out over a range of bed temperatures (200-500°C) and cooled specimen surface temperatures (115-500°C), with a maximum temperature difference between the two of 320°C. Although specimens exposed isothermally still showed maximum wastage at intermediate temperatures (about 350°C), those which were cooled showed high levels of wastage at temperatures as low as 200°C in a similar manner to FBC boilers. Cooling may modify the isothermal erosion-corrosion curve, causing it to broaden and the maximum wastage rate to shift to lower temperatures. © 1995.

Sequential decision making in general state space models

Many problems in control and signal processing can be formulated as sequential decision problems for general state space models. However, except for some simple models one cannot obtain analytical solutions and has to resort to approximation. In this thesis, we have investigated problems where Sequential Monte Carlo (SMC) methods can be combined with a gradient based search to provide solutions to online optimisation problems. We summarise the main contributions of the thesis as follows. Chapter 4 focuses on solving the sensor scheduling problem when cast as a controlled Hidden Markov Model. We consider the case in which the state, observation and action spaces are continuous. This general case is important as it is the natural framework for many applications. In sensor scheduling, our aim is to minimise the variance of the estimation error of the hidden state with respect to the action sequence. We present a novel SMC method that uses a stochastic gradient algorithm to find optimal actions. This is in contrast to existing works in the literature that only solve approximations to the original problem. In Chapter 5 we presented how an SMC can be used to solve a risk sensitive control problem. We adopt the use of the Feynman-Kac representation of a controlled Markov chain flow and exploit the properties of the logarithmic Lyapunov exponent, which lead to a policy gradient solution for the parameterised problem. The resulting SMC algorithm follows a similar structure with the Recursive Maximum Likelihood(RML) algorithm for online parameter estimation. In Chapters 6, 7 and 8, dynamic Graphical models were combined with with state space models for the purpose of online decentralised inference. We have concentrated more on the distributed parameter estimation problem using two Maximum Likelihood techniques, namely Recursive Maximum Likelihood (RML) and Expectation Maximization (EM). The resulting algorithms can be interpreted as an extension of the Belief Propagation (BP) algorithm to compute likelihood gradients. In order to design an SMC algorithm, in Chapter 8 uses a nonparametric approximations for Belief Propagation. The algorithms were successfully applied to solve the sensor localisation problem for sensor networks of small and medium size.

Probabilistic inference for fast learning in control

A novel framework is provided for very fast model-based reinforcement learning in continuous state and action spaces. It requires probabilistic models that explicitly characterize their levels of condence. Within the framework, exible, non-parametric models are used to describe the world based on previously collected experience. It demonstrates learning on the cart-pole problem in a setting where very limited prior knowledge about the task has been provided. Learning progressed rapidly, and a good policy found after only a small number of iterations.