System simulation using digital stochastic computing structures.

McLean, Hector R.

Abstract

This thesis is a detailed study of the potential applications of digital stochastic computers. In particular, this work has considered the simulation of stochastic networks using digital computer software written in FORTRAN. The study of these networks was aided by hybrid computer simulations which were used to check on the stability of stochastic networks. The introduction to the thesis compares and contrasts analogue, digital, hybrid and stochastic computers. A close comparison is made between digital stochastic computers and other forms of parallel digital computers such as the Digital Differential Analyser and the phase computer. In chapter 1 the single line, symmetric, bipolar representation was chosen as the most economical method of representing problem variables in terms of hardware. Thus, the stochastic operators presented in this chapter are based on the bipolar mapping. The mathematics used is uncomplicated and the behaviour of digital circuits containing counters has been approximated by linear and non-linear differential equations in the main text. More precise analyses of digital circuits are to be found in the appendices but it was found that these studies yielded no more information than the approximate methods and were much more awkward to manipulate. Chapter 2 is concerned with developing software written in FORTRAN to simulate the operation of the basic stochastic operators. The random number generator used in these simulations is based on the Lehmer Congruence method and a detailed account of its properties is given with particular reference to the ELLIOT 4120 digital computer for which the software was written. The stochastic operators simulated include the negator, summer, multiplier, squarer, integrator and output interface. Some simple circuits involving the basic operators were investigated in chapter 3. These circuits included networks for square-root extraction, the solution of a linear equation, examining the transient behaviour of a second order stochastic system and sine/cosine generation. The second order system highlighted a problem which was not taken into account in the original definition of stochastic computation. Simple mathematical models are used to explain the transient behaviour of each circuit simulated. In chapter 4 two simple circuits for solving sets of linear equations were investigated. The first is based on an error criterion and the second circuit uses the method of steepest descent. Each circuit is analysed as a continuous system in the main text, but a discrete time analysis of each network is given in the appendices. Close attention is paid to the stability and convergence of each method. A well known linear programming algorith is adapted for use on a stochastic computer in chapter 5. This study also demonstrates the way in which threshold switching is obtained in the stochastic computer. The problem examined in this chapter is a maximisation problem but the mathematics can be easily altered to cope with a minimisation problem. Circuits for determining the parameters of first and second order systems were investigated in chapter 6. The circuit for identifying the parameters of a first order system revealed a difficulty in scaling when the method of steepest descent is used to identify system parameters but a procedure is adopted which overcomes this problem. An alternative algorithm for identifying a first order system was successfully demonstrated. The second order system was used to demonstrate the kind of difficulty which might be encountered when using a stochastic computer for parameter identification, namely induced oscillation arising from the random variance inherent in the stochastic computation method. These studies were extensively aided by hybrid computer simulations of the steepest descent algorithm. As a result of the simulation work carried out on the first order system identification a new output interface, the non-linear adaptive digital element, is proposed and this circuit is analysed in detailed in appendix 6.C. Chapter 7 is a review of the work discussed in the previous chapters and presents suggestions for further work with particular reference to Markov chains and systems which are inherently stochastic.

Citation

MCLEAN, H.R. 1975. System simulation using digital stochastic computing structures. Robert Gordon's Institute of Technology, MPhil thesis. Hosted on OpenAIR [online]. Available from: https://doi.org/10.48526/rgu-wt-1993272

• Thesis Type: Thesis
• Deposit Date: Oct 23, 2024
• Publicly Available Date: Oct 23, 2024
• DOI: https://doi.org/10.48526/rgu-wt-1993272
• Public URL: https://rgu-repository.worktribe.com/output/1993272
• Award Date: Aug 31, 1975