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Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010


QUANTIFICATION OF UNCERTAINTY IN MANOEUVRING CHARACTERISTICS FOR DESIGN OF UNDERWATER VEHICLES


Amit Ray, Indian Institute of Technology Delhi, India Debabrata Sen, Indian Institute of Technology Kharagpur, India SN Singh and V Seshadri, Indian Institute of Technology Delhi, India (DOI No: 10.3940/rina.ijme.2010.a2.174)


SUMMARY


The prediction of manoeuvring characteristics of underwater vehicles during design involves approximations at various stages. This paper attempts to quantify some of the uncertainties involved in the manoeuvring characteristics of underwater vehicles. The first source of uncertainty is in idealization of mathematical model selected for trajectory simulation. This is illustrated for alternative mathematical models in trajectory simulation programs. Next, the values of the hydrodynamic coefficients (HDCs) in the equations of motion have their own levels of uncertainty, depending upon the methods used to determine them. The sensitivity of trajectory simulation results to uncertainty levels in various HDCs is examined. Finally, the level of uncertainty in full-scale measurements of manoeuvres of underwater vehicles is discussed and estimated. It emerges that the cumulative errors in the prediction process during design need to be reduced further, in order to maintain their levels of uncertainty below those of the validation process.


NOMENCLATURE F ={X,Y,Z}





M = {K,M,N} 


Vehicles (AUVs) used for many commercial and scientific applications [7, 8].


External force on the body and its components along x, y and z directions


Moment of the external force and its components along x, y and z directions


{xG, yG, zG} Coordinates of the body’s center of gravity (CG) with respect to the body- fixed system oxyz Mass of the vehicle


m Iij


u, v, w p, q, r g 1. Moments of inertia about the body-


fixed system oxyz, where the indices i,j correspond to x,y,z coordinates.


Straight-line velocities of the body along x, y and z directions in the body- fixed frame of reference


Angular velocities of the body about x, y and z directions in the body-fixed frame of reference


Acceleration due to gravity INTRODUCTION


The study of manoeuvring characteristics of underwater vehicles includes assessment of motion stability, controllability and trajectory simulation in six degrees of freedom. These have important operational implications for all types of underwater vehicles. There are a variety of approaches (empirical/analytical, experimental and numerical/computational techniques) for manoeuvring studies of underwater vehicles [1]. The problem of mathematical modelling of the motion of marine vehicles for trajectory simulation has been studied extensively over many decades [2-6]. The subject has gained renewed interest after the proliferation of Unmanned Underwater Vehicles (UUVs), which include Remotely Operated Vehicles (ROVs) and Autonomous Underwater


Manoeuvring characteristics of underwater vehicles are difficult to predict accurately during initial stages of design. Frequently, recourse is made to empirical or semi-empirical methods for the purpose. Even after more detailed information is available from time-taking studies using tools like Computational Fluid Dynamics (CFD), or from expensive model


tests, there are inherent


uncertainties in the prediction process for manoeuvring qualities. All too often, attention is concentrated on particular aspects of the problem, such as model testing, CFD, control system design, system identification, or trajectory simulation. It is necessary to estimate the magnitude of uncertainty for the overall process of prediction of manoeuvring characteristics.


In order to quantify these uncertainties, it is necessary to understand the choices being made at each stage of the prediction process and their implications on the ultimate result. These


aspects or stages for manoeuvring


prediction / evaluation may be outlined as follows. • • •





Formulation of mathematical model for trajectory simulation


Estimation of values of Hydrodynamic Coefficients (HDCs) for the body


Simulation of trajectories for various manoeuvres


Full-scale trials for standard manoeuvres and comparison with predictions


Each of these aspects has inherent uncertainties. The ultimate benchmark for evaluating any set of predictions should be comparing them with full-scale trial results for a set of standard manoeuvres. These are the only ‘true’ values


against which the ‘errors’ in each stage of


manoeuvrability prediction must be judged. However, not


only are the full-scale measurements rarely ©2010: The Royal Institution of Naval Architects A - 71


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