Developments in functional analysis of ship dynamics

Wright, Jeremy Huntley Greet (1976) Developments in functional analysis of ship dynamics. University of Southampton, Doctoral Thesis.

Abstract

Mathematical .models of the motions of shins in yaw and sway are taken; and unified. The general model is multi-i_i_inite-dimensional: and nonlinear but it yields to stability analysis by methods which closely resemble those applied to finite-dimensional systems. A reduced version having the form,-r,.' a Ham;aerctcin operator' is proposed based on the assumption that' the nonlinear and linear behaviour may be observed separately and are respectively associated with the quasi-static and historical':asaects of the motion. Paramoterisations are avoided because little i~•.known about the fine structure of the system, so the suggested method of identification of the reduced model has two functional stages.A If the steady-state response function is' obtained by a conventional experiment, the linear ized operator may be identified after routine, tram formations. This procedure is appropriate for both stable and unstable ships. Extensive attention is devoted to the identification of the impulse response of the linear component. First it is desirable to optimize the identification by choice of an efficient t6st signal, and suitable criteria are deduced from the _tifi _ concept of information. Working first in a discrete environment it is shown that maximizing the mutual information between the impulse response and the observations' effectively optimizes the least-squares identification procedure. Extension to continuous signals enables the optimization criteria to be established.Input signals based on pseudo-random binary sequences are discussed tand their potential for near-optimal identification is emphasized. i Their, use may also enable contaminating signals to be removed before the solution for the impulse response is obtained. 'r. Algorithms for obtaining this solution from the Wiener-Hopf equation are considered and the classical 7eumann series is transformed into a preferred algorithm. This technique is iterative, convergence is strong and may be accelerated.Some experiments are described in which a pseudo-random binary sequence ::*as used to drive the rudder of a free-running ship model. The yaw rate impulse response function is computed and some simulations performed.

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