Parallel Type-2 Fuzzy Logic Co-Processors for Engine Management

Marine diesel engines operate in highly dynamic and uncertain environments, hence they require robust and accurate speed controllers that can handle the encountered uncertainties. Type-2 Fuzzy Logic Controllers (FLCs) have shown that they can handle such uncertainties and give a superior performance to the existing commercial controllers. However, there are a number of computational bottlenecks that pose as significant barriers to the widespread deployment of type-2 FLCs in commercial embedded control systems. This paper explores the use of parallel hardware implementations of interval type-2 FLC as a means to eradicate these barriers thus producing bespoke co-processors for a soft core implementation of a FPGA based 32 bit RISC micro-processor. These co-processors will perform functions such as fuzzification and type reduction and are currently utilised as part of a larger embedded interval Type-2 Fuzzy Engine Management System (T2FEMS). Numerous timing comparisons were undertaken between the co-processors and their sequential counterparts where the type-2 co-processors reduced significantly the computational cycles required by the type-2 FLC. This reduction in computational cycles allowed the T2FEMS to produce faster control responses whilst offering a superior control performance to the commercial engine management systems. Thus the proposed co-processors enable us to fully explore the potential of interval and possibly general type-2 FLCs in commercial embedded applications. © 2007 IEEE

Fractional Stochastic Dynamics in Structural Stability Analysis

The objective of this thesis is to develop a novel methodology of fractional stochastic dynamics to study stochastic stability of viscoelastic systems under stochastic loadings. Numerous structures in civil engineering are driven by dynamic forces, such as seismic and wind loads, which can be described satisfactorily only by using probabilistic models, such as white noise processes, real noise processes, or bounded noise processes. Viscoelastic materials exhibit time-dependent stress relaxation and creep; it has been shown that fractional calculus provide a unique and powerful mathematical tool to model such a hereditary property. Investigation of stochastic stability of viscoelastic systems with fractional calculus frequently leads to a parametrized family of fractional stochastic differential equations of motion. Parametric excitation may cause parametric resonance or instability, which is more dangerous than ordinary resonance as it is characterized by exponential growth of the response amplitudes even in the presence of damping. The Lyapunov exponents and moment Lyapunov exponents provide not only the information about stability or instability of stochastic systems, but also how rapidly the response grows or diminishes with time. Lyapunov exponents characterizes sample stability or instability. However, this sample stability cannot assure the moment stability. Hence, to obtain a complete picture of the dynamic stability, it is important to study both the top Lyapunov exponent and the moment Lyapunov exponent. Unfortunately, it is very difficult to obtain the accurate values of theses two exponents. One has to resort to numerical and approximate approaches. The main contributions of this thesis are: (1) A new numerical simulation method is proposed to determine moment Lyapunov exponents of fractional stochastic systems, in which three steps are involved: discretization of fractional derivatives, numerical solution of the fractional equation, and an algorithm for calculating Lyapunov exponents from small data sets. (2) Higher-order stochastic averaging method is developed and applied to investigate stochastic stability of fractional viscoelastic single-degree-of-freedom structures under white noise, real noise, or bounded noise excitation. (3) For two-degree-of-freedom coupled non-gyroscopic and gyroscopic viscoelastic systems under random excitation, the Stratonovich equations of motion are set up, and then decoupled into four-dimensional Ito stochastic differential equations, by making use of the method of stochastic averaging for the non-viscoelastic terms and the method of Larionov for viscoelastic terms. An elegant scheme for formulating the eigenvalue problems is presented by using Khasminskii and Wedig’s mathematical transformations from the decoupled Ito equations. Moment Lyapunov exponents are approximately determined by solving the eigenvalue problems through Fourier series expansion. Stability boundaries, critical excitations, and stability index are obtained. The effects of various parameters on the stochastic stability of the system are discussed. Parametric resonances are studied in detail. Approximate analytical results are confirmed by numerical simulations.1 yea