Sources of error

(a) Signal showing the three force transducers and how they are varying in amplitude and phase

75 76 77 78 79 80 81

(b) Total heave force by summing all the three forces

Figure 5.16: Plot of individual force transducers that were attached to the ROV and the total heave force

5.6 Sources of error

When doing an experiment it is desirable that the experiment represents the model in real con-ditions. There can be errors arising from various phenomena during experiments. These have to be minimized. Therefore, it is essential to have a good test plan and be aware of the possi-ble error sources affecting the experiments. First, it is essential to identify all error sources to limit the uncertainty of the experiment. The primary sources in the model test are listed below.

Figure 5.17: Errors due to interaction in seakeeping model tests

Tank wall effects

Figure 5.17 identifies the primary bias and prediction errors in the seakeeping experiment of the SWATH. A towing tank has a limited width and length. Due to the limited width, tank wall effects, or sidewall effects, a vital bias error can impact the results when running zero speed tests in a towing tank. It is not only the width of the tank that determines the side wall effects.

Yuan et al. (2018) explains that the geometry of the model, depth of the tank, and forward speed of the model also impact the tank wall effects. In the experiments, there will be zero forward speed. In the twenty-first towing tank conference, Messalle (1987), stated that when testing ships at slow or zero speed, the results will be affected by large experimental scatters due to thank wall effects. This will create wave reflections from the moving model because of radiated and diffracted waves by the model. To minimize the wave reflection problem for zero and low speed can be done by keeping the small model relative to the size of the basin or width of the tank. In some basins, there are also installed effective wave damping devices. Table 5.11 provided details about the error quantification for the instruments used in the test.

Reflections from beaches

Another source of error can be wave reflection from the beach. The wave reflection in this experiment has not been calculated.

Model inaccuracies

Model inaccuracies are a more distinct and understandable error that is related to the model.

First of all, if the shape of the model is inaccurate, it will give a wrong result of the full-scale hull. It is, therefore, important that the production of the model is correct. In an experiment, the model often needs to be ballasted to achieve the required draught. Error due to inaccurate draught can be minimized by ballasting to correct weight, not to the specified draught. It is also crucial that the model surface is not too rough.

Meniscus effect

Faltinsen & Timokha (2009) explained the error source named meniscus effect could appear for the measured wave elevation due to the steel wires that the wave probes are made of. The meniscus effect can cause an error if the measured wave elevation is less than the diameter of the steel wire.

Calibration

The test setup can influence the results. First of all, the right equipment has to be used to ensure that the measurements wished to measure, gets measured. Moffat (1988) describes that errors in measurement systems can arise, for example, in the strain gain, ripple in power supplies, or drift due to temperature changes in the instrument. Calibration procedures should be implemented to minimize measurement errors during the experiments. Errors due to environmental modeling

5.6. SOURCES OF ERROR

is a factor that needs to be accounted for. Wave parameters and spectral shape are the two essential factors. It is, therefore, important to always calibrate the waves used in the experiment.

The result of the calibration can then be used instead of specific waves.

Oqus system and accelerometers

The model was equipped with three Oqus markers. For heave, RAO significant variance was shown in the uncertainty analysis. This must come due to fault in the measurement from the Oqus system.

Repetition test

Repetition tests were only carried out for regular waves, as shown in Table 5.5, with one repetition for four different test conditions, due to limited time. Repetitions test should be carried out for both regular and irregular test for five repetitions to get an accurate result.

Table 5.11: Error/uncertainty for the instruments used in the experiment Instrument Error/Uncertainty Unit

Wave Probes 0.001-0.002 m Accelerometers 0.05-0.1 m/s²

Oqus system 1 deg °

Oqus system 0.01-0.02 m

5.6.1 Calculation of precision error

The error in an experiment can be described as the difference between the real results and the test results. It is difficult to predict the error, and it is a sum of bias (systematic errors) and precision (random errors) sources. The bias and precision error can be estimated with a confidence level of 95%. Five runs are often the recommended amount of repeated runs to get a proper uncertainty analysis. As presented in Table 5.7, one additional set of repetitions were conducted for four different test conditions. The repetitions were done to check the uncertainty and repeatability of the experiment. Unfortunately, repetition of all periods was not performed due to limited time available in the tank.

ITTC (2014b) gives a guide to the expression of uncertainty in experimental hydrodynamics.

For standard uncertainty, the best available estimate of the expected value of a batch "q" that alter randomly for "n" observations. From this, the mean or average is expressed as:

¯

n is the number of observations that have been done during the experiment. The number of observations depends on how many repeated tests that get performed during the experiment.

When the test is repeated, a standard deviation can be found. ITTC (2014b) suggests that

at least ten repeated test needs to be performed to get a reasonable estimate of the standard deviation. Repeated tests are expensive and time-consuming. Therefore, typically about five repeated runs are performed.

When the mean or average value if found the experimental variance of the observation can be calculated. This estimates the variance, s, of the normal probability distribution of "q":

s=

In experiments correlation is often mentioned. In a stationary time series, the uncertainty is dependent on the correlation which is white noise. In a situation where there is no white noise, the standard uncertainty can be expressed as:

u(¯q) = s

√n (5.16)

When having a series of measurements which has given a mean value, standard deviation and that one measurement has given a large deviation,δ, from the mean value. One can then choose a criterion for disregarding the the measurement that the probability of exceeding δ with one of the measurement in the series (Huse 1994). When having n measurements the probability that one of them will exceed the given boundary is

p=n(1−A) (5.17)

A traditional choice is to set p = 0.5 and one have the criterion for disregarding the measure-ments by

Figure 5.18: Standard deviation with mean values as a function of heave RAO for bare model and model with fin type 1 in regular waves

5.6. SOURCES OF ERROR

Figure 5.19: Standard deviation with mean values as a function of pitch RAO for bare model and model with fin type 1 in regular waves

Figure 5.18 shows a large standard deviation for heave motion, especially for head sea. The error is linked ether to phase 1 or phase 2, where some faults in the measurement of heave motion must have been wrong. A standard deviation of 0.58is found for T = 1.3 s.

Chapter 6 Results

This chapter will present the results from the experiments and the numerical simulations done in WAMIT. First, the results from the experiments on the SWATH is presented. Next, the two different designs’ motion characteristics and operability of the ROV will be compared.