"---" ""-' "'- OTC Wave Direction Feed-Forward on Basis of Relative Motion Measurements To Improve Dynamic Positioning Performance

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1 OTC 5445 Wave Direction Feed-Forward on Basis of Relative Motion Measurements To Improve Dynamic Positioning Performance by A.B. Aalbers and U. Nienhuis, Maritime Research Inst. Netherlands Copyright 1987 Offshore Technology Conference This paper was presented at the 19th Annual OTC in Houston, Texas, April 27-30, to copy is restricted to an abstract of not more than 300 words. The material is subject to correction by the author. Permission ABSTRACT A method is described which may improve the dynamic positioning of large ships in wind and waves, especially in case of non-parallel wind and wave directions. The proposed method applies the measurement of relative motions at two opposite side locations to estimate the wave direction and the wave drift force level. Combination with the wind measurement leads to an optimum heading set-point. The potential improvements are illustrated by results of tests and dynamic positioning simulations. INTRODUCTION Dynamic p~itioniny; The offshore industry is making use of a growing number of dynamically positioned ships, e.g. for diving support, supply, drilling and in the near future for production (the BP SWOPS vessel). This growth reflects the appreciation of operational flexibility which is characteristic for dynamic positioning. Furthemore, the positioning accuracy which can be achieved by dynamic positioning is sufficient activities like diving pipeline burial by means of gravel dumping etc. The advantages of dynamic positioning have to be considered in view of the capital expenditure and fuel consumption of a dynamic positioning system. These costs are related to the fact that the complicated dynamic positioning control systems are still crude the thruster that is needed to stay on position. Two typical problems should be mentioned (see Fig. 1): The position filtering system, which gives a "best estimate" of the position error with respect to the set-points, suffers from phase lag. Due to the inertia of the ship, the position measuring system measures position changes due to forces on the ship some time ago. References and illustrations at end of paper. Since the "best estimate" of position error is fed into the PID-controller (feed-back system) and thrust allocation is based on the "current" force estimate of the position filter the two above problems lead the that the ship's DP is late in its reaction environmental In many cases the consequence is Over-dimensiOning thrusters and high Sumpti0n. Research efforts in recent years are aimed at methods to obtain an earlier assessment of the forces acting on the ship and on methods to find optimum headings for the ship. In this respect it should be realized that the relative importance of the environmental forces depends on the size of the ship. "---" ""-' "'- Dynamic ~ositionin~for lar~ shies Whereas wind forces are the major environmental force on relatively small ships such as diving support vessels or supply boats, the wave drift forces are the dominant forces on large vessels. In open sea the currents are usually low and nearly constant. Wind and wave drift forces are slowly varying forces which require varying thruster response. Dynamic positioning will if a good, time, estimate these can be in the The low frequency drift force variations are described in Ref. [l] and [z]. For large ships the ma nitude of the variations may be considerable Ref. [37. a large ship is dynamically posi'cinned, it is expected that applying a method to incorporate the drift forces in the control system will improve the positioning* Especially because the phase b g and feed-back properties of a conventional DP system a large ship a large hertia momentum under the influence of wave drift forces before the position error is detected. When finally thruster activity to restore position starts, much power may be required. The relatively high magnitude of the drift forces on a large ship will cause additional problems for the dynamic positioning if the wind and wave direction are not parallel. Ori eatation of tfie ship on wind direction will lead to large wave drift

2 2 IMPROVED DYNAMIC POSITIONING OTC 5445 forces (see Fig. 2) when a high wave group passes. In that case the heading may become even more unfavourable and drift-off is likely to occur "Feed-f orward" methods The methods which are utilized to incorporate an environmental force estimate with minimum or zero delay into the dynamic positioning control are called "feed-forward" methods. The name is chosen to make clear the difference with the "f eed-back" method of position error estimate in conventional Systems. For instance, wind "f eed-f orward" implies the utilization of wind measurement in the thrust allocation and in the Kalman filter assessment of position error with respect to the set-points. The heading set-point is chosen close to the mean wind direction in order to reduce the wind loads. On small ships this method proved to be a significant im rovement and finds general application (see Ref. l471 - Feed-forward methods for wave drift forces have been proposed in publications (see Ref. [5]), but have not yet been put into action on ships. The reason is that it is relatively simple to measure wind direction and wlnd speed on a ship, but measuring wave drift forces is not so straight forward. In the present paper a method will be discussed to incorporate one important aspect of the wave drift forces into a DP system: the wave direction. The method is used to estimate the ship heading which is the optimum in the wind and wave conditions present. WAVE DIfillCTION FEED-FORWARD METHOD board side of the ship respectively. The results of this investigation will show that from these two probes a relatively accurate estimate of wave direction and a reasonable estimate of the wave drift force level can be obtained. Application of only the wave direction information in a "feed-forward" mode will basically lead to a heading set-point for. the ship at which the wave drift forces are at minimum. This is, however, insufficient in conditions with non-parallel wind and waves. Combination with wind "feed-forward" is needed to find and optimum heading and this requires an estimate of the drift force level to be compared with the wind force. The principles of the method are given in the following: The irregular relative motion time trace s(t) at the side of a ship may be described as a sun of regular oscillations with independent phase and frequency: 1. The relative motion spectrum is denoted Ss(w) the spectral density is given by: and It is assumed that the relative motion response functions measured at the two opposite locations on the ship's sides are similar in shape and may be expressed as follows (in which 1 stands for starboard side and 2 stands for port side). S (U) = A(1-11 (U) (5) 'a a This is illustrated in Fig. 3. The factor A(p) depends on the wave direction p The relative motion spectra differ by a factor A(c()' because: In Ref. [l] a detailed description of the wave drift forces is given based on t pressure integration theory. The drift forces F a ship follows from the second order press~~::n~('y in the fluid around the under water hull (S) of the ship. F(2) = -p // p(2) 5. ds (1) S The major contribution to the drift forces is due to the relative motions around the ship. Its magnitude is found by integrating along the waterline (WL) of the ship the low frequency part of the relative motion squared : This particular aspect may be used in a "feedforward" method. A good estimate of the wave drift forces, however, requires the use of many measurement locations for the relative motion in order to perform the waterline integration. For instance, in Ref. [S] model tests are described in which eight measurement locations were chosen. Wave direction feed-forward As a first step in the development a method is considered to apply the wave direction information in "feed-forward" mode. A much simpler measurement system is possible, involving only two relative motion wave probes positioned at the port and star- According to eq. (4) the relative motion amplitudes in the sum of sinussus representation of to eq. (3) differ by a factor A(p). The estimate of the level of the wave drift forces and of the direction of the waves with respect to the slowly yawing ship will have to be a real time value. 13y applying a real time low pass filter to the relative motion squared, the low frequency real time estimate is obtained. This filtering procedure will not introduce any appreciable phase lag in the low frequency estimate since the relative motion squared signal consists of a low frequency part which is well separated from the high frequency part. This will be shown by the following: 2 S (t) = {t SilY2 Cos(uit + Ei)12 = 1,2 i l = C C-S 2 i1,2 sj1,2 cos{(u -U )t + (E$-E~)] C i j i j Hence, the real time low pass filter applied on the relative motion squared is approximately equal to the low frequency component of eq. (7): -LF

3 1 The ratio of the starboard and port side signals is: 1 C C-S, 2 il 'jl cos{(w -U )t + (Ei-cj)} i j X c-s 1 i2 sj2 COS{(~~-U )t + (E~-E~)) i j j The factor ~~(1.1) depends on the heading of the ship on the waves and if the logarithm is taken an antisymmetric relationship follows. A reasonable estimate of the level of the drift forces follows from the real time low pass filtered sum of the relative motions squared. Hydrodynamic investigations will be necessary to establish the proportionality coefficients. In practical applications the real time low pass filtering will not be perfect. This may result in un-economic thruster activity. The wave direction and drift force estimates should therefore be smoothed and be used in combination with similarly smoothed wind data to calculate the optimum heading set-point. This smoothing may be done in an averaging process over a time At which is in the order of a few wave periods. The feasibility of the wave direction "feedforward" method on basis of relative motion measurements will be illustrated in the discussion of the results of some experiments and computer simulation~. Answers are required to the questions: - Is the relative motion measurement a good indicator for the wave direction and how well can the wave drift force level be estimated. - Will the method of wave direction l'feed-forward" improve the dynamic positioning. Since there is a strong contribution of the waterline integration of the relative motions squared in the drift forces, it is realistic to assume that the drift forces acting on a ship are lowest if the ship is heading into the waves. It is on basis of this assumption that DP improvement is expected from applying the wave direction "feed-forward" method. RESULTS Wave direction estimate The quality of the method of estimating the wave direction from two relative motion measurements depends on the magnitude of the variation of the with the wave direction p* Since the '(P) ship is preferably heading into the waves, the relative motions will be largest near the bow. On the other hand, the diffraction effects which lead to the differences between weatherside and leeward side relative motions will not appear if the measurements are too close to the bow. For a large type of ship the relative notions at Station 19 were investigated. In Fig. 4 the function A(y) was established by taking the average ratio of the response function for the relative motions. In the figure also the standard deviation of the A(y) values over the frequency range of operational wave conditions (0.5 ( w ( 1.0 rad/s) is given. Although the results obtained for Afg) are crude, the variation with wave direction is clear. It should be noted that for other measurement locations the function A(u) may be different. The results for lower wave frequencies appeared to be strongly affected by the ship's roll motions and could not be used for wave direction estimate. This means that the function A(y) not only depends on measurement location but also on ship natural roll period. If the ship shows resonant roll behaviour in the operational wave conditions for dynamic positioning, the method will probably not be feasible but on the other hand operations will probably also be impossible due to the roll motions (see for instance Ref. [7]). Relative motion contribution to drift forces A short model test program has been carried out to illustrate that the relative motions at a ship are indicative for the wave drift forces acting on it. It concerns a drillship in head waves. The relative motion measured at the bow (squared and low pass filtered) was used to steer a constant tension winch connected to the bow. It was expected that the winch action would considerably reduce the low frequency surge motions of the model in waves. This was tested in an irregular wave condition corresponding to a Beaufort 8 condition on the North Sea. The test set-up is sketched in Fig. 5. The model is initially moored between soft springs. In Fig. 6 the standard deviation of the measured surge motions is plotted as a function of the gapn setting of the constant tension winch used to supply the mooring force at the bow. In Fig. 7 a typical time trace of the surge motion without and with optimum winch action is shown. The surge standard deviation could be reduced to 50% of the vaue measured in the same wave condition without winch action. The result indicates that a strong relation exists between the relative motion at the bow and the surge wave drift force. This supports the working hypothesis for the wave direction "feed-forward" method that the relative motion measurement near the bow may serve as a reasonable indicator for the drift force level. I Wave direction feed-forwe 227 The wave direction "feed-forward" method was incorporated in the dynamic positioning simulation program DPSIM available at WIN. The features of the program have been described extensively in Ref. [6] and [7]. The method to incorporate the wave direction "feed-forward" in such a way that it can be combined with wind "feed-forward'' is below* In the computer program the instantaneous value of the wave drift force, its direction and of the wind force and its direction are available. These are the "trueff values which are kransfohned to "estimated" values by applying a random error.

4 IMPROVED DYNAMIC On basis of the standard deviations in A(p) for wave directions close to head-on, it is realistic to assume that the relative motion measurement in DP conditions will be able to indicate the wave direction with 10 degrees accuracy. On basis of the calculations given in Ref. [l] it can be illustrated that the relative motion mesurement will be able to estimate the drift force level with an accuracy of 50% or better. This may be further improved if detailed hydrodynamic investigations for the ship are available. The estimated wave direction and force level was used to estimate the yaw drift moment and the longitudinal and transverse drift force. hst(wave) m I.'true F( 2) y est * RND(1) in degrees = ~(~)*(0.5 + lu?d(l)) Y Similar relations hold for the estimated wind forces. The moments and transverse forces due to wind and waves are used to estimate an optimum heading. The set-point value for the heading is then fed into the control system under the requirement of smooth transition. The update time At of the heading set-point is chosen at 20 seconds (which is several wave periods) to simulate the effect of the time delay in the real time low pass filter systems. Per dynamic positioning time step AT (typically 4 seconds) a maximum increment condition is introduced in order to have a smooth transition to the new heading. {set-point p(t-~t)}-{set-point p(t)} <max. increment (AtIAr) Dynamic positioning simulations were carried out for three ship types, i.e. a large tanker, a drillship and a supply boat. The selected sea condition was typical for a Beaufort 8 condition on the North Sea with 4.5 m significant wave height and 8.3 seconds average wave period. Wind and waves make a 40 degrees angle. The ships will try to keep the midships at the reference position. For each ship 3 dynamic positioning simulation runs were made with the following "feed-forwardrr applications: A. wave direction "feed-forward" (optimum) B. heading set-point into the wave direction C. heading set-point into the wind direction For the tanker also DP simulations were made for a 20 degrees angle between the wave and wind directions. In Table 1 the results in terms of statistical quantities are shown and in Fig. 8 through 10 plots are given of the DP simulations for the large tanker. The results may be characterized as follows: For the large tanker The wave drift forces are dominant and the results show that for A and B the dynamic positioning is better than for the case C. For the conditions with 20 degrees angle between the wave and wind direction the three cases stay on position. However, when the angle between the wave and wind direction is 40 degrees, the case A cannot stay on I POSITIONLNG GTC 545 Position. As shown in Fig. 10 the heading is lost under the influence of the unfavourable wave direction and the ship turns almost 180 degrees. In that orientation the loads are so much reduced that the reference position can be approximated, although at a large heading off-set. For the drillship For this type of ship the wave drift forces and wind forces are of the same order. The results show that for the cases A and B the dynamic positioning is better than for case C. For the supply boat A small ship is more affected by the wind than by the wave drift force. The results show that dynamic positioning for cases A, B and C is almost equivalent. When considering the above results, ft should be kept in mind that the dynamic positioning simulations did not include the effect of current. Furthermore, in practical applications preference will be given to the wave direction "feed-forwardr' above a heading set-point into the waves, because the latter may be very unfavourable in case of relatlvely high wind speeds. CONCLUSIONS A method for improvement of dynamic positioning by means of wave direction "feed-forward" has been investigated as to its feasibility. The wave direction "feed-forward" is based on measurement of the relative motions at only two locations on the ship. The results of model measurements and calculations indicate that it is basically possible to estimate the wave direction and to obtain a reasonable estimate of the wave drift force level from the relative motion signals. This data is combined with wind data to estimate an optimum heading set-point for dynamic positioning. DP simulations were carried out for a Large tanker, a drillship and a supply boat in wind and waves corresponding to a Beaufort 8 condition on the North Sea. Comparing the results for the three ships the general conclusion is that the wave direction "feed-forward" method, resulting in an optimum heading set-point is an improvement for all ship types but is not considered necessary for a small ship provided with a wind "feed-forward" system. The improvement in this respect is that the method may reduce the required thruster power and may improve the positioning accuracy. For quantification and design further hydrodynamic investigations will be necessary. REFERENCES 1. Pinkster, J.A.: "Low frequency second order wave exiting forces on floating structures", Ph.D. Thesis, Technical University Delft, Hooft, J.P.: "Advance dynamics of marine structures", Wiley Intersience, New York, ISBN , Davison, N.J. et. al: "A study of the hydrodynamic factors influencing the workability of the SWOPS vessel", WEMT Conference, Amsterdam, Balchen, J.G., Jenssen, N.A., Mathisen, E. and S2lid, S.: "A dynamic positioning system based on Kalman filtering and optimal control", Modeling, Identification and Control, Vol. I, No. 3, pp , 1980.

5 5. Pinkster, J.A.: "Wave feed-forward as a means to improve dynamic positioning", Proceedings 10th OTC, Paper No. 3057, Houston, Nienhuis, U.: "Simulations of low frequency motions of dynamically positioned offshore structures", RINA spring meeting, Paper No. 7, London Aalbers, A.B., Dallinga, R.P. and Nienhuis, U. : "Computer prediction of the workability of dynamically positioned diving support vessels", ASME Conference "Current practices and New Technology in Ocean Engineering", New Orleans, TABLE 1-RESULTS OF THE DP SlMULATlONS Initial directions Standard dev. *l Thrust requirements (st.dev. and range f Ship type Heading set-point Posi- Wind Waves tion Heading Longitudinal Transverse Yaw moment radius in deg. in deg. in m in deg. in tf in tf in tfm Tanker ' Optlmum Tanker Intowaves Tanker Into wind *-*"---. " Tanker Optimum Tanker Intowaves Tanker Into wind *.,--* Drillship Optimum Drillship Into waves Drill ship Into wind _ dd-d---ii *--- Supplyer Optimum Supplyer Into waves Supplyer Into wind

6 \ 1 AFTER PASSAGE OF A HIGH WAVE GROUP: THRUSTER THRUST ACTION I I ALLOCATION U Fig. I--Schematic representailon of DP system. Fig. 2-illustration of DP problema for a large ship in non-parallel wind and waver. 4 DIFFRAC CALC. (HEAN and ST.DEII o MODEL EXPERIMENT WAVE FREOUENCY I 1 I l t I WAVE DIRECTION OFF BOW IN DEG. Fig. 3-Relative motion reaponse at opposlte locationson the sldeof alarpe 8hlp for r wave dlr*ctian 45 degrees off the bow. Fig. 4-Calculated and measured values for lunction Ilfrf, AT CONSTANT VALUE 0 SPRINGS r C.T. WINCH AT STEERED VAlUE Fig. 5-Mooring satup for tests with a drillship model. I I I I I I I GAIN SETTING FOR WINCH STEERING - Fig. 6-The effect of C.T. winch steering on the surge motion of S driftship model In head waves.

7 WAVE SURGE YITH FEED-FORWARD" TIME IN S I I Fig. 7-Surge motions of drillship model without "feed-forward" and with optimized "feed-forward" surge positioning control. iy WAVE DIRECTION "FEED-FORWARDn Fig. 8-Plot of tanker position during DP simulations; wave direction "feed-forward" method.

8 I HEADING SET-POINT INTO THE WAVES Fig. 9-Plot of tanker position during DP simulations; heading set-point into the waves. I HEADING SET-POINT INTO THE WINO Fig. 10-Plot of tanker position during DP simulations; heading set-point into the wind.