Trans RINA, Vol 152, Part A2, Intl J Maritime Eng, Apr-Jun 2010
6. CUMULATIVE UNCERTAINTY IN MANOEUVRABILITY PREDICTION
The likely ranges of uncertainty due to choice of type of mathematical model (Section 4), and values of HDCs (Section 5) have been examined for two bodies. The effect of these variations on the parameters of the vertical plane zigzag manoeuvre has been explored by trajectory simulation. For the cases considered, we now attempt to assess the cumulative uncertainty in the parameters of the definitive manoeuvres due to the stages manoeuvring prediction process.
of the
We consider the maximum variation in zigzag parameters due to choice of mathematical model
(in
trajectory simulation program) for the axisymmetric body, as listed in Table 2 as one source of uncertainty. The other source of uncertainty is due to variation in HDC values by ±10%, typical of model test values, as listed in Table 6 for axisymmetric body (Listed as case (a) in Table 8, with values taken from Table 6). Effect of variation of HDCs by ±50% is also listed (as case (b), with values taken from Table 4).
Summing these, we obtain the cumulative uncertainty in prediction for the axisymmetric body in Table 8 and for the SUBOFF body in Table 9. The range of total uncertainty may thus be estimated as 11% to 55% for ±10% variation of HDCs of axisymmetric body, for the manoeuvre considered. These values would be up to 45% for the SUBOFF body (using earlier results of Table 7). In case of ±50% variation of HDCs, the total uncertainty values would increase to up to 231% for axisymmetric body (and roughly up to 92% for SUBOFF body).
Parameters of Zigzag → Source of Uncertainty ↓
Mathematica l model (Trajectory simulation)
HDC value (b) ±50 %
(a) ±10 %
Total
Parameters of Zigzag → Source of
Uncertainty↓
Mathematical model (Trajectory simulation)
6% 5% 1% 5% 7% Total
(a) HDC ±10% 9% 4% 7% 4% 4% value (b) ±50% 55% 19% 57% 39% 42% (a)
15% 9% 8% 9% 11% Table 9 Estimation of
(b) 61% 24% 58% 44% 49% uncertainty
in manoeuvring
prediction process for 15/5 vertical plane zigzag at 5 knots – SUBOFF body
7. UNCERTAINTY IN FULL-SCALE TRIALS
For each stage of the trajectory simulation process described above (formulation of mathematical model, program for trajectory simulation and estimating values of HDCs), the ultimate check for the manoeuvrability prediction procedure is to compare the predicted trajectory with the measured values during full-scale trials. However, such comparisons are not only rare [2, 7, 19], but are also fraught with the uncertainties due to noise in the data obtained during full-scale trials, since laboratory conditions (say, of model testing for obtaining HDCs) cannot be replicated.
θO zO te tc 37% 33% 6% 6% td 10% 18% 14% 9% 5% 6% 164% 198% 29% 69% 50%
(a) 55% (b) 201%
Table 8 Estimation of 47% 231%
15% 35%
uncertainty
11% 75%
16% 60%
in manoeuvring
prediction process for 15/5 vertical plane zigzag at 5 knots – Axisymmetric body
Focusing our attention on zigzag manoeuvres in the vertical plane for underwater vehicles, we may identify the possible sources of bias errors in full-scale trials as: • Errors in measuring instruments for depth, pitch angle and speed of the vehicle
• Set in inertial navigation or other motion / position-recording instruments
• Hydrostatic imbalance of the vehicle
It is therefore necessary to quantify typical levels of uncertainty in the full-scale measurement process in order to arrive at realistic estimates of the accuracy required of the entire process of manoeuvrability prediction. This is applicable for large manned submarines as well as small UUVs.
7.1 SOURCES OF ERRORS
As per uncertainty analysis described in [11], the errors in measurement can be of two types: bias errors (which are constant
measurements in the same sense) and precision errors (which are experiment).
throughout an experiment, affecting all random
θO
zO
te
tc
td
scatter in results during an
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©2010: The Royal Institution of Naval Architects
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