Improving the sea keeping behaviour of fast ships using a proactive ride control system

Improving the sea keeping behaviour of fast ships using a proactive ride control system

A. A . K . Rijkens, Ship Hydromechanics and Structures, Delft University o f Technology, D e l f l , The Netherlands

S U M M A R Y

This article presents a proactive ride control system that is specifically designed to reduce the extremes i n the vertical acceleration signal o f a fast ship i n waves. The ride control system uses an anticipatory control strategy to be able to inteivene prior to the actual wave impact. The feasibility and performance o f this proactive approach has been investigated using a ship motion simulation program. During the simulation continuous real-time ship response predictions are made based on the incident wave to estimate the acceleration level. The control system intervenes when the predicted vertical accelerations exceed a certain threshold value by adjusting the forward speed and the pitch motion o f t h e vessel.

The computational results demonstrate a significant improvement i n the operability by using this proactive ride control system. The vessel can maintain a high average forward speed, while most peak accelerations can be limited to the specified threshold value.

1. I N T R O D U C T I O N

Ride control systems are regularly applied in various marine concepts in order to improve the operational performance o f the ship at speed. These systems are often used to reduce the heave, phch and/or roll motions o f the vessel in waves. Generally, a substantial improvement can be achieved i n the motions or acceleration signals. These performance improvements are often indicated by comparing the average or significant values o f the particular response signals, which is i n accordance with the more commonly used methods in linear ship motion analyses.

However, these linear procedures are generally not applicable in the field o f relatively small high speed ships [1]. Fast ships are frequently subjected to large wave impact events, while sailing at high forward speeds in head sea conditions. These wave impact, or vertical peak accelerations, are strongly nonlinear with respect to the incoming waves. For such strong nonlinear systems no distinct relation between the significant and the extreme values in the response signal exists. The average or significant value can therefore not be used as a measure for the maximum values in the acceleration signal. Instead, the actual distribution o f the peaks i n the nonlinear response signal should be considered to determine the operability o f the ship [ 2 ] .

Full scale trails have indicated that particularly the larger vertical peak accelerations pose the most important limiting criterion fiom a human perspective [ 3 ] . I n addition, the maximum peak accelerations also increase the damage potential to on board equipment or, i n some cases, may even compromise the structural integrity o f the ship [ 4 ] . These insights have led to the conclusion that operability improvement o f these fast ships can actually be realized by reducing the extreme values i n the vertical acceleration signal.

So, i f the large peak accelerations are the dominant factor for damage potential or discomfort o f the crew on high speed ships, than these should be reduced as much as possible by the ride control system. Controlling the peak accelerations is, however, not an easy task to perform. One o f the issues is the large difference in time scale o f these fierce disturbances i n relation to the relatively slow motion response o f the ship on a control action. A method that is commonly used by experienced operators, to overcome this problem, is to temporarily reduce the forward speed o f the vessel several seconds before an expected wave impact. Anticipating on a fiiture impact and reducing the thrust allows the vessel to decelerate for short period o f time to arrive at lower speed at instant o f the actual wave impact, which i n general leads to a lower peak acceleration value.

This manual throttle control requires a skilled operator who is able to anticipate on the waves in front o f the vessel and apply the necessary thiaist adjustments. W i t h these brief thrust reductions some foreseeable wave impacts may be evaded. However, even the most experienced operators still make occasional misjudgements o f the peak accelerations. A n incorrect assessment o f a wave impact can be aggravated due to various causes e.g. fatigue, distraction or loss o f concentration. I n addition, the operator's view can be hampered by excessive spray, severe weather conditions or darlaiess, which may lead to a further deterioration o f the wave impact estimation. V a n Deyzen et al. [5] found a significant increase o f the average forward speed during f i i l l scale trails on board a Dutch Search and Rescue vessel using throttle control. But at the same time the level o f vertical accelerations were higher compared to the reference run at a constant forward speed. He suggested that these larger impacts could be attributed to the misjudgements o f t h e operator. Another explanation could be that the crew has a different perception o f the acceleradon level due to a certain "feeling o f being i n

control" when the operator is allowed to make throttle adjustments [ 5 ] .

Subsequently, van Deyzen et al. [6] made an initial study to the automation o f thrust control by using a proactive method. He formulated a fundamental mathematical model which is based on a nonlinear mass-damper-spring system approach to approximate the behaviour o f a fast ship i n waves. D u r i n g a time simulation with this model, continues short-term predictions are made at regular time intervals to determine the peak acceleration level i n the near future. The proactive system w i l l intervene once a predicted impact exceeds a certain threshold value, by making a series o f additional predictions at successive thrust reductions. The actual thrust setting that is selected among these predictions has to comply w i t h an acceleration threshold value at the expense o f a m i n i m u m speed loss.

W i t h this mathematical model the effect o f the human intervention is eliminated and replaced by a more consistent automated proactive controller. The results indicated a theoretical increase o f the operability o f a fast ship i n waves. B y using the proactive control method a significant reduction o f the peak accelerations could be achieved while the average forward speed was comparable with the benchmark simulation at a constant forward speed [ 6 ] .

The promising results o f the above described control method, raises the question whether this proactive strategy can be further exploited f o r additional control variables. Besides the forward speed, another w e l l -knovm operational parameter that has an important effect on the vertical peak accelerations is the t r i m o f the vessel. The strong correlation between the trim angle and the vertical accelerations for fast ships has been indicated by, amongst others, Fridsma [7] and Keuning [ 1 ] . Wang [8] investigated the effects o f transom flaps on a fast ship to actively control the running t r i m i n regular waves. The deflection angle o f the transoms flaps was controlled using a pitch velocity feedback system. This feedback control type proved be very effective for the reduction o f the pitch and heave motion, especially near the resonance region. I n addition, a reduction o f the vertical acceleration was found. Later, Rijkens et al. [9] used simulations to show that this control scheme also leads to a reduction o f the vertical peak acceleration level in irregular waves.

A general issue w i t h these motion control systems is the selection o f the proper control gains. Pre-specified control settings may become less effective for the motion reduction o f the vessel i n changing environmental or operational conditions [10]. Finding adequate gains f o r the reduction o f the vertical peak accelerations may prove to be even more d i f f i c u l t , whereas no unambiguous relation between the motion response and extent o f a (future) wave impact exists. I n other words, an impact

does not necessarily has to coincide w i t h large motion or velocity amplitudes o f t h e ship.

I n the current article a proactive control strategy has been used i n order to reduce the large vertical peak accelerations. The proactive ride control system evaluates various transom flap control gains and the thrust settings prior the actual wave impact. A m o n g these computed predictions a tailored solution is determined that is most suited for the specific situation. The feasibility and performance o f this proactive approach has been investigated using a dedicated ship motion simulation program.

D E S I G N OF A P R O A C T I V E R I D E C O N T R O L S Y S T E M

Proactive models anticipate on future disturbances and attempt to address them before they actually become a problem. A proactive control system uses a real-time' simulation model to predict the relevant dynamics and detect any future undesired behaviour. A f t e r detection o f a disturbance, the consequences o f various control actions can be computed w i t h same simulation model. Among the available control actions a trade-off is made to f i n d the one that best meets the required objectives. W i t h respect to the current application two control objectives have been defined i n order to improve the operability o f a high speed vessel:

• limit the peak accelerations to a particular threshold value

• maximise the forward speed o f the ship, or keep it as close as possible to a desired reference speed

2. P R O A C T I V E C O N T R O L S T R A T E G Y The proactive system is based on a strategy that is also known as model predictive control [ 1 1 ] . This strategy consists o f a repetitive sequence o f discrete control cycles. I n each control cycle a prediction is made over a certain period o f time, which is also referred to as the prediction horizon. A long prediction horizon enables an early detection o f any relevant disturbances, which allows more time for a control action to change the behaviour o f the dynamic system. However, very long prediction horizons are generally not manageable due to the increase o f the computational time. Moreover, longer response predictions are generally associated w i t h a larger uncertainty. For fast ships, a prediction horizon in

' The term "real-time" is this sense means that the simulation model must be able to complete it prediction without any significant delay, the processing time should however be much less than the time duration o f the physical event.

the order o f several seconds seems to be an appropriate compromise [ 6 ] .

At the start o f a control cycle the incident wave and instantaneous state o f the vessel are sampled by the proactive system. This information is used by simulation model to compute the response prediction. The aim o f the control strategy is to optimize the performance according to the objectives that were specified. I f all objectives are satisfied, hence no action is required, the proactive system proceeds w i t h the next control cycle. However, i f a disturbance is identified that violates one o f the objectives, additional predictions are computed by the simulation model starting f r o m the state at the beginning o f the current cycle. The additional predictions are computed using a systematically variation o f the available control actions. A m o n g these predictions the best solution is selected and this action is implemented until the beginning o f the next cycle. The successive cycle starts using updated information and new control actions can be determined. This process repeats itself continuously.

This proactive ride control system is dependent on sensors to obtain the ambient wave conditions and the instantaneous state o f vessel. Practical issues regarding the availability and technique o f these advanced sensors, especially w i t h the respect to the wave measurements, are recognized, however these issues w i l l not be elaborated in the current article. A t this moment the objective is to investigate the feasibility and performance o f a proactive control method. It is assumed that the incident wave is known and available to the control system.

2.1 S I M U L A T I O N M O D E L

The proactive control strategy demands a simulation model that can predict sea keeping behaviour o f a fast ship in a (very) short period o f time. This poses a strict limitation on the processing time o f the computational prediction model. In general, a strong relation exists between the complexity o f the simulation model and its CPU time. This correlation precludes most o f the more detailed, and thus time-consuming, panel based methods. I n order to compute these predications i n a real-time environment a so-called "first principle" simulation model has been selected for the proactive ride control system. This simulation model was originally developed by Zarnick [12] in 1978. Zarnick formulated a basic time domain mathematical model according to a nonlinear semi-empirical strip theory approach to investigate the behaviour o f planing prismatic hull shapes w i t h a constant deadrise i n regular waves.

Later, Keuning [1] improved the applicability o f this model by extending it for more realistically shaped hard chine hull forms with variable deadrise i n irregular waves. I n addition, a procedure was developed to determine two empirical coefficients that results in a

proper calm reference position o f the vessel at speed. One correction coefficient accounts for the reduction o f the hydrostatic buoyancy due to ventilation o f the transom stern and f l o w separation at a part o f the chines. These effects induce a pressure reduction i n the particular regions which yields a lower overall buoyancy force than that could be assumed based on the pressure integration o f the geometrical submerged part o f the hull at high forward speed. The other coefficient is associated w i t h the sectional added mass, which is, among other things, dependent on the geometry o f the vessel.

Zarnick [12] used fixed values f o r both the buoyancy correction factor (0.5) and the added mass coefficient (1.0). These values were derived f o r very high speeds and a simplified hull shape. Fixing the value o f these coefficients did not give very satisfactory results for the reference position at lower speeds nor for different hull geometries. Hence, Keuning [1] suggested a different approach i n which polynomial expressions or model test results were used to obtain the still water reference position o f the particular vessel at speed. The (semi-) empirical data can be used to calculate the corresponding coefficients. This procedure can be repeated f o r different forward speeds to f m d the coefficients over a wider speed range. Realistic values o f these coefficients were obtained for Froude displacement numbers between Fry = 1.6 and F r y = 3.0 [1].

Previously, the simulation model was used to predict the sea keeping behaviour o f fast ships at a constant forward speed. This requires one set o f coefficients f o r each individual simulation. The current model is modified to allow a variable speed during the computation. The two correction coefficients are pre-calculated over the valid speed range for a certain number o f forward speeds. Linear interpolation is used to f m d the coefficients f o r intermediate speed values. The coefficients are updated at every time step during a simulation.

In 2011, Rijkens et al. [9] extended the simulation model w i t h an empirical formulation to account for the hydrodynamic forces o f active transom flaps. The forces o f the control surfaces are determined according to a quasi-stationary approach. This extended model could be used to compare different control settings o f the flaps and investigate the effects on the motion behaviour o f the vessel. Simulations w i t h these active flaps were validated with the model test results o f Wang [8] and a good correlation was found between the numerical and experimental heave and pitch responses o f the vessel f o r various pitch velocity gains.

2.2 H U L L D E S I G N

The hull f o r m that is considered to demonstrate the control system performance was designed i n 2006 by Keuning and Van Walree [ 3 ] . Here it was used as a benchmark vessel and the hull was developed according to the philosophy which is commonly referred to as the "Enlarged Ship C o n c e p f (ESC). This vessel (Figure 1)

has been used i n many research studies at the D e l f t University o f Technology which resulted i n an extensive number o f towing tank measurements both in calm water and i n waves.

Figure 1: Lines plan and rendering o f the hull f o r m o f the "Enlarged Ship C o n c e p f (ESC)

The large quantity o f experimental data on the ESC makes it particularly suited for a current research application, since i t enables a thorough validation o f the simulation model. The original ( f u l l scale) waterline length o f the ESC is 55 meters [ 3 ] . However, f o r the current research application a smaller length was preferred, whereas thrust control would be more effective on smaller sized high speed vessels due to their relatively high power to weight ratio and because these vessels generally operate at higher Froude numbers. For these reasons it was decided to reduce the "prototype" waterline length to 22 meters. The main particular o f this 22 meters version o f the ESC are listed i n Table 1.

Table 1: M a i n particulars ESC 22 m

Designation Symbol Value Unit

Length overall 23.5 m

Length waterline 22.0 m

Beam waterline BOA 3.38 m

D r a f t T L06 m Displacement V 33.0 m^ Longitudinal position 9.00 m centre o f gravity Wetted surface

_s

In the present simulation model only the motions i n the vertical plane are being considered. A further simplification is introduced by assuming that the forward speed is only dependent on the equilibrium o f the thrust force and the calm water resistance. Hence, no coupling between the surge motion and heave and pitch motion is taken into account and the model neglects any change i n

forward speed due to the (horizontal) wave exciting forces.

These simplifications i n the surge equation w i l l have an influence on the vertical motions and accelerations o f the vessel to a certain extent. However, it is believed that at this stage it may be justified to use this simplified version o f the surge equation for a qualitative comparison. I n this case, the simulations w i t h thrust control are evaluated i n relation to benchmark simulations at constant forward speed, this means that the wave induced surge oscillations are neglected in both scenarios. Moreover, the magnitude o f the perturbations i n the forward speed due to waves is thought to be much less significant in comparison w i t h the more dominant effect o f reducing the thrust for some period o f time.

The calm water resistance curve o f the ESC is presented Figure 2. The deceleration o f the vessel, at the time o f a thrust reduction, is directly determined by the difference in thrust force and the speed dependent calm water resistance. 5 0 I . . . . • : 1 40 z _ A- - R -meas tot A A / A ; .y. '• / '• • / / : : A : er Q l • • • • • ' 1 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Frv H

Figure 2: Total calm water resistance o f the 22 meters ESC

Two active transoms flaps are being used to control the motions o f the vessel i n waves. The hydrodynamic characteristics o f these transom flaps are based on a series o f systematic experiments and the resulting empirical relations for the added l i f t forces are implemented in the simulation model [ 9 ] . The range o f the control force is restricted by the hydrodynamic properties o f the control device. I n the case o f transom flaps, for example, a strong transition i n the hydrodynamic l i f t is present at upward angles as a consequence o f flow separation.

Next to the limitations o f the control force from a hydrodynamic point o f view, additional constraints are imposed by the actuator system. For instance, transient motions o f the flap may not be achieved due to mechanical limitations. Especially, large gains can easily

cause saturation o f tlie actuator. For a proactive system tliis may become even more important due to the receding behaviour o f the control gains. Neglecting actuator saturation can result in an over predicting o f the system performance. Hence, in these simulation limitations have been set regarding the maximum values for the angular velocity and angular acceleration o f the flap. These limits ensure a gradual change i n the flap motion. The dimensions and the deflection range o f the transom flaps together properties o f the actuator system are tabulated i n Table 2.

Table 2: Particulars transom flap and actuator system

Designation Symbol Value Unit

W i d t h a L30 m

Length X 0.40 m

Area A 0.52

M i n . deflection angle ^min -5 deg Max deflection angle _^max 30 deg Max. angular velocity _^max 60 deg/s Max. angular

^max 200 deg/s^ acceleration

2.4 D E C I S I O N M A K I N G PROCESS

A f t e r the detection o f a disturbance, the proactive control system starts computing the performance o f the available control actions. The two control variables (i.e. the thrust o f the vessel and the pitch velocity gain o f the flap) are systematically varied, which results i n a number o f possible solutions. The resuhs o f these individual predictions are combined in a performance matrix i n order to decide which o f these control actions would be most suited f o r implementation.

Figure 3 displays a graphical representation o f a performance matrix. This figure indicates the effect o f the various control actions on the magnitude o f a particular acceleration peak. A threshold value o f 20 m/s^ has been defined and the prediction horizon equals 4 seconds. The thrust ( u ) is reduced f r o m its maximum value to zero i n five regular intervals. The control gain

(Kg) for the flap is varied between zero and six. Without

any control action the acceleration level at the bow would have a value o f approximately 45 m/s^ (black marker). 50 -| 40 -E, 30 -: bow ) 20 -JD 10 0 -6 / 100 / 80 40 ^ 0 ° [deg/(deg/s)]

Figure 3: Example o f the performance matrix, the initial condition is indicated w i t h the black marker and the selected solution is indicated with the red marker

A m o n g all possible control options a first selection is made based on the acceleration threshold value. The remaining valid solutions are further assessed using the second objective. This objective states that a better operational performance can be achieved i f the speed loss during a control action is minimized, therefore a valid solution at the highest possible thrust is preferred. W i t h this procedure the thrust setting can be determine, however still multiple valid solutions may exist for the flap control gain. I n that case no decisive answer is found, whereas these valid solutions all satisfy the required objectives. Therefore, an additional constraint is specified to obtain the final unique solution. For the case o f multiple valid flap control gains, the lowest gain value, resulting i n a minimal control effort, w i l l be selected.

2.5 P R O G R A M A R C H I T E C T U R E

I n a computational environment one may silently assume that the predictions itself do not require any processing time. I n that case it is assumed that the information that is used to initiate a control action at a particular control cycle is also valid at the moment o f the actual implementation. However, i n a physical environment the computation o f the predictions does take a certain amount o f time, which w i l l resuh i n a processing delay. This delay w i l l affect the control systems performance in two different ways. First o f all, the delay w i l l influence the accuracy o f t h e control predictions. This is due to the fact that the position o f the vessel, at the time o f the implementation o f the control action, has changed w i t h respect to its position at the start o f the control cycle. This difference becomes more important as the processing delay increases. The second effect is that the delay reduces the effective prediction horizon, which leaves less time f o r the control action to change the behaviour o f the ship.

Special attention has been paid to the structure o f the program to enable a fast computation o f the performance matrix. I t was found that a sequential calculation order would either consume too much time or, on the other hand, w o u l d strongly l i m i t the number o f response predictions. To solve this issue, a parallel calculation approach has been adopted.

The ship motion prediction model is programmed in the Fortran programming language. A M A T L A B computing environment has been used to design the proactive ride control system, w h i c h involves the control o f the predictions as w e l l as the decision making process. The distribution o f the predictions over the available workers o f the particular computer system is governed by the M A T L A B parallel computing toolbox. The Fortran subroutines o f the simulation model are compiled into a M E X - f i l e to allow an efficient data transfer between the two languages. This type o f interface provides a good overall performance o f the program, whereas the computational efficiency o f the Fortran language is combined w i t h the high level functionality o f M A T L A B . The parallel coinputing approach significantly reduces the time to calculate a large number o f the predictions. The total time duration f o r constructing a performance matrix, containing 30 individual predictions and obtaining the desired solution, typically takes around 0.3 - 0.4 seconds on a local computer system w i t h 12 workers. I n this example the predictions have a prediction horizon o f 4 seconds, which leaves approximately 3.5 seconds o f effective implementation time o f the conttol action before a wave impact.

3. S I M U L A T I O N S

I n this section the results o f the simulations w i t h the proactive ride conttol system w i l l be elaborated. I n order to assess the accuracy o f the motion predictions, a comparison is made using available model test data published by De Jong [13]. The experimental test data presented i n this reference has been extrapolated once again using the new scaling factor to obtain the f u l l scale values o f the current 22 meters version o f the ESC. The validation study specifically focuses on the prediction o f the peak accelerations, since this signal is used for the test criterion i n the ride control system. Subsequently, the simulations w i t h the proactive system are compared with benchmark simulations without control to indicate the improvement i n the sea keeping behaviour.

3.1 M O D E L C A L I B R A T I O N

For a proper prediction o f the calm water reference position o f the vessel, two empirical coefficients need to be determined over the valid speed range. The buoyancy correction factor and the added mass coefficient are calibrated using a direct comparison w i t h the calm water model test results o f the ESC. B o t h the measured as w e l l as the calculated rise and t r i m are presented i n Figure 4. A satisfactory correlation is found i n the rise o f the

vessel, however for the trim a small discrepancy exists i n the middle speed range. The measured hump i n the calm water t r i m is not represented i n the computed resuhs. I n order to introduce this "hump" i n the calculations the coefficients would require a value that lead to a deterioration i n the motion predictions, hence it is decided to slightly underestimate the t r i m position o f the ship i n that area.

Several representative experimental resuhs presented i n the graphs o f this section are provided w i t h 95% confidence bounds. A detailed description about the uncertainty analysis o f these experiments can be found i n De Jong [13].

Figure 4: Calm water rise and t r i m (positive: bow up) 3.2 V A L I D A T I O N OF T H E P R E D I C T I O N M O D E L I n the validation process a set o f regular head waves was considered allowing a deterministic comparison between the simulations and the experiments. The measured and calculated response signals are processed by applying a harmonic analysis at the particular wave frequency. I n this way the amplitudes o f the response signals can be determined, which are used to compute the transfer functions or Response Amplitude Operators (RAOs). The measured and calculated values o f the heave and pitch RAOs are presented in Figure 5 and Figure 6 respectively.

RAOs are frequently used in a linear ship motion analysis. I n this procedure the input signal (waves) and the motion responses o f the vessel are being expressed using harmonic components, which can be quantified i n terms o f frequencies, amplitudes and phase angles. Moreover, it is assumed that a linear relation exists between the input and the output signals. I n this linear approach one can combine the R A O s w i t h a wave spectrum to obtain the sea keeping behaviour o f a vessel in the particular sea state.

However, in the case o f high speed ships the motions and especially the vertical accelerations may be strongly

nonlinear with respect to the amplitude o f the incoming wave [ 1 ] . This means that the main assumptions behind the use o f RAOs (i.e. harmonic signals and linearity o f the system) are being violated. The RAOs derived fi-om high speed ships may therefore become invalid for determining the motion behaviour in irregular seas. A fijrther detailed discussion about the restrictions o f RAOs in the sea keeping analysis o f high speed ships can be found i n Keuning [2] and De Jong [13].

Although there are significant constrains in the applicability o f RAOs i n field o f high speed ships, it still remains an attractive tool for describing the motion behaviour in regular waves. This may be justified, at least for comparison or validation purposes, by the fact that the heave and pitch motions o f high speed ships in regular waves are still largely dominated by a harmonic response at the wave frequency.

2.0 1.6 1.2 0.8 0.4 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Figure 5: Comparison o f the heave response at 22 knots, at a constant wave steepness o f K = 1/30

o)(L/g)'

Figure 6: Comparison o f the pitch response at 22 knots, at a constant wave steepness o f K: = 1/30

The vertical accelerations o f a fast ship are, i n contrast to the heave and pitch motions, characterised by a rather strong non-harmonic response, particularly f o r the more severe regular wave condhions. For these situations a strong peak occurs i n the acceleration signal at each wave encounter. These peaks cannot be captured by a harmonic approximation at the wave frequency. The RAOs w i l l therefore only give a partial description o f the vertical acceleration response for a large number o f cases.

To quantify the maximum values in the acceleration response signal, De Jong [13] introduced the so-called Response M a x i m u m Operator ( R M O ) which can be used supplementary to the conventional R A O . The maxima are determined by finding the peak value at every wave cycle in the (filtered) acceleration signal and these values are averaged over the total number o f wave encounters in the particular time signal.

I n Figure 7 the R A O and the R M O are plotted f o r both the measured as the calculated acceleration response. It can be seen that peaks i n the acceleration signal are most pronounced i n the middle wave frequency range. The peak values i n the high fi-equency range correspond very close to the amplitudes o f the harmonic signal. This may be explained by the choice o f having a constant wave steepness i n the motion analysis, resulting i n relatively small wave amplitudes at higher wave frequencies, which causes a more "linear" behaviour in that area. I n general, the computational results are i n good agreement w i t h the experiments, however i n the resonance region an overestimation o f the computed peak values is noticed.

5.0 4.0 .2» 2.0 1.0 0.0 • RAO - meas RAO-calc A RMO - meas RMO-calc 0.0 0.5 1.0 2.0 , 1 / 2 2.5 3.0 3.5 1.5 cü(L/g)'

Figure 7: Comparison o f the vertical acceleration response and the maximum acceleration peaks at 22 knots, at a constant wave steepness o f K = 1/30

Figure 8 shows the dependence o f the maximum acceleration values with respect to the wave steepness. I t can be noted that a strong nonlinear relation exists between the wave amplitudes and the peak acceleration values. A t a wave steepness o f K = 1/60 the acceleration

peaks are virtually non-existent whereas the peaks at a wave steepness o f /c = 1/20 show a very strong increase i n magnitude. The results indicate a good similarity between o f the measured and calculated peak values. A n accurate prediction o f these peak accelerations is o f great importance since this determines whether or not the proactive ride control system has to intervene.

Figure 8: Comparison o f the maximum accelerations peaks and their dependence on the wave steepness

C O N T R O L S Y S T E M

To investigate the operability performance o f the current control method an extensive sea keeping analysis is performed w i t h the computational model i n head sea conditions. The main objective here was to quantify the performance increase o f the vessel and determine the influence o f various settings o f the proactive control system. I n this article the effect o f the individual and the combined use o f the control variables (thrust and/or transom flaps) w i l l be further elaborated.

The simulations i n irregular waves have been performed using a JONSWAP spectrum with a peak period o f 6.5 seconds and a significant wave height o f 1.5 meters. The prediction horizon i n these simulations equals 4 seconds and the succession o f the control cycles is performed at a 0.5 seconds interval. The threshold acceleration value at the bow location o f the vessel is set to 20 m/s^, which is typically the maximum peak acceleration accepted by the crew o f high speed ships [ 3 ] .

A short time trace o f the simulations is given in Figure 9. I n this figure a comparison is made f o r identical wave realisations between an uncontrolled benchmark simulation and a simulation w i t h the proactive control system. The inhial speed o f the vessel is 26 knots. A t approximately 9 seconds a large peak appears i n the acceleration signal o f the benchmark simulation that exceeds the defined threshold value. I n case o f the controlled simulation, the system anticipates on the wave

impact by actuating the transom flaps and reducing the thrust o f the ship several seconds prior the (predicted) wave impact. The initiated control actions reduce the impact i n such a way that it complies with the defmed threshold value.

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Figure 9: Comparison o f the time traces o f the benchmark simulation (blue line) and a simulation w i t h the proactive ride control system (red line)

The operability comparison is performed by analysing the statistical properties o f the vertical acceleration signal at the bow location o f the ship. A peak finding algorithm is used to extract the relevant rigid body accelerations f r o m the computed time traces. The algorithm identifies one maximum between two zero-crossings and discards any peak values lower than 10 % o f the standard deviation o f the signal. This procedure avoids the inclusion o f (most) local maxima, which are irrelevant for the operability assessment.

The counted peak values are used to construct a distribution plot that can be used f o r a graphical comparison o f the sea keeping behaviour. These so-called Rayleigh plots have a modified horizontal scale w h i c h presents Rayleigh distributed maxima as a straight line. Wave amplitudes are generally assumed to be Rayleigh distributed, which means that the maxima o f a linear response signal o f a ship can be indicated by a straight line i n the Rayleigh plot. A n y deviation f r o m this line indicates the existence o f nonlinear maxima i n the response signal o f the ship.

A Rayleigh plot containing the results o f four separate simulations is given in Figure 10. This figure presents the probability o f exceedance o f the vertical peak acceleration level at the bow location o f the ESC. The benchmark simulation is computed at a constant forward speed o f 26 knots. The second distribution gives the results o f a simulation with the proactive system using only the thrust control variable. The distribution curve clearly shows a reduction o f the maximum values, but at the same time the speed o f the vessel drops to an average o f 22.7 loiots. The third distribution indicates the results o f the proactive system with only the flap control variable. Again, a reduction in the peak accelerations in noticed, but for this case the vessel maintains hs initial speed o f 26 knots. The final distribution presents the outcome o f the simulation using a combination o f the two control variables. A fiirther reduction o f the maximum acceleration values is achieved, while the average forward speed is only slightly lower compared to the benchmark simulation.

limit o f the simulation model ( F r y = 1-6) or insufficient time was available to decelerate.

The significant value o f the acceleration signals are indicated by the intersections w i t h the vertical line at approximately 13.5 % i n the Rayleigh plot. I t can be noted that the significant value o f the simulation w i t h the proactive control system is more or less equal to the significant value o f the reference run at 26 knots. However, a large difference i n the distributions curves can be seen for the more extreme acceleration values with a low probability o f occurrence, i.e. at the right hand side o f the Rayleigh plot. I n this region, the acceleration level o f the controlled simulations is substantially reduced. The extreme acceleration values i n the distribution are even lower than the ones i n the reference run at 18 knots, while the average speed o f the controlled simulation is just above 25 laiots.

For the construction o f these distributions approximately 1800 counted peak accelerations are considered, which corresponds to a simulation time between 3300 and 3600 seconds dependent on the average forward speed o f the ship i n the simulation.

26 kn A benchmark, V = 26.0 kn A thrust, V = 22.7 kn A f l a p , V = 26.0 kn thrusts flap, V = 25.1 kn 50 20 10 5 Prob. of Exceedance [%] 0.1

Figure 10: Rayleigh plot indicating the effect o f the proactive control system w h h one or two control variables in relation to the benchmark simulation

3.4 ASSESSMENT OF T f l E O P E R A B I L I T Y

Figure 11 presents the distribution o f the vertical accelerations o f the proactive simulation with both control variables together w i t h the results o f three reference runs at a constant forward speed. I t can be seen that the proactive control system is able to reduce most o f the peak accelerations to such an extent that it meets the defined threshold value. Only i n a f e w rare cases the threshold value is exceeded. I t was observed, at closer inspection o f the time traces, that f o r these specific shuations the vessel had ehher reached the lower speed

50 20 10 5 Prob. of Exceedance l%]

Figure 1 1 : Rayleigh plot indicating the exceedance o f the vertical peak accelerations with the proactive control system i n comparison w i t h three reference simulations at a constant forward speed o f 18, 22 and 26 knots

4. C O N C L U S I O N S

It may be concluded, based on the computational results presented i n this article, that the proactive control strategy can significantly improve the sea keeping behaviour o f relatively small and fast ships. The proactive ride control system is able to reduce the extremes i n the vertical acceleration signal while a high average forward speed o f the ship can be maintained. I t is found that the combined use o f proactive thrust control and proactive transom flap actuation leads to a higher operability performance, i n comparison w h h the cases i n which only one o f the two control variables was applied. I n addhion, a feasibility study was initiated to determine i f the proactive control method would be a viable approach in a physical (experimental) environment. The validation study demonstrates that the prediction model

is well able to predict the magnitude o f the vertical peak accelerations i n waves. Moreover, it was shown that the computational speed o f the simulation program has now reached a level w h i c h enables real-time application o f a proactive control method.

A C K N O W L E D G E M E N T S

The author wishes to thanlc the partners i n the consortium, D e l f t University o f Technology, M A R I N , Damen Shipyards, Bureau Veritas, L l o y d ' s Register, Quantum Controls, Imtech Marine Netherlands and the Dutch Ministry o f Defence f o r facilitating this research and their willingness to allow publication o f the results. R E F E R E N C E S

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