STUDY OF LOCAL PRESSURE DISTRIBUTION AND SYNCHRONIZATION DURING FREQUENCY LOCK-IN

Abstract

A cylindrical compliant model was equipped with tactile sensors and exposed to drifting level ice in a series of model tests in the Large Ice Basin of HSVA. Different failure modes have been observed and the corresponding distribution of local pressures has been recorded. Under certain conditions, the structure was set into lock-in vibrations with a steady-state of load and response. Cross-correlation functions were used in order to monitor the synchronization between discrete areas located around the structure's circumference. In addition, frequency analysis of local loads reveals harmonic and sub harmonic frequencies in the local load spectra. The paper describes the test setup used for the model tests in ice, quality and accurateness of the tactile sensor measurements, analysis procedure of the discrete areas and discussion of results. INTRODUCTION Frequency Lock-In (FLI) is a topic which has been discussed in the ice engineering community over the past decades and is still under debate because the fundamental physical mechanisms leading to lock-in and keeping the lock-in condition alive are not fully understood yet. This lack of understanding aggravates the numerical representation of FLI and consequently prevents reliable prediction of its occurrence (Kärnä et al., 2013). Synchronization of failure around the circumference of an offshore structure is deemed decisive for the onset of lock-in vibrations. This assumption is supported by full scale measurements e.g. at Norströmsgrund Lighthouse (STRICE EU project) which show synchronization of loads on up to nine load measuring panels (e.g. studied by Palmer and Bjerkas, 2013). However, these panels are quite large and do not allow for detailed spatial analysis of loads. A suitable technique to monitor local ice loads with higher spatial resolution is the application of tactile sensors. Such application has been described for experiments with full scale ice e.g. by Sodhi et al. (2006) and has also been tested in different laboratories for scaled model tests (e.g. Bechthold et al. (2014)). In the presented research, a previously used test setup for monitoring FLI at model scale (see Onken et al., 2013) has been equipped with tactile sensors and tested in the Large Ice Basin of HSVA. Aim of this study is to evaluate the practicability of using tactile sensors for the described problem and to define a testing and data processing procedure which can be used for future tests.

Full text

STUDY OF LOCAL PRESSURE DISTRIBUTION AND
SYNCHRONIZATION DURING FREQUENCY LOCK-IN
Gesa Ziemer 1,2, Clemens Deutsch 3
1 Hamburg Ship Model Basin (HSVA), D-22305 Hamburg, Germany
2 Institute for Structural Dynamics, D-21307 Hamburg, Germany
³ Bremen University of Applied Science, D-28199 Bremen, Germany
ABSTRACT
A cylindrical compliant model was equipped with tactile sensors and exposed to drifting level
ice in a series of model tests in the Large Ice Basin of HSVA. Different failure modes have
been observed and the corresponding distribution of local pressures has been recorded. Under
certain conditions, the structure was set into lock-in vibrations with a steady-state of load and
response. Cross-correlation functions were used in order to monitor the synchronization
between discrete areas located around the structure’s circumference. In addition, frequency
analysis of local loads reveals harmonic and sub harmonic frequencies in the local load
spectra.
The paper describes the test setup used for the model tests in ice, quality and accurateness of
the tactile sensor measurements, analysis procedure of the discrete areas and discussion of
results.
INTRODUCTION
Frequency Lock-In (FLI) is a topic which has been discussed in the ice engineering
community over the past decades and is still under debate because the fundamental physical
mechanisms leading to lock-in and keeping the lock-in condition alive are not fully
understood yet. This lack of understanding aggravates the numerical representation of FLI and
consequently prevents reliable prediction of its occurrence (Kärnä et al., 2013).
Synchronization of failure around the circumference of an offshore structure is deemed
decisive for the onset of lock-in vibrations. This assumption is supported by full scale
measurements e.g. at Norströmsgrund Lighthouse (STRICE EU project) which show
synchronization of loads on up to nine load measuring panels (e.g. studied by Palmer and
Bjerkas, 2013). However, these panels are quite large and do not allow for detailed spatial
analysis of loads.
A suitable technique to monitor local ice loads with higher spatial resolution is the application
of tactile sensors. Such application has been described for experiments with full scale ice e.g.
by Sodhi et al. (2006) and has also been tested in different laboratories for scaled model tests
(e.g. Bechthold et al. (2014)). In the presented research, a previously used test setup for
monitoring FLI at model scale (see Onken et al., 2013) has been equipped with tactile sensors
and tested in the Large Ice Basin of HSVA. Aim of this study is to evaluate the practicability
of using tactile sensors for the described problem and to define a testing and data processing
procedure which can be used for future tests.
POAC’15
Trondheim, Norway
Proceedings of the 23nd International Conference on
Port and Ocean Engineering under Arctic Conditions
June 14-18, 2015
Trondheim, Norway

PHYSICAL MODEL TESTS
The physical model which is used in the present research has been designed as part of the
BRICE project and its capability of representing FLI at model scale has been proven in two
test campaigns. Details concerning the physical test setup are described in Onken et al. (2013)
and van het Hooft (2014). The setup is shown in Figure 1 and its main properties are
summarized in Table 1. It basically consists of a rigid cylinder mounted to a support frame
which is free to move on linear bearings in x- and y-direction with a certain stiffness defined
by spring clusters.
Table 1. Properties of the physical model.
Property
Value
Diameter
0.83 m
Translational
stiffness in x- and y-
direction at water
level
2282 N/mm
Natural Frequency
(structure in the
basin, no ice)
5.12 Hz
Figure 1: Sketch of the physical model.
Tactile Sensors
In order to cover the full upstream half of the structure’s circumference, three sensors of type
5260 from Tekscan are located next to each other at the ice-structure interaction area. Each
sensor consists of 2288 pressure sensitive areas called “sensels”, distributed in 44 rows and 52
columns. Each sensel has a size of 9.3 mm x 6.7 mm. Their maximum pressure range is 3.45
kPa per sensel, converted by 8 bit converter into 255 distinguishable load levels. The
maximum pressure can be lowered according to the model test’s needs, providing a better
load resolution. The sensors are connected to Evolution Multiplexers for data acquisition and
storage, allowing for sampling rates up to 100 Hz.
The sensors are made watertight by application of thin adhesive plastic foil and protected
against ice abrasion by window safety foil. This procedure has been developed and tested by
Bechthold et al. (2014).
Test Matrix
Tests have been performed in level ice with a thickness of 45-50 mm, flexural strength
45-55 kPa and compressive strength 120-165 kPa. Velocities between 1 cm/s and 17 cm/s
have been tested in order to monitor different failure mechanism. A total number of 15 test
runs have been conducted.

POST-PROCESSING OF TACTILE DATA
Equilibration
An essential post-processing procedure for application of tactile sensors for the assessment of
very small pressure fluctuations is the equilibration. Equilibration means that the whole
sensor is loaded with a uniform pressure. Due to internal stress, varying wear of individual
sensels and mechanical defects, sensels respond differently to this load due to slightly
different sensitivity. Equilibration evens out such discrepancies and adjusts each cell such that
the uniform load results in uniform sensel response. An example for equilibration is given in
Figure 2. It shows an area of more sensitive sensels (“Hot Cells”) in the middle of the sensor,
which corresponds to the height of water level during the tests and is caused by more frequent
cyclic loading of those sensels. Also, there is a diagonal line with less sensitive sensels which
probably was caused by mechanical defects resulting from installation of the sensor on the
structure.
Figure 2. Visualization of equilibration (after testing).
Data Post-Processing
Matrices obtained from the three individual tactile sensors are combined to one large matrix.
Figure 3 shows an exemplary plot of combined local loads measured during an FLI event.
Obviously, there are loaded sensels high above the water line which most probably result
from internal stress of the sensors or intruded water. To remove these, a threshold is set which
removes data from all sensels which are located more than twice the ice thickness higher than
the waterline. All remaining sensel loads are integrated over the loaded height. Therefore, the
ice load is treated as a line load. This is a major simplification, but the small thickness of the
used model ice does not allow for spatial load analysis over ice thickness anyway. Data has
been converted into a MATLAB data file for easier and faster handling.
Figure 3. Example of loads measured by the tactile sensors.

Global Load Comparison
To assess the correctness of the loads measured by the tactile sensors, the normal loads acting
locally on all sensels are converted into a global ice force in ice drift direction, which is
compared to ice forces measured by the six-component-scales. Note that the load cell
measurements also include inertia forces which have to be removed from the measurements
first. The used approach has been discussed by Onken et al. (2013). The comparison shows
satisfying results regarding magnitude of total loads, but insufficient temporal resolution as
illustrated exemplarily in Figure 4. High frequency fluctuations captured by the load cell
sandwich (sampling rate 200 Hz) are not recognized by the tactile sensors.
Figure 4. Comparison of load in ice drift direction measured by Tactile sensors (black) and 6-
component load cell sandwich (red, without inertia forces).
RESULTS
Considered Events
The basic analysis presented in this paper deals with FLI events only. Therefore, suitable
events were chosen according to following criteria:
1. Loading frequency equals frequency of response and is close to the natural frequency
of the structure
2. Amplitudes of displacement are higher than 0.6 mm
3. The event has a duration of at least 4 seconds (corresponding to 20 cycles)
15 lock-in events have been found which match all requirements. They occurred at ice drift
speeds between 2 and 5 cm/s and their load and response frequencies vary between 4.8 and
5.2 Hz. General observations explained in the following subsections refer to all of those
events, although only a small number of them is illustrated in this paper.
Cross-Correlation
The idea of lock-in being excited by synchronized failure around the circumference of the
structure suggests a high cross-correlation of loads on individual discrete areas.
An example of cross-correlation factors during the steady state of FLI and their significance is
given in Figure 5.

Figure 5. Left: Cross-correlation coefficients for individual sensels during a 8s FLI event.
Only steady-state condition is taken into account. Right: Significance test for coefficients
shown left. Green area indicates significance (p<0.05).
The overall correlation is high; however, the plot illustrates that neighbouring elements do not
necessarily correlate and the correlation decreases towards the sides of the structure. But also
in the centre part, some elements do not seem to be synchronized with the other areas.
The development of correlation during onset of FLI is illustrated by an example shown in
Figure 6. The considered event is most suitable for such an analysis because it is the only
occasion where failure de- and re-synchronizes. In all other events, FLI ends by global
flexural failure of the ice. The corresponding correlation factors are presented and commented
in Table 2.
Figure 6. Top: Normalized total forces in ice drift direction, bottom: structural response.
A
B
C
D
E

Table 2. Crosscorrelation plots for time intervals indicated in Figure 4.
Interval
Crosscorrelation Factors
Comment
A
Interval A begins when the ice starts interacting with
the structure. No global synchronization has taken
place.
Correlation is high along the diagonal,
meaning that ice on neighbouring sensels is likely to
fail at the same time while sensels further apart
experience a different load time history.
B
The displacement measurement shows that the
structure starts to shake severely during Interval B.
The displacem
ent amplitudes increase and all
frequencies despite the structure’s natural frequency
diminish. The global correlation does not increase,
but it is spread wider across the structure’s
circumference. Single areas are synchronizing.
C
Interval C contains 7 cycles of FLI. The overall
correlation is much higher and is spread almost
uniformly over the whole circumference, despite a
clear area of maximum correlation at the center line,
which corresponds to observations shown in
Figure 5.
D
For some reason, the high correlation at center line is
not persistent and almost vanishes in Interval D. The
global correlation stays at a high level compared to
the condition before FLI.
E
A short and unsteady FLI event of 4 cycles takes
place during Interval E. Again, the global correlation
increases. The area of maximum correlation shifts
from center to port side of the structure.
The example shown above illustrates that load synchronization indeed is the key factor
initiating lock-in and keeping lock-in alive. However, this does not necessarily mean that the
ice fails simultaneously around the structure all at once. But it shows that parts of the loading
and unloading mechanisms are synchronized.

Spectral Analysis
Cross-correlation plots reveal that the overall correlation increases during FLI, but sensels are
not fully synchronized. This is further investigated by spectral analysis. An event is used
which has a long duration and pronounced steady-state. The chosen event is shown in
Figure 7. Despite a short interruption at t=99 s, the appearance of load and deflection is quite
steady.
Figure 7. Top: Normalized total force in ice drift direction, bottom: structural response
Figure 8 shows FFT for global ice load and structural response. Next to the pronounced peak
at 4.8 Hz, the load spectrum contains distinct peaks at 9.6 and 14.5 Hz, which are second and
(close to) third harmonic of the natural frequency. Looking at FFT of individual sensels, also
the first sub harmonic (2.4 Hz) is visible (Figure 9).
Figure 8. FFT for ice load and structural response during FLI event shown in Figure 5.
Figure 9. FFT for all individual sensels during FLI event shown in Figure 5. Magnitude of
peak amplitude is indicated by colour.

Time Domain Analysis
The FFT and cross-correlation considerations suggest that the apparent simultaneous failure
results from a superposition of individual failure loads which are not fully synchronized in
time. This is illustrated by plotting loads on different scales, which is exemplarily done for a
single loading and unloading cycle in Figure 10.
Figure 10. a) Total normal load (sum of all sensel loads) on 1.4m width of circumference, b)
load split on the three sensors (each having a width of 0.48 m), c) load split into 10 discrete
areas (width = 0.14 m), d) all sensel loads (width = 0.0093 m).
In Figure 10a, the total normal load is shown which has a saw-tooth shaped appearance with
long build-up and rather short collapse phase. The build-up appears rather steady. Looking at
each sensor individually (Figure 10b), one can see that the highest loads naturally appear on
the front sensor (green), while the starboard sensor (blue) is not loaded, probably due to
asymmetric ice contact after global failure. Ice on the front sensor fails later than ice on the
port side sensor (red).
Figure 10c shows the sensors split up into 10 areas. One can see the saw-tooth shape on two
of them (blue & yellow graph); having moderate load build-up and afterwards decreasing
simultaneously. A third area (black) correlates to the build-up at first, but misses the high
peak. It returns to a pressure value near zero earlier than the better synchronized areas, and the
decrease takes longer. A fourth area (pink) also plays a significant role in the loading cycle
which increases its load more rapidly and fails a little later than the other sections.
Figure 10d shows all individual sensel loads. Four different groups of sensels can be
distinguished by the appearance of their loading and unloading time history:
1. Saw-tooth shape
Some of the sensels show the saw-tooth shape one would expect from the FFT
and the global load time history. Their cross correlation is high (e.g. light blue
and yellow graphs).
a)
b)
c)
d)

2. Curved saw-tooth shape
Sensels following the curved saw-tooth shape (similar to the pink graph in
Figure 10c, e.g. dark blue in Figure 10d) have the same loading frequency as
group 1, but with a small phase shift. They tend to fail a little later than the first
group.
3. Plateau
Some sensels show a rapidly increasing load at the beginning of the loading
cycle and remain quite constant for half of the loading period. In the global load
decrease phase they collapse first, significantly earlier than group 1 and 2.
Examples for this group are the red and black graphs.
4. Random
About 10% of the loaded sensels do not fit into any of the above mentioned
groups. They tend to load and unload more frequent, but with no distinct
periodicity.
DISCUSSION
Tactile sensors prove to be a suitable solution for monitoring the interfacial processes during
ice-structure interaction. Valuable data has been collected during the evaluation tests already
and further investigation of the recorded local loads is required to extract more results and
meaningful findings from it. The preliminary analysis presented in this paper reveals that at
least for the structure that was subject to this specific test campaign, the local loads are less
synchronized and shaped differently than anticipated beforehand. Apparently, there are
different types of load shapes which lead to consecutive failure of the ice at different locations
around the circumference of the structure. Further research is needed to evaluate whether such
characteristic appears during FLI of structures with other dynamic properties as well, and to
develop a theory about its formation.
Furthermore, the presented data lacks of high frequency processes which may alter the picture
of individual sensel loads. For future test campaigns, the tactile sensors have to be used with
hardware enabling higher sampling frequencies. Additionally, sensors with higher spatial
resolution are required in order to monitor local loads over the height of the ice sheet as well,
which is important to study the contact area.
ACKNOWLEDGEMENTS
The authors would like to thank the HSVA ice tank crew for the professional execution of the
tests. Furthermore, the authors wish to acknowledge Torodd S. Nord and Catherine Y.
Pedersen from the Research Council of Norway supported Centre for Research-based
Innovation SAMCoT, and the support of all SAMCoT partners. Their research has been an
inspiration for the presented study, and their MATLAB routine has been a useful basis for the
developed tactile measurement analysis MATLAB script.
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