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.

Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics

Simulation of materials at the atomistic level is an important tool in studying microscopic structure and processes. The atomic interactions necessary for the simulation are correctly described by Quantum Mechanics. However, the computational resources required to solve the quantum mechanical equations limits the use of Quantum Mechanics at most to a few hundreds of atoms and only to a small fraction of the available configurational space. This thesis presents the results of my research on the development of a new interatomic potential generation scheme, which we refer to as Gaussian Approximation Potentials. In our framework, the quantum mechanical potential energy surface is interpolated between a set of predetermined values at different points in atomic configurational space by a non-linear, non-parametric regression method, the Gaussian Process. To perform the fitting, we represent the atomic environments by the bispectrum, which is invariant to permutations of the atoms in the neighbourhood and to global rotations. The result is a general scheme, that allows one to generate interatomic potentials based on arbitrary quantum mechanical data. We built a series of Gaussian Approximation Potentials using data obtained from Density Functional Theory and tested the capabilities of the method. We showed that our models reproduce the quantum mechanical potential energy surface remarkably well for the group IV semiconductors, iron and gallium nitride. Our potentials, while maintaining quantum mechanical accuracy, are several orders of magnitude faster than Quantum Mechanical methods.

Balanced realisations of all-pass systems using exact arithmetic with application to the approximation of delay systems

Numerically well-conditioned state-space realisations for all-pass systems, such as Padé approximations to exp(-s), are derived that can be computed using exact integer arithmetic. This is then applied to the a series of functions of exp(-s). It is also shown that the H-infinity norm of the transfer function from the input to the state of a balanced realisation of the Padé approximation of exp(-s) is unity. © 2012 IEEE.

IGBT converters conducted EMI analysis by controlled multiple-slope switching waveform approximation

IGBTs realise high-performance power converters. Unfortunately, with fast switching of the IGBT-free wheel diode chopper cell, such circuits are intrinsic sources of high-level EMI. Therefore, costly EMI filters or shielding are normally needed on the load and supply side. In order to design these EMI suppression components, designers need to predict the EMI level with reasonable accuracy for a given structure and operating mode. Simplifying the transient IGBT switching current and voltage into a multiple slope switching waveform approximation offers a feasible way to estimate conducted EMI with some accuracy. This method is dependent on the availability of high-fidelity measurements. Also, that multiple slope approximation needs careful and time-costly IGBT parameters optimisation process to approach the real switching waveform. In this paper, Active Voltage Control Gate Drive(AVC GD) is employed to shape IGBT switching into several defined slopes. As a result, Conducted EMI prediction by multiple slope switching approximation could be more accurate, less costly but more friendly for implementation. © 2013 IEEE.