Predicting the capability-polar-plots for dynamic positioning systems for offshore platforms using artificial neural networks

Transcription

1 Ocean Engineering 34 (27) Predicting the capability-polar-plots for dynamic positioning systems for offshore platforms using artificial neural networks Ayman B. Mahfouz Department of Naval Architecture and Marine Engineering, Faculty of Engineering, Alexandria University, P.O. Box 21544, Alexandria, Egypt Received 31 January 26; accepted 1 August 26 Available online 13 November 26 Abstract As the capability of polar plots becomes better understood, improved dynamic positioning (DP) systems are possible as the control algorithms greatly depend on the accuracy of the aerodynamic and hydrodynamic models. The measurements and estimation of the environmental disturbances have an important role in the optimal design and selection of a DP system for offshore platforms. The main objective of this work is to present a new method of predicting the Capability-Polar-Plots for offshore platforms using the combination of the artificial neural networks (NNs) and the capability polar plots program (CPPP). The estimated results from a case study for a scientific drilling vessel are presented. A trained artificial NN is designed in this work and is able to predict the maximum wind speed at which the DP thrusters are able to maintain the offshore platform in a station-keeping mode in the field site. This prediction for the maximum wind speed will be a helpful tool for DP operators in managing station-keeping for offshore platforms in an emergency situation where the automation of the DP systems is disabled. It is obvious from the obtained results that the developed technique has potential for the estimation of the capability-polar-plots for offshore platforms. This tool would be suitable for DP operators to predict the maximum wind speed and direction in a very short period of time. r 26 Elsevier Ltd. All rights reserved. Keywords: Offshore safety; Artificial neural networks; Aerodynamics; Hydrodynamics; Dynamic positioning systems (DPS); Floating, production, storage and offloading (FPSO); Tunnel thrusters; Azimuth thrusters; Marine vessels; Floating production units; Environmental forces; Wind forces; Current forces; Wave drift forces; Capability polar plots program (CPPP) 1. Introduction Dynamic positioning systems (DPS) consist of three primary units: the sensors unit, the control and monitoring unit, and the actuators unit. The sensors unit includes the position and heading sensors and wind sensor. Information from these sensors is processed in the control and monitoring unit that produces the required control signals to the actuators unit. The actuators unit develops the required thrust and direction for each actuator among the thrusters configuration with respect to the surge and sway axis (see Fay, 199). A DPS is an essential requirement for offshore platforms and in many offshore platform operations, especially in deepwater production/storage units, in order to maintain addresses: abmmahfouz@yahoo.com, abmmahfouz@gmail.com (A.B. Mahfouz). desired position and heading in the presence of environmental disturbances from wind, waves, and current. Offshore platform operations include floating production unit operations, drilling, anchor handling, and cable and pipe laying. Over the last four decades dynamic positioning (DP) in deepwater has been used in the marine sector, oil and gas industries, and military services in many tasks such as drilling, oil and gas floating production platforms, cable and pipe laying, docking and towing, fire fighting, supply, search and rescue, surveying, and mobile offshore bases (MOB). Each of these operations benefits from a DP system s ability to include precise position-keeping, freedom from the restrictions of mooring spread systems, the ability to move quickly from one site to another, and trackkeeping capabilities. The main objective of this paper is to describe the development of a robust tool that is able to predict the /$ - see front matter r 26 Elsevier Ltd. All rights reserved. doi:1.116/j.oceaneng

2 1152 ARTICLE IN PRESS A.B. Mahfouz / Ocean Engineering 34 (27) maximum wind speed for station-keeping of the offshore platform in filed sites in emergency cases where the automation of the DP systems is disabled. The development of such tool is based on the combination of the artificial neural networks (NNs) and the Capability Polar Plots Program (CPPP). The new tool is able to estimate the capability polar plots for offshore platforms and floating production units for oil and gas industries. The paper is logically organized in distinct sections. The estimation for the environmental forces and moments due to wind, current and drift waves is presented in Section 2. The thruster forces and moments estimation are presented in Section 3. CPPP is described in Section 4 and the developed artificial NN is presented in Section 5. The outputs of using the developed tool for a case study for a scientific drilling vessel are presented in Section 6. Finally, discussion and the main conclusions of the obtained results are given in Section Environmental forces and moments The environmental forces and moments acting on a vessel arise from three main components: wind, wave drift, and current loads with particular directions as shown in Fig. 1. Each individual component produces steady-state displacements in the x- and y-axis and a turning moment about the z-axis. The force and moment due to each component are evaluated individually and summed to evaluate the total steady-state disturbing forces and turning moment (see API, 1987). The total forces and turning moment will displace the vessel away from its required position. The vessel will surge and sway about the x- and y- axis and yaw about the z-axis. These displacements and rotation in the horizontal plane should be prevented. Therefore, a system that can prevent these movements especially in deep-water operations is required. This system is called DP. The first step in designing an efficient DP system is to estimate the environmental forces and turning moments acting on a vessel since the thruster types and locations should be selected to counteract these forces and moments. The environmental condition must be defined before designing a dynamic position system and is dependent on the site of drilling/survey operation, sea state, wind and current velocities and directions. The total steady environmental forces and turning moments on dynamically positioned offshore platforms are generally computed from the sum of the individual components of the wind, wave, and current loads (see MPT/OPL, 2). The calculations for each individual component are briefly given in the following sections Wind forces and moments The wind force on a marine vessel is proportional to the projected area above the waterline and square of the wind speed. Close attention must be paid in the calculations of the projected area subjected to wind. The projected area should include all columns, deck members, deckhouses, derrick structure, drilling derrick, truss members, and crane booms as well as the portion of the hull structure above the waterline. In short, all areas above the waterline that are subjected to wind must be included in the total projected area. The structure above the waterline that is exposed to wind is subdivided into elements for which wellestablished aerodynamic drag coefficients exist. This is known as the building block approach. The total wind force on the vessel is computed as the sum of elemental Fig. 1. Environmental forces on a marine vessel.

3 A.B. Mahfouz / Ocean Engineering 34 (27) forces as shown in the following equation (see API, 1987): X N e F wind ¼ C w ðc si C hi A i ÞV 2 wind, (1) i¼1 where F wind and V wind are the wind force in N and wind speed in m/s, respectively; C w, C si, and C hi are wind coefficient ¼.615 N s 2 /m 4, shape coefficient for each element, and height coefficient for each element, respectively. A i and N e are the vertical transverse or longitudinal projected areas of the building blocks and the number of the building blocks, respectively. Subsequently, the wind forces in the transverse and longitudinal directions, F WX and F WY, respectively can be determined. Therefore, the total wind force for a given wind direction with respect to the positive x-axis, g, can be determined from the following equation (see API, 1987): F g W ¼ F 2 cos 2 ðgþ 2 sin 2 ðgþ WX 1 þ cos 2 þ F WY ðgþ 1 þ sin 2. (2) ðgþ The components of the wind force in the body coordinates of the vessel can be determined from decomposing the wind force, F g W in the x- and y-axis as follows: F wx ¼ F g W cosðgþ, (3) F wy ¼ F g W sinðgþ. (4) The turning moment due to wind force components is determined by multiplying these components by the perpendicular distances between the centres of the transverse and longitudinal projected areas and the centre of rotation (COR). The positive moment is in a clockwise direction while the positive force is in the direction of the ship s body axis. Although this approach is well known, wind tunnel tests and scale-model tests are used to identify the wind coefficient (wind force/speed 2 ) for the majority of floating structures. Two main parameters have significant influences on the model test results for full-scale forces: height of the block above 1 m level and scale effects. The height coefficient is used for the blocks above this level since the wind speed increased above this limit. The scale effect (Reynolds number) on scale-model tests has great significance on scaling the operating location. Certain elements on the vessel such as circular semi-submersible columns and derrick tubulars should be scaled with more attention (see MPT/OPL, 2) Wave drift forces and moments The horizontal components of the mean and lowfrequency second-order wave forces are known as the drift forces. The free vessel will drift in the direction of the wave propagation and possibly a change of heading by the effect of the drift forces. The drift forces are much smaller than wave forces that excite surge and sway response. Although the main drift forces are smaller than the wave-exciting forces, it may still contribute significantly to the total environmental forces. Therefore, the drift forces influence dynamically positioned vessels, which remain stationary in a particular operating position by actuators. In irregular sea, the drift force includes components with frequencies close to the natural frequencies of the horizontal motions (surge, sway, and yaw) that will lead to large amplitude resonant behaviour of those motions (Pinkster, 198; Standing et al., 1981). Wave drift force in regular waves consists of four main components: relative wave height component, pressure drop due to speed square, pressure due to gradient of firstorder pressure, and first-order motion, and component due to first-order inertial force and first-order rotation. It has been found that the contribution of relative wave height is dominant (see Hooft, 1982). Therefore, the wave drift force at a given wave frequency is proportional to the square of the wave height. The force is reduced with increased wave periods tending to zero at long wave periods (MPT/OPL, 2). In this work, the main contribution due to wave height component is considered for the calculations of the wave drift force in irregular sea. Wave drift forces are calculated either from the wave diffraction theory or from scale-model tests. These forces are less well understood and less easy to predict than firstorder forces. Great attention must be taken when carrying out scale-model tests in the wave tank since the forces are small and can be extremely sensitive to the wave-exciting spectrum (Standing et al., 1981). An estimate of the wave mean drift force in regular and irregular waves can be adopted when the mean drift force coefficients are unavailable as given in (MPT/OPL, 2): Regular waves: F drift ¼ 1 2 rgbz2. (5) Irregular waves: F drift ¼ 1 2 rgbð1 8 H2 s Þ, (6) where r, g and B are the mass density of water, acceleration of gravity, and the breadth of the vessel, respectively. H s and z are the significant wave height and the regular wave height, respectively. The water plane of the vessel exposed to waves is subdivided into segment elements for which the mean drift force can be computed. Then, the total mean drift force acting on the vessel is computed as the sum of elemental forces. In addition, the total turning moment due to mean drift force is calculated as the sum of the moments of the elemental forces around the COR Current forces and moments The current acts on the underwater part of the ship by means of drift force and a turning yaw moment. Scalemodel tests are mainly used for estimating the forces and moment due to current with different velocities and

4 1154 ARTICLE IN PRESS A.B. Mahfouz / Ocean Engineering 34 (27) directions. The scale effect (Reynolds number) on the model test results has great significance on the scaling at the operating site. Therefore, it is an essential requirement in carrying out successful model tests to map the operating location to the wave tank. As with the wind force calculations, all areas under the waterline that are subjected to current have to be included in the total wetted surface area. The underwater part of the ship exposed to current is subdivided into elements for which well-established hydrodynamic drag coefficients exist. Then, the total current force on the drilling unit is computed as the sum of elemental forces. Additionally, the total turning moment due to current is calculated as the sum of the moments of the elemental forces around the COR. The formula used to calculate the force and turning moment due to current are shown as follows (see Fay, 199): F cx ¼ 1 2 rs xc x ðyþv 2 c, (7) F cy ¼ 1 2 rs yc y ðyþv 2 c, (8) M c ¼ 1 2 rs ylc c ðyþv 2 c, (9) where r and L are the mass density of water and ship length. S cx and S cy are the vertical transverse and longitudinal cross-sections subjected to water current. C x (y), C y (y), and C c (y) are the dimensional hydrodynamic drag coefficients. V c and y are current speed and the direction of approaching current with respect to the positive x-axis, respectively. The values of the hydrodynamic drag coefficients depend on the shape of the hull and the direction of approaching current with respect to the positive x-axis. Approximated values for the drag coefficients for any new projects are given in reference (Fay, 199). The total steady environmental forces, F X and F Y, and total turning moment, M FZ, on a marine vessel are presented in Eqs. (1) (12). They are generally computed from the sum of the individual components of the estimated wind, wave, and current loads as described above F X ¼ XN E F Xj, (1) j¼1 F Y ¼ XN E F Yj ; (11) j¼1 M FZ ¼ XN E j¼1 M Ej, (12) where F Xj, F Yj, and M Ej are the environmental force components in x and y-axis and their turning moment components about z-axis, respectively. N E is the number of environmental force components, which are three (wind, current, and wave drift). 3. Thrusters forces and moments Two main types of thrusters are available for DP systems: steerable and non-steerable. Steerable thrusters include azimuthal thrusters, cycloidal thrusters, and jet thrusters. Non-steerable thrusters include thrusters with fixed or controllable pitch with or without a nozzel, jet thrusters housed in the hull, tunnel-mounted thrusters, and shaft-mounted propellers (Fay, 199; Morgan, 1978). The main function of the thrusters in DP systems is to develop the required forces and moments to counteract the environmental disturbance forces and moments acting on the vessel. The total steady counteracting forces, T X and T Y and total counteracting moment, M TZ, on a marine vessel are generally computed from the sum of the individual components of the estimated wind, wave, and current loads as described above T X ¼ XN T T Xi, (13) i¼1 T Y ¼ XN T T Yi, (14) i¼1 M TZ ¼ XN T M Ti, (15) i¼1 where T Xi, T Yi, and M Ti are the counteracting thrust forces in x and y-axis and the counteracting moment about z-axis for each thruster, respectively. N T is the number of thrusters in the DP system. 4. Capability polar plots program (CPPP) The capability polar plot of a given vessel is used to determine the operational serviceability limits for a DP system for the vessel. The capability polar plot presents the maximum wind speed at which the thrusters system is able to counteract the resulting effects of wind, current, and wave drift forces at a given wind direction and a specific current speed. A computer program called the CPPP was developed using MATLAB s to generate the capability polar plots for marine vessels (Mahfouz and El-Tahan, 25). The CPPP calculates the environmental forces and turning moments on the vessel due to wind, current, and wave drift at specific wind direction and constant current speed. The calculated individual environmental forces and turning moments due to wind, current, and wave drift are added together to determine the total environmental disturbances on the vessel. The total environmental forces and turning moments are compared with counteracting forces and moments developed by the thrusters configuration system in order to test the capability of the system taking into account thruster/thruster interaction, thruster/

5 A.B. Mahfouz / Ocean Engineering 34 (27) Thrusters Model Wind Direction Current Model hull interaction, thruster/current interaction, and dynamic effects allowance (Lough, 1985). These interactions are beyond the scope of the present work. The above procedure is repeated while increasing the wind speed by an increment of one knot until the equilibrium between the environmental forces and moments and those developed by the thrusters system is reached. A flowchart illustrating the logic and data flow of a developed software program, CPPP is shown in Fig. 2 (Mahfouz and El-Tahan, 24a,b). The CPPP searches for the maximum wind speed at which the thrusters configuration can counteract the disturbances of the environmental forces on the vessel, without overloading, at each wind angle from 1 to 361, with a wind angle increment of 11. This has been achieved through iteration. The capability polar plot, which is a relationship of the maximum wind speed at each wind angle from 1 to 361 at which the vessel can maintain station, can then be constructed and plotted at constant current speeds. 5. Artificial neural networks Wind Model Wave Drift Model Environmental Disturbances Model No IF EQUAL Maximum Wind Speed Wind Direction Increment IF > 36 STOP Wind Speed Increment Artificial NNs have been used extensively in the approximation modelling of dynamic systems. The most recent application is in the design of controller algorithms for these systems. In general, artificial NNs try to mimic the biological network. The present artificial NNs are Yes Yes No Fig. 2. Capability polar plot program (CPPP) flowchart. considered much simpler compared to the biological networks especially in the number of neurons, size, and construction complexity (Flood and Kartam, 1994). Multiple-linear regression algorithms may be used to estimate the parameters in a linear mathematical model; however, for a nonlinear model with a large number of independent parameters, the accuracy of the algorithm decreases. One of the limitations of using a multi-linear regression algorithm is that there is no control over the values that the method allocates to the different parameters in the model. For a multiple-parameter model, there is some sort of energy sharing between the different parameters. This sometimes results in a phenomenon where an estimated value of a parameter is larger than it should be, while the estimated value of another parameter decreases to compensate for the increase in the value of the first parameter. In general, research on artificial NNs models has a long history. Development of detailed mathematical models began more than six decades ago (Lippmann, 1987). Current interest in the field of artificial NNs is due to the vast development of new network topologies and learning and training algorithms. Due to the rapid growth in the range of alternative neural network systems, it is necessary that these systems be classified. This classification is based on four characteristics: data format, mode of operation, principal connection shape, and learning and training process (Flood and Kartam, 1994). The network topology, neuron characteristics, and training algorithms specify NN systems (Masri et al., 1993). Artificial NNs have been proven to be more successful as a robust tool for identification of discrete nonlinear control systems than conventional statistical techniques. This is because there are many more processing nodes, each with primary local connections. In an artificial NN, the outputs can feed back to the input layer to adapt its weights by using learning algorithms. However, the main current concern area in NNs is to improve the training algorithms. Since the conventional techniques typically process all training data simultaneously before being used with new data, strong assumptions have been made concerning underlying distributions of the input elements. On the contrary, these assumptions do not exist in the artificial NNs. This is because NNs have a large number of simple processing elements operating in parallel (Lippmann, 1987). Currently, artificial NNs are used in almost all branches of engineering. For example, in ocean, mechanical and civil engineering, artificial NNs are used in the modelling of dynamic systems such as ships and underwater robotic vehicles for both design and control strategies (Masri et al., 1993; Mahfouz, 21, 24; Mahfouz et al., 21). The use of the conventional controllers has been restricted by the difficulties in the mathematical modelling of dynamic systems working in hazardous environments. The emergence of NNs as an effective learning system for a wide variety of applications has resulted in the use of

6 1156 ARTICLE IN PRESS A.B. Mahfouz / Ocean Engineering 34 (27) these networks as learning controllers for dynamic systems. One of the most important advantages of using NNs for control applications is that the dynamics of systems being controlled need not be completely known as a prior condition for controller design. Masri used a NN in the identification of nonlinearity in a single-degree-of-freedom dynamic system (Masri et al., 1993). However, Haddara used NNs techniques successfully in the identification of the hydrodynamic parameters in the equations describing the coupled sway and yaw motions for a ship (Haddara and Wang, 1996; Haddara and Sabin, 1995). In addition, Haddara suggested a method, which is used as a part of continuous monitoring system to provide information about instantaneous values of ship stability. This method has been made by using the NNs technique to identify stability parameters (Haddara, 1995). Lainiotis has developed a comparison between the Kalman filter estimator and the NN one. The conclusion from this comparison is that the NNs estimator requires only very little information about the dynamics of the system compared to that required by the Kalman filter estimator (Lainiotis et al., 1993). Nevertheless, the performance of the conventional statistical techniques depends basically on the information about the possible variations of the unknown parameters. The prediction of the DC actuator position by using a NNs estimator is much better than that obtained by using a Kalman filter estimator in cases where the underlying statistics and dynamics of the system are not completely known to the estimator. The identification of the nonlinear dynamic systems has been done using two popular types of artificial NNs. These types are feedforward neural networks (FNNs) and recurrent neural networks (RNNs). RNNs are the networks with internal or external feedback in which the past system outputs are replaced by the past outputs of the network, while in FNNs, past system inputs and outputs are used as NN inputs. Any dynamic system can be modelled using FNNs with at least one hidden layer to any level of accuracy (Korbicz and Janczak, 1996). However, Flood suggested that FNNs with at least two hidden layers would provide a greater flexibility in the modelling of any dynamic system (Flood and Kartam, 1994). In the mean time Haddara obtained good results by using FNNs with one hidden layer in the modelling of dynamic systems. It is concluded that FNNs with one hidden layer is more efficient to model most dynamic systems (Mahfouz, 21, 24; Mahfouz et al., 21; Haddara and Sabin, 1995). Artificial NNs should be regarded as a complement part to conventional computing techniques. A NNs model reflects only the input output behaviour of a dynamic system regardless of the internal physical mechanism that reproduces the outputs. The artificial NNs approach does not require any assumptions about the internal structure of the system to be made (Flood and Kartam, 1994). The operating mechanism of the NNs can be easily understood by knowing the main concepts, construction elements and their functions in the network, and how these elements work simultaneously in the network. Ge et al. developed a friction compensation technique by separating the dynamic friction calculated by LuGre model into two parts: the viscous friction with unknown constant coefficient and the unknown, unmeasured dynamic friction, which is bounded by a function that is independent of the internal friction state. Then, the NN is used to approximate the unknown bounded function (Ge et al., 2). However, the separation of the dynamic friction into components may lead to inaccurate friction compensation, which leads to jerks and vibration in the response of the dynamic system. The maximum wind speed that the offshore platform can withstand in the field site is predicted using an artificial NN developed in this work. An artificial NN is able to create an approximate model without prior knowledge regarding the structure of the modelled phenomena as required by most of parametric identification techniques. The training procedure is based mainly on accurate learning of the dynamic behaviour of the harmonic drive actuator in several loading conditions and environments. A continuous record of the significant wave height in metre, current velocity in knots and direction in degrees and the estimated maximum wind velocity in knots is used to learn the behaviour of the offshore platform in different environments using artificial NNs. A multi-layer perceptrons (MLP) artificial NN is shown in Fig. 3. The network consists of two hidden layers in addition to input and output layers. The input to the network is a vector, which includes independent parameters [X 1, X 2, X 3 y X n ]. The output from the network is a vector, which includes dependant parameters, [Y 1, Y 2, Y 3 y Y m ]. The first and second layers have numbers of neurons K and L, and activation functions s and d, and bias U k and V l, respectively. Also, the output layer has activation function, r and a bias W i. The synaptic weights of the first and X 1 X 2 X n 1 U kj 1 σ 1 σ 2 σ K σ 1 V 1k W i1 j k l i Fig. 3. Multi-layer perceptrons (MLP) neural network. δ 1 δ 2 δ L δ ρ ρ Y 1 Y m

7 A.B. Mahfouz / Ocean Engineering 34 (27) second hidden layers and the output layer are U kj and V lk and W il, respectively. The counter of the neurons in the input, first hidden, second hidden, and the output layers are j, k, l, and i, respectively. The output vectors, Y i of the multi-layer perceptrons network is given in the following equation: " (! Y i ¼ r XL X K W il d V lk s Xn U kj X j þ U k )þ V l l¼1 k¼1 j¼1 þ W i #; i ¼ 1; 2;...; m. ð16þ The numbers of neurons, types of activation function, and training algorithms in each layer has been chosen based on the nature of the trained data sets collected from the dynamic system. The network is used to predict the maximum wind speed, which is an essential criterion for station-keeping for the offshore platform in the field site. Two hidden layers are chosen for the above network s structure. The activation function for these layers is chosen as tansh function which the output of each neuron squashed between 1. and +1.. Each hidden layer may consist of several neurons. In this paper, 33 neurons in each of the first and second hidden layers provide sufficient accuracy in the estimation of the required torque. The input to the network is a vector having the significant wave height, current velocity, direction, and a bias. The training algorithm of the network can be achieved using any optimization approaches such as back-propagation, Levenberg Marquardt, gradient-descent back-propagation, etc. Using an arbitrary starting set of weights, an initial value of the torque is obtained. The obtained value is compared to the actual target torque value. The difference between these two responses is the error. The synaptic weights are then updated and the process is repeated in an iterative fashion until the error in the response is minimized. The minimization procedure is achieved using the gradient-descent back-propagation algorithm. 6. Case study scientific drilling vessel Several case studies were investigated using the CPPP and the artificial NNs technique. An example of the results is presented for a case study of a scientific drilling vessel. The main objective is to develop a robust tool using artificial NNs to predict the maximum wind speed that the offshore platform can withstand in station-keeping mode in the field site. Additionally, the capability polar plots developed by the CPPP are to be presented and the effect of wind and current speeds on the polar plots propagation is to be investigated. The details of the drilling vessel are shown in Table 1. The number of thrusters, types, specifications and their locations with respect to COR are given in Table 1 and shown in Fig. 4. The thrusters configuration has four azimuth thrusters with a maximum deliverable thrust of 3.6 ton as given in the previous table. The main function of the thrusters configuration is to develop the required total counteracting thrusts and moments with minimum power consumption. The static equilibrium of the thrusters is based on the following equilibrium equations: T X ¼ F X, (17) T Y ¼ F Y, (18) M TZ ¼ M FZ, (19) 7.6 m Not to scale 25.1 m 23.1 m 3 4 L.O.A. = 53. m Fig. 4. Thrusters configuration for the drilling vessel. 1 2 Table 1 Particulars of the scientific drilling vessel Vessel name Drilling vessel LOA, length overall 53. m ft LBP, length between perpendiculars 52. m 17. ft B, beam 12. m ft T, draft 1.7 m 5.58 ft D, depth 2.6 m 8.53 ft Propulsor details Thruster number and thruster information Power Thrust Offsets (from COR +fwd +stbd) kw Hp (ton) X (m) X (ft) Y (m) Y (ft) 1: Bow AZ drive : Bow AZ drive : Stern AZ drive : Stern AZ drive

8 1158 A.B. Mahfouz / Ocean Engineering 34 (27) Table 2 Capability-polar-plot results Weather Thruster data Force Dir. (deg.) Mag (knots or m) Surge X force (kn) Sway Y force (kn) Yaw Z moment (kn m) Thrust No Thurst (%) Thrust (kn) Thrust dir. (deg.) X-thrust (kn) Y-thrust (kn) Z-moment (kn m) Wind Wave Current Total Wind Wave Current Total Wind Wave Current Total Wind Wave Current Total Wind Wave Current Total Wind Wave Current Total CPPP-. knots CPPP-1. knots CPPP-2. knots CPPP-3. knots CPPP-4. knots 27 Wind Speed, knots Draft=1.7 m CPPP-Actual Fig. 5. Capability-polar-plots for using CPPP.

9 A.B. Mahfouz / Ocean Engineering 34 (27) Solving Eqs. (17) (19) provides the required thrust and direction for each thruster. The tabulated polar plots results are shown in Table 2. The CPPP searches for the maximum wind speed at which Eqs. (17) (19) are valid. The maximum wind speed is then plotted with respect to the wind direction and the results are shown in Fig. 5. In addition, the effect of the current speed on the capability polar plots propagation is investigated as shown in the previous figure. 7. Discussion and conclusions A MATLAB s software program entitled Capability Polar Plots Program (CPPP) was developed to estimate the 3 6 NN-. knots NN-1. knots NN-2. knots NN-3. knots NN-4. knots 27 Wind Speedknots, Draft = 1.7 m NN-Prediction Fig. 6. Capability-polar-plots using NN. 3 CPPP-Actual NN-Prediction 6 27 Wind Speed, knots Draft = 1.7 m Current Velocity=. knots Fig. 7. Predicted capability-polar-plots using NN [V c ¼ : knots].

10 116 A.B. Mahfouz / Ocean Engineering 34 (27) environmental disturbances on offshore platforms due to wind, current, and wave drift and the estimation of the required counteracting thrusts and moments. The CPPP searches for the maximum wind speed at which the equilibrium between the effect of the environmental disturbances and the developed thrusts and moments is valid. The main outputs that the software program provides are the tabulated capability polar plots results and the capability polar plots as shown in Table 2 and Fig. 5, respectively (see Mahfouz and El-Tahan, 25). The above referenced table shows the tabulated capability polar plot results for constant current speed of one knot and wind direction varying from 1 to 751 with respect to the x-axis. For the drilling vessel, it is shown that for a 3 CPPP-Actual NN-Prediction 6 27 Wind Speed, knots Draft = 1.7 m Current Velocity = 1. knots Fig. 8. Predicted capability-polar-plots using NN [V c ¼ 1: knots]. 3 CPPP-Actual NN-Prediction 6 27 Wind Speed, knots Draft = 1.7 m Current Velocity = 2. knots Fig. 9. Predicted capability-polar-plots using NN [V c ¼ 2: knots].

11 A.B. Mahfouz / Ocean Engineering 34 (27) wind direction of 451, the total environmental forces and turning moments in surge and sway directions are 53.96, KN and KN m, respectively as shown in Table 2. Those forces and moments are balanced with the developed thrusts and moments as shown in the previous table. Each thruster develops only a percentage of its maximum deliverable thrust value, which is a part of the total developed thrust by the DP system. An example of the results is shown in Table 2 where thruster 1 develops 67% of its maximum allowable thrust with 571 from the x-axis for drilling vessel. The capability polar plots were generated for constant current speeds of, 1., 2., 3., and 4. knots for the 3 CPPP-Actual NN-Prediction 6 27 Wind Speed, knots Draft = 1.7 m Current Velocity = 3. knots Fig. 1. Predicted capability-polar-plots using NN [V c ¼ 3: knots]. 3 CPPP-Actual NN-Prediction 6 27 Wind Speed, knots Draft = 1.7 m Current Velocity = 4. knots Fig. 11. Predicted capability-polar-plots using NN [V c ¼ 4: knots].

12 1162 A.B. Mahfouz / Ocean Engineering 34 (27) Actual and Predicted Maximum Wind Speed NN-Maximum Wind Speed [knots] CPPP-Maximum Wind Speed [knots] Fig. 12. Prediction of the maximum wind speed. drilling vessel. The vessel can remain stationary in the operating filed site when the wind speed is 5 knots with directions of 351 off and after the bow for the drilling vessel. When the direction of the wind speed is changed from bow (1) to the beam (91) direction, the maximum wind speed decreases. An example of the results is obvious for a polar plot of current speed 1 knot for the drilling vessel. The maximum wind speed at 451 off the bow is 5 knots and at 751 off the bow is 37 knots. It was expected that the drilling vessel could withstand high wind speeds at bow/stern and small wind speed at beam since the projected wind area at beam is quite larger than that at bow/stern. The effect of the current speed is obvious in the capability polar plots shown in Fig. 5. As the current speed increases, the maximum wind speed at which the vessel can stay stationary decreases especially when the wind direction is nearly 91 (beam direction). The capability polar plots for the drilling vessel using the CPPP software is presented in Fig. 5 for constant current velocity range (. 4. knots). The capability polar plots predicted using an artificial NN developed in this work is presented in Fig. 6. The inputs for the developed artificial NN are: the significant wave height in metre, current velocity in knot, and direction in degree while the output is the maximum wind speed. These inputs and output are collected using the CPPP for the drilling vessel. A comparison between the actual capability polar plots obtained using CPPP and the predicted ones using the developed artificial NN are shown in Figs for current velocities of., 1., 2., 3., and 4. knots, respectively. It is obvious that the predicted plots are in excellent agreement with the actual ones as shown in the previous figures. As current velocity increases, the prediction accuracy for the plots deteriorates a little bit. The overall prediction accuracy for the capability polar plots is excellent. This conclusion is obvious in Fig. 12 where the predicted maximum wind speed and the actual ones are distributed around a 451 trend line. The predicted wind speed with such accuracy using the artificial NN is enough for DP operators in station-keeping the offshore platform in emergency cases where the automation of the DP system is disabled. In conclusion, the developed artificial NN is capable of estimating the maximum wind speed that the offshore platform can withstand in the operating site. It can be used as a marine tool in predicting the maximum wind speed in emergency cases where the automation of the DP system is disabled for offshore platforms. The more understanding that exists of the capability polar plots, the better a DP system can be designed since the control algorithms greatly depend on the accuracy of the aerodynamic and hydrodynamic models. Acknowledgement The author would like to thank Miss Shana Murphy and Mr. David Chafe, InCoreTec Inc., St. John s, Newfoundland, Canada, for reviewing the paper. References American Petroleum Institute (API), May Analysis of spread mooring systems for floating drilling units, recommended practice RP 2P-87, second ed. Approved July 12, Fay, H., 199. Dynamic Positioning Systems: Principles, Design, and Applications (Trans. from the French by N. Marshall). Editions Technip, Paris. Flood, I., Kartam, N., Neural network in civil engineering I: principles and understanding. Journal of Computing in Civil Engineering 8 (2),

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