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


• Changes in temperature of water with depth (affecting density and viscosity)


• Ocean currents at different depths


Sources of precision errors may be listed as follows: • Errors in recording and processing data, depending on frequency of measurements


• Unknown and random sea water disturbances • Errors due to variation in time for applying control forces


7.2 UNCERTAINTY ESTIMATES


Most of the above errors are impossible to quantify exactly, but the expected variations can be estimated, albeit somewhat crudely.


7.2(a) Instrumentation Bias


During full-scale sea trials on manned underwater vehicles reported in [19], the instrument resolution (least count)


for on-board instrumentation of parameters was as follows.


• Depth: 1 metre • Pitch angle: 1 degree • Time: 0.5 seconds • Plane angle: 1 degree • Speed: 0.5 knots


Based on the above values, the uncertainty in each of the parameters of interest in the zigzag manoeuvre may be quantified for typical assumed values, as shown in Table 10. The values used are those for the axisymmetric body parameters (Table 1) for the 15/5 zigzag.


Parameter Typical Value


Overshoot (θO)


pitch angle


Overshoot change depth (zO)


Time to reach execute (te)


2 degrees


of 3 metres 6 seconds


Time to check pitch (tc) 9 seconds Time to check depth (td) 19 seconds Table 10 Typical


Instrument Uncertainty 0.500


0.333 0.083 0.111


0.026 bias error estimated based on measuring instrument resolution (least count)


For UUVs, the values would change according to the resolution of


the instruments installed,


estimated using the same approach. 7.2(b) Sea Water Density Variation


The variation in density of sea water of tropical waters may be from 1.015 to 1.030 tons/m3. Change of vehicle depth in a region with sharp temperature gradient may cause imbalance between weight and buoyancy, which


but may be various


may be as much as 0.25% of the vehicle displacement. The effect of this magnitude of change during the course of a typical zigzag manoeuvre was found to be marginal. The uncertainty due to this source of error may be roughly estimated (on the higher side) as 0.003 for θO and 0.005 for zO.


7.2(c) Errors in Data Recording


The value of precision error due to recording and processing data may be estimated in model testing by repeating a particular observation at different points of time. However, for sea trials, it is near-impossible to repeat the experiment in exactly the same fashion with the same environmental conditions to gauge the errors in the instrumentation or recording process. However, the values of error in data recording may be estimated to be of the order of the least count of the instruments for depth,


pitch angle, time and speed. This suggests


additional uncertainty values similar to those listed in Table 10.


Currents have not been mentioned explicitly, but their effects may be included in the uncertainties affecting the data


recording


environmental process.


Currents may not affect the recorded motion parameters if the UUV measures speed through water, but could significantly bias the results if instead, its speed over the ground is measured using a Doppler velocity log.


7.2(d) Error in Control Force Application


Precision errors due to control force application result from inexact or asynchronous application of plane angles. Particularly in case of manned submarines, the time required to apply plane angle when ordered may vary from operator to operator and may not exactly coincide with the moment the execute pitch angle is reached. Typical variations are of the order of 2 seconds, leading to uncertainties in all time parameters of the zigzag manoeuvre by the same amount, and a variation in the overshoot angle by as much as 1-2 degrees, and variation in overshoot change of depth by 2-5 metres. These values are typical for low speeds (3 to 5 knots) and may be somewhat higher for


consequent uncertainties in the parameters of interest, for sample values listed in Table 10, may be (lower values): 0.50 for θO , 0.67 for zO, 0.33 for te, 0.22 for tc, and 0.11 for td.


In case of UUVs, this error due to human action would not be present. However, the uncertainty in time lag for actuation of control surfaces based on a logical input may need to be estimated for unmanned vehicles.


7.3 CUMULATIVE UNCERTAINTY IN FULL- SCALE MEASUREMENTS


In the worst case scenario, all the errors quantified above can occur simultaneously and hence the uncertainties


greater speeds. The


©2010: The Royal Institution of Naval Architects


A - 81


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