Design of Adaptive Inverse Mode Wavelet Neural

Network Controller of Fin StabilizerHui Li and Chen Guo

Automation and Elec. Eng. CollegeDalian Maritime UniversityDalian 116026, P.R.China

E-mail: delxf@263.net and guoc(dlmu.edu.cn

Abstract-Based on the characteristics of ship roil motion,study of design of the adaptive inverse mode wavelet neuralnetwork (IMWNN) controller is presented and applied to theship fin stabilizer control system, and the pseudo randombinary signal (PRBS) is adopted as simulation input signalof wave slope angle to establish the ship roil motion model inthis paper. Simulation results indicate the method can improvethe shortcoming of poor adaptability of conventional PIDcontrol, and the control system has better characteristics offault tolerance and stronger nonlinear adapting ability. Theeffectiveness of reducing ship roil motion is obviously observedin the simulation experiments.

I. INTRODUCTION

The primary influences of ship motion are roll motion.Excessive ship roll motion influences the seaworthiness of avessel, and may occasionally lead to the followingconsequences: capsizing of the ship, flooding of the deck,disturbing the operation on a vessel, decreasing the speed ofa vessel, and a decrease in the accuracy of gunning inwar-ships. In order to dampen roll motion, ships are usuallyequipped with various types of roll reducing devices knownas bilge keels, anti-rolling tanks, and fin stabilizers [1][2].

Fin stabilizers are the most effective and popularanti-rolling devices in use. Fin stabilizers have been usedextensively for higher-speed vessels, particular on war shipsand. Lift forces on the fins are generated to counteract theroll motion induced by waves. Since the lift force dependson the relative inflow speed, the fin stabilizers are effectiveonly when the ship is sailing at relatively high speed [3].

Generally, PID controller based anti-moment principlehas been commonly adopted in ship fm stabilizer system.The performance of the controller mainly depends onnatural period of ship roll motion and non-dimensional rolldamping coefficient. Because of complexity, non-linearity,time-varying of ship roll motion and uncertainty of seacondition, satisfied control effect is very difficult to beobtained with conventional PID controller. The effectivemeasure to solve the problem is applying the advancedcontrol strategies. Fuzzy control method basing on empiricalif-then rules has also been introduced to the design of thefm stabilization system [4]. Application of the adaptive LQmethod to the stabilizer for a monohull ship is reported [5],

Hongzhang JinAutomation College

Harbin Engineering UniversityHarbin 150001, P.R.ChinaE-mail: heujinhz@l63.com

and Hco control design method has been employed inthe design of a robust stabilizing fm controller [6].

In resent years, wavelet neural networks (WNN) inspiredby both the feed forward neural networks and waveletdecompositions have received considerable attention andbecome a popular tool for function approximation. By"marrying" the wavelet and neural network, WNNincorporate the good learning ability and generalization ofwavelet transform. WNN have shown superiority to themulti-layer perceptron (MLP) in many applications.

Based on the characteristics of ship roll motion, study ofdesign of adaptive inverse mode wavelet neural networkcontroller for ship fm stabilized system is presented in thispaper. In the method, pseudo random binary signal isadopted as simulation input signal of wave slopeangle to establish the ship roll model. The effectivenessof reducing ship roll motion is obviously observed.Simulation results indicate this method can improve theshortcoming of poor adaptability of conventional PIDcontrol, and the control system has better characteristics offault tolerance and stronger nonlinear adapting ability.

II. SYSTEM DESCRIPTION

The architecture of the ship fin stabilizer control system isillustrated in Fig. 1. a is the slope angle of wave surface,g is the roll angle of the ship.

Sea waves

Fig. 1. Ship fin stabilized control system architecture

Basically, the active fm stabilizer system consists of twoelectro-hydraulic servos, a controllers and a roll motionsensor. Based on the ship roll information, the controlleroutput the control command to control the fm rotation

0-7803-9422-4/05/$20.00 02005 IEEE1745

through electro-hydraulic servo, the fm angles shall becontinuously changed along with the various roll motions,and the stabilizing moment (lift forces) is generated by thefins to counteract the roll moment induced by waves.Based on the theory of the random process, the irregular

sea waves can be modeled by [1][2]N |)n

a; E2 JS,I()dw cos(6nt + 'n) (1)n=1 O)n-I

where con represents the wave angular frequency, E6n israndom initial phase (0 2r), Sa(r) is the spectrum ofwave slope, which related with wave spectrum S-(co) by

c4Sa(a) = - S-(w) The wave spectrum is the best

grepresentation of the wave's behavior under the irregularwave.

Based on Conolly theory, the motion of ship roll motionis written as

(Ix + MAx)) + 2Nb+Dho = -Dha (2)where Ix, AIX are the moment of inertia of ship roll massand added mass respectively, 2N is the ship roll dampingmoment coefficient, D is the vessel tonnage, h is theheight of transverse metacenter.

Considered the initial condition fb(O) = q(O) = $b(0) = 0,the transfer function describing the input-output relationshipfrom the slope angle ofwave surface to the roll angle can bedetermined by Laplace transform

O(5) 1 (31a(s) T 2s2 +2T nos+ 1

where is the natural period of ship roll motion, no is thenon-dimensional roll damping coefficient.

m. WAVELET NEURAL NETWORK

In multi-resolution analysis, for the squareintegrable function space L2 (R), there exists anested chain of closed subspaces [7][8]:

{0}c ...c V 1 c V0 c VI c V2c ... c L2(R)such that

V ={0}, close u Vj = L2 (R)jEZ J 1

jE

where Vj is the subspace spanned by the dilationand translation of a scaling function V(t):

Vj,k (t) = 2"j/2 (2-i t - k)An orthogonal complement space Wj is existed

for each of Vj in Vj+l and they meet:

Vj+1= Vj E Wj, Vj I Wjso we have

L2 (R) = ED WjJ

where Wj is the subspace spanned by orthogonalwavelet basis Vjj (t) = 2-j/2 V(2-j t - k).

The above discussions suggest two schemes fordecomposing the function f(t) in L2(R), they are:

f(t) = /fEj,k )j,k (t)j,k

(4)

and

f(t) = Z (f (OJ,k )'PJ,k (t) + E (f Vj,k )Vj,k (t) (5)k j>J,k

What is more important for the functiondecomposition is that for sufficiently large J, anyf(t)eL (R) can be approximated arbitrarily closely inWJ.Thatisforany e>0

f(t) - (f (PJ,k )(OJ,k (t) < (6)

The approximation by the truncated waveletdecomposition can be expressed as:

f(t) ;: (f, 'J,k )(J,k (t) = ECk'Pj,k (t)k k

(7)

The expression (7) means some fine components(high frequency) that belong to wavelet space Wjfor the function are neglected and coarse components(low frequency) that belong to scaling space V1 arepreserved to approximate the originate function underJ scale. In fact, most dynamic processes are low pass.This expression has similar structure for a 3 layerneural network as shown in Fig. 2 [9]-[l1].

Ck4

t

Cki

Fig. 2. The 3-layer wavelet neural network

In the figure 2, the wavelet scaling functionreplaces the role of sigmoid function in the hiddenunit. The number of hidden nodes is decided by

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wavelet translation k that depends on the supportset of f(t). Here we can assume a positive integerK to form a range [- K, K] that can cover the supportset of f(t) .

In the 1-D case, for a given J the number ofscaling function whose centers are inside [-1/2,1/2] is

roughly 2J +1.. So the number of hidden nodes is nomore than 2J + p, where p . 1 is a small integer.Often p is selected to be greater than 1 in order toprovide some safeguard. To determine a proper J,we can use the following simple scheme [10]:

(1) To start from a small J.(2) To computed the mean square error (MSE).(3) To increase J by 1 and repeat from first step

if MSE is bigger than threshold.For the multiple dimension case, the scaling functions or

wavelets are generated by the tensor products of onedimensional scaling functions or wavelets, so the schemeabove can be generalized straightforward.

IV. ADAPTIVE IMWNN CONTROLLER OF FIN STABILIZER

The main characteristic of Inverse mode neuralnetwork process is that the network can use theprevious input and output to calculate the input(control signal) u(t) at the time t = kT . To applyIMWNN in the ship roll reducing control, threesystematic steps are taken in the following:

Step 1- Generating the Inputs and Outputs of theShip Roll Motion Process: In order to establish aprocess model that has better extensive ability, theappropriate input and output data are required.

Theoretically, the distributing frequency ranger ofsea wave spectrum acting on the ship is 0 -o, but it isimpossible to simulate sea waves with wave components ofall various frequencies. Luckily, according to thetheory of random sea waves, all the wave spectrumsunder the various sea states are narrow band spectrums, thewave energy mainly concentrate on a certain frequency band.In our simulation studies, by introducing a signal consistingof a constant value multiplied by pseudo random binarysignal as simulated input signal of wave slope angle, thebuilt roll model gets better extensive ability for differentinput signals. In theory, for roll reducing control, the desiredoutput of the system should be zero, but if zero value isadopted as input of IMWNN, the neural network weightswill not be updated, so we select the tenth of real roll angleto act as the desired output. In addition, the desired outputshould change along with the various sea states, therefore,the constant value of simulated input signal should takedifferent values, in terms of reference [1]-[3], the seaconditions can be divided into three different ranges

according to the different wave height and wind speed, suchas considering wind speed, the sea state can be divided intothree grades as v<8mIs , 8mIs-12mIs , v>12mIs,therefore, the size of the constant part can only be takenthree different values.Based on the expression (3), the roll model of a

certain ship is as following:

0.22z-1 +0.21z-21-1.4z-1 +0.83z-2

In the experiments, we take the wind speed v = 12m / s,the constant value is selected as zero, the length and thealtitude of PRBS sequence are 1023 and an unit respectively,Fig. 3 shows the discrete PRBS input (control variable u(t))and output (y(t) ) of ship roll model expression (8).

-4' L

0 50 100 150 200 250Time(s)

300

Fig. 3. The discrete input and output signals of ship roll model

Step 2- Identifying IMWNN Controller Model: Inthis step, we use u(t) and y(t) of the first step to train amultiple-input/single-output (MISO) IMWNN controllermodel shown in Fig. 4. uN(t)and yN(t)indicate thenormalization signals of u(t) and y(t) respectively. Inorder to ensure the forecast characteristic of control law, thesystem output signal YN (t + 1) is used as the networkinput.

YN(t+1)YN (t) -

YN(t-1)YN (t-2)UN(t-1)UN (t-2)

UN (t)

Fig. 4. The IMWNN controller model

In our experiments, in order to reduce calculatingcomplexity, the Morlet(morl) wavelets functionp(x) = cos(l.75x) exp(-x2 /2) is selected as networkhidden function. The mean square error thresholdisMSE < 10-3.

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After identifying the IMWNN controller model, theweights of the controller need to be saved as theinitial weights of online adaptive IMWNN controllerin step 3.

Step 3- Implementing Adaptive IMWNN Control:Fig. 5 shows the architecture of the adaptive IMWNNcontrol of fin stabilizer, in Fig. 5, N representsnormalization, DN represents de-normalization.

Fig. 5. The architecture of adaptive IMWNN control offm stabilizer

By de-normalizing of the controller output signalUN (t), the control variable u(t) can be directly applied inthe process control. In order to cancel the steady stateerror, the system output error is back propagated tothe IMWNN controller to update weights. Due to thenetwork weights of the step 2 being used as the initialweights, the static error is completely canceled.

In the simulation experiments, for the ship model,D=1457.26ton , h=1.15m the natural period of rollmotion T = 9s, the damping coefficient nP = 0.265, thesignificant wave height is 3.8m, the angle of waveencounter is 900. Fig. 6 shows stabilized ship roll motion.the tenth of real roll angle is selected as the desired output.

1

q3)

-c °~o.00C -0.5

50 100 150 200Time(s)

250 300

Fig. 6. Stabilized ship roll motion (the dot-dash line indicates desiredvalue, the solid line indicates control system output respectively)

effective to restrain disturb and improve control character.(2) In step 2 of simulation, lMWNN is used to

identifying process model, the gained weights is adopted asinitial weights of the online adaptive IMWNN controller,thus, the control system has definite online adaptive ability.In addition, the idea of forecast control is contained in step 3,it can improve the forecast characteristic of IMWNNcontroller.

Similar experiments have been performed for various seastates under the different wind speeds and different wavedirection angle. Simulation results also show the presentedmethod is correct and effective.

ACKNOWLEDGMENT

This work was supported in part by the SpecializedResearch Fund for the Doctoral Program of HigherEducation of P.R.C. under grant (20040151007), and in partby the Ministry of Communications of P.R.C. under grant(200432922504).

REFERENCES

[1] R. Bhattacharyya, Dynamics of Marine Vehicles, New York, Willey,1978.

[2] H.Z. Jin, and X.L. Yao, The Theory of Ship Control, HarbinEngineering University Press, 2001.

[3] C.Y. Zeng, and C.Y Wu "On the design and analysis of ship stabilizingfin controller," Journal ofMarine Science and Technology, Vol. 8, No.2,pp. 117-124,2000.

[4] R. Sutton, GIN. Robert, and S.R. Dearden. "Design study of a fuzzycontrol for ship roll stabilization," Electronics and CommunicationEngineer Journal, July/August, pp. 159-166, 1989.

[5] L. Fortuna, and G Muscato. "A roll stabilization system for a monohullship: modeling, identification and adaptive control," IEEE Transactionon Control System Technology, Vol. 4, No. 1, pp. 18-28, 1996.

[6] N.A. Hickney, M.J. Grimble, M. Johnson, and R. Katebi. "H-infinityfin roll stabilization control system design," Proceedings, 3rd IFACWorkshop on Control Applications in Marine System, Trondheim,Norway, pp. 304-311,1995.

[7] S.G Mallat, "A theory of multi-resolution signal decomposition: Thewavelets representation," IEEE Transaction on Pattern Analysis andMachine Intelligence, vol. 11, no. 7, pp. 674-693, 1989.

[8] I. Daubechies, "The wavelet transform, time-frequency localizationand signal analysis," IEEE Transaction on Information Theory, vol. 36,no. 5, pp. 961-1005 1990.

[9] Q. Zhang, and A. Benveniste, "Wavelet Network," IEEE Transactionon Neural Networks, vol. 3, no. 6, pp. 889-898, 1992.

[10] J. Zhang, CiG Walter, Y Miao, and W.N.W. Lee,. "Wavelet neuralnetwork for function learning", IEEE Transactions on SignalProcessing, vol. 43, pp. 1485-1497, June 1995

[11] L.C. Jiao, Application and Realization of Neural Network, Xi'anScience and Technology Press, 1993..

V. CONCLUSIONS

The adaptive IMWNN controller is applied to the finstabilizer of ship in this paper, simulation results indicate:

(1) WNN possesses the characteristics of faster trainingand convergence speed, especially stronger approximationability in situation of curve saltation, at the same time, it is

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MPV\14V\V\V-1