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OCR for page 223
Simulation of Ship Maneuvers
Using Recursive Neural Neh~-orks
D Hess, W. Failer (Naval Surface Warfare Center, Carderock Division, USA)
ABSTRACT
An improved Recursiw Neural Netw rk
(RNN) m meuvenng simulation tool for smfa e ships is
described inputs to the simulation, ca t in file to m of
forces md moments, a e redefined md emended in a
mmner that more a cun Italy cultures the physics of
ship motion; file new model is used to extend initia
effo ts toward RNN so fat e ship simulations These
extensions include improved to mutations of propeller
thrust, lifl trom deflected rudder, md the explicit
inclusion of roll md pitch righting moments Tw
m meuvers are simulated: to tick cu cles md honzonta
overshoots Simulation emus for file circles averaged
over al mrleusrs for such variables a speed,
tmjecto y components md heading were 5% or less
The bon onto overshoot simulation emus were aso
5% or less for file same va iables with the exception of
the t msve~e hajecto y component The emlmation
for the latter deficiency is believed to be file result of
the exclusion of wind forces a ting on the vehicle,
which will be the subject of later w dk
INTRODUCTION
The Neural Netw rk Development Laborato y
wa e tablished at the Nawvl Su fat e Wafae Center
NSWC) m 1995 with the directive to mply nema
netw dk technology a a predictive tool to problems of
intere t to the Na y That such a tool might be
successful wa mticipated a a result of w rk using
RNNs to predict a d control three-dimensiona
unsteady separated flow helds Caller et al, 1995a)
md dy amic reatta hment Caller et al, 1995b) The
subsequent development of m RNN-baed simulation
tool for submarine mmeuvenng wa documented in
IFallel et al, 1997) a d Faller, et al, 1996a) RNN
simulations have been craned using data trom both
model md f 11-scae submarine 111rleUSr5 in the
latter ca e, incomplete data mea ured on file full-sca e
vehicle wa Pigmented by using feedfmward nema
netw dks a Dirt al sensors to mtelligently e timate the
missmg data Mess, et al, 1999) The creation of
simulations at bodh scares pe mitted file exploration of
scaring differences between the tw whicles which is
described m Caller etal, 1996b)
More recent etlo ts have extended these
techniques to the development of simulations of ship
IllrleUSr5 A initia to mutation of the problem
using m RNN model for use wish ships is described m
Mess, et al, 1996) Speed md tmjecto y predi tions
for novel IllrleUSr5 segregated fiom the set used to
ham the netw rk exhibited werage rl~l5 of 5-6% m
peed md trajectory components for tactical cacle
IllrleUSel5 This level of :Tor demonshated file
fen ibility of file method, md Lowed Hat the gross
features of the m meuvffsing behavior had been
capt red
Elsewhere, neural networks are in use or are
planned in several mplications Notable among these
is a neural netw dk flight conhol sy tem for a
wavender subsonic vehicle (Sal 1., et al, 1997) The
neura conhol system will be used to conhol flight
so la es md to mgment stability on the remotely
piloted te t whicle Anodher intelligent flight control
system mco porating pre-tramed md on-line homed
neura netw rks (Totah, 1997) ha been te ted on a
modified F-15 aircraft The on-line netwodk is
designed to lean alrc~dt dynamics m realtime md
detect une mected ch mges in operation resulting fi om
damage to the arcrafl Ad mtive feedba k provided to
file conholler might then Plow reconEguhtion for
better pe fommamce under f mlt conditions
Neura netw rks have been used to a sist a
time-domain numerical model for prediction of pitch
md heave motions of atrima m fugue in regula head
sea (Atla, et al, 1997) md (Mesbahi md Rllau,
1996) Experiments conducted to complement file
cacula ions were then used to tl am a neural netw rk to
predict pitch md heave motions for wave frequencies
not contained within the homing data Also in file
domam of ship research is the staion-keepmg
(dynamic positioning) problem tha ha been
considered by (Li md Gu, 1996) They devised a
neura net controller to mamtam bon onto position m
file presence of wind md wave motions, md then
tested it undies simula ed conditions withm a computer
This p Her exam d. file eat lier ship simula ion
effo t Recmsiw neura netw rks hwe been twined to
predict to tical circle a d horizontal or hoot
OCR for page 224
maneuvers for two surface ships. An RNN is a
computational technique for developing time-
dependent nonlinear equation systems that relate input
control variables to output state variables. A recursive
network is one that employs feedback; namely, the
information stream issuing from the outputs is
redirected to form additional inputs to the network.
For this application, the RNNs are used to predict the
time histories of maneuvering variables of full-scale
vehicles conducting maneuvers in the open ocean.
Full-scale data describing a series of maneuvers with
varying rudder deflection angles and approach speeds
have been acquired for each of two ships, and these
data have been used to train and validate three neural
networks, one for each ship and type of maneuver.
Upon completion of training, data from maneuvers not
included in the set of training maneuvers are input into
the simulation, and predictions of the motion of the
vehicle are obtained. The input data required for the
model consists of time histories of the control
variables: two propeller rotation speeds and two rudder
deflection angles, along with the initial conditions of
the vehicle at some prescribed starting location. As the
simulation proceeds, these inputs are combined with
past predicted values of the outputs to estimate the
forces and moments that are acting on the vehicle. The
resulting outputs are predictions of the time histories of
the state variables: linear and angular velocity
components which can then be used to recover the
remaining hydrodynamic variables required to describe
the motion of the vehicle. A schematic representation
of the technique is shown in Fig. 1. Environmental
data in the form of relative wind speed and direction
are measured; future input forces and moments using
these quantities are planned. Further details of the
implementation of this model follow in subsequent
sections, beginning with a description of the
maneuvering data used for training and validation.
, Environment,
' Wind ~ Waves,
b
Red ~
I Signals I I Force Modulesl
FtNN
~,
6-DOF Trajectory
State Variables ~ Angles
u(t) x(t)
v(t) y(t)
w(t) ~ z(t)
p(t) 9(t)
q(t) 8(t)
r(t) ye)
Fig. 1 RNN surface ship simulation.
DESCRIPTION OF DATA
Data for training and validating the neural
networks was acquired from two ships operating in the
open ocean. Each ship is equipped with two propellers
and two rudders. One ship is larger than the other such
that differences in size, especially with respect to the
rudders and propellers, make separate simulations of
interest. Henceforward these ships will be referred to
simply as Ship 1 and Ship 2.
For each ship, the standard coordinate system
attached to the center of gravity of the vehicle is
assumed; namely, x is the longitudinal axis and is
positive towards the bow, y is the transverse axis and is
positive to starboard and the vertical axis z is positive
downwards. Linear velocities in this coordinate system
are indicated by u, v and w, and angular velocities byp,
q and r. Accelerations are denoted similarly but with a
dot above the letter to indicate a time derivative.
Angles of roll, pitch and yaw are given by A, ~ and
fir, respectively. The speed of the vehicle is referred to
by U. The vessel's controls are two propeller rotation
speeds, n, and n2, and two rudder deflection angles:
id, and ire . Relative wind speed and direction will be
indicated by VR and f9R, whereas the true wind speed
and direction will be denoted by VT and (AT . These are
the data that define the motion of the maneuvering
vehicle, the controls that propel and direct the vessel
and the details of the wind. They are summarized
below in Table 1. The shading for each variable is
added to indicate data that are directly measured,
variables that may be derived from directly measured
data and information not measured. For example, x
and y, which refer to trajectory components relative to
an inertial coordinate system placed at the starting
location of a maneuver, are derived from latitude and
longitude as measured by a global positioning satellite.
Linear
Velocities
Accelerations
Controls
Environmental
_ __ Angular
Trajectory / Angles t~ ED
~1~ 1~EJ71
i ~~ ~9~
Speed (Re to fluid) ~
~[~
[it
Table 1 Required and measured data.
Key
Measured
_
tJ Derived
OK ~
~ | Unknown
The neural networks have been trained to
simulate two maneuvers: tactical circles and horizontal
overshoots. The existing data are as follows. For
Ship 1, 15 tactical circle maneuvers are available with
rudder deflection angles which vary over a range of 10°
to 35° and for a series of approach speeds from
5.1m/s to 11.6m/s (lOknto22.5kn). Twenty-five
tactical circle maneuvers are available for Ship 2 with
rudder deflection angles from 10° to 35° and for
approach speeds from 5.1 m/s to 15.4m/s (10 kit to
30 kn). Because ships with multiple propellers often
exhibit similar turning characteristics for both right and
left turns, the bulk of the data are right turns with a
small number of left turns. Ten horizontal overshoot
maneuvers are available for Ship2 with rudder
OCR for page 225
checking angles of 10° and 20° and for approach
speeds from 3.4 m/s to 8.1 m/s (6.6 kn to 15.7 kn). A
description of each of these maneuvers follows.
Tactical circles are conducted in order to
determine the inherent turning characteristics of the
ship. Of particular interest are such quantities as
advance, transfer, tactical and steady diameters, speed
loss and steady speed in the turn. The typical
procedure for these maneuvers is to first establish
steady initial conditions for approach velocity and
propeller rotation speeds and to maintain these
conditions for 30s. Then, an order to Commence
Execution (COMEX) of the run is given. Data
acquisition at a rate of 1 Hz begins and steady
conditions are maintained for an additional 60 s. At
this time an EXECUTE command is given and the
rudders are deflected to the desired angle and
maintained for the duration of the maneuver. These
conditions are continued until the heading of the
vehicle has changed by 540°; the maneuver is then
terminated. An ideal tactical circle maneuver
illustrating these terms is shown in Fig. 2. Note that
Figs. 2 and 4 were reproduced from (Stepson and
Hundley, 1989) and are used with permission.
Corrected Approach Course ’|~Advance
~ Comex Execute _ |
C _~
A
stew ~
Turning
DiamstQ,
180 Degrees Change of Heading
/ 90 Degrees \ Transfer
Change of Heading go
_ _ _ TIC t d Tactical
~ or~ac ['iale'8r
_ r ~ ~0 ~
+
Fig. 2 Tactical circle maneuver.
b
However, conditions in the open ocean are
rarely ideal. Environmental factors such as moderate
winds and unfavorable ocean currents can combine to
produce the actual circle trajectory shown in Fig. 3.
Knowledge of the time histories of wind speed and
direction along with details of any prevailing ocean
currents should allow one to formulate the appropriate
force contributions that alter the trajectory of the
vehicle. This is one of the areas in which future efforts
will be directed. For the simulated maneuvers reported
here, the problem was simplified by removing
environmental effects. An automated procedure for
removing the effects of drift was devised and applied to
each of the maneuvers. This was possible because one
assumes that the vehicle would indeed travel in a circle
in the absence of environmental effects. Therefore, the
trajectories were corrected by aligning overlapping
portions of the circle and computing the unwanted drift
velocity components which were then removed. An
example of a corrected circle, rotated for convenience
to place the steady state approach along the x-axis, is
also shown in Fig. 3
-250
-250
250-
Y (m) 750
1 250
X( -
250 750 1250
\ f~
Fig. 3 Typical actual and corrected tactical circle.
Horizontal overshoot maneuvers are
performed to characterize the handling response and
rudder effectiveness of the vehicle, and such quantities
as the heading overshoot angle, overshoot time, reach
and period are used to establish this behavior. As with
the circles, a 30 s period of steady initial conditions is
followed by COMEX with a further 60s elapsing
before the EXECUTE order is given. After EXECUTE
the rudders are deflected to a predetermined entrance
angle and maintained in this position. The heading of
the vehicle changes in response to the rudder
deflection; when the heading has changed by a desired
amount (typically equal to the entrance angle), the
rudder is reversed and set to the rudder checking angle
(usually equal to the entrance angle). Because the
vessel does not respond instantly, the heading
continues in the same direction for a period of time
before slowing and then reversing. This overshoot
angle measures the inherent ability of the ship to
change direction. The procedure is typically repeated
for 2.5 cycles. Unlike the circles, environmental
effects cannot readily be removed from this data;
however, the maneuvers are conducted such that the
approach course is oriented parallel (or anti-parallel) to
the true wind direction. In this manner any influence
of the wind on the ship's turning characteristics should
be minimized for both left and right turns. Figure 4
shows superimposed plots of rudder deflection angle
and heading during a typical overshoot maneuver and
depicts useful terms. The neural network simulations
were trained and validated using these maneuvers; a
OCR for page 226
description of the structure of the neural networks
follows next.
300
250
in
200
of
o
C)
ciao 150
by
50
r,
_
_
_ _
_~ ~
. ~
_~
EXECUTES
.~
-
_
OVER
SHOOT
T
1~ -~-----~
RUDDER ANGLE
PERIO D
11 1
~Ir
~1' 1
~1-
15 1Q 5 0 5 10 15
LEFT MIGHT
RUDDER ANGLE AND CHANGE OF HEADING IN DEGREES
Fig. 4 Horizontal overshoot maneuver.
RNN ARCHITECTURE
The architecture of the neural network is
illustrated schematically in Fig. 5.
Feed Forward Hidden Layer(s)
Connections ~
- Output Layer
Input
Vector
Recursive (Recurrent)
Connections
Fig. 5 Recursive neural network.
The network consists of four layers: an input layer, two
hidden layers and an output layer. Within each layer
are nodes, which contain a nonlinear transfer function
that operates on the inputs to the node and produces a
smoothly varying output. The binary sigmoid function
was used for this work; for input x ranging from
~ to no, it produces the output y which varies from O
to 1 and is defined by
y (X) = ~ + i!
Note that the nodes in the input layer simply serve as a
means to couple the inputs to the network; no
computations are performed within these nodes. The
nodes in each layer are fully connected to those in the
next layer by weighted links. As data travels along a
link to a node in the next layer it is multiplied by the
weight associated with that link. The weighted data on
all links terminating at a given node is then summed
and forms the input to the transfer function within that
node. The output of the transfer function then travels
along multiple links to all the nodes in the next layer,
and so on. So, as shown in Fig. 5, an input vector at a
given time step travels from left to right through the
network where it is operated on many times before it
finally produces an output vector on the output side of
the network. Not shown in Fig. 5 is the fact that most
nodes have a bias; this is implemented in the form of
an extra weighted link to the node. The input to the
bias link is the constant 1 which is multiplied by the
weight associated with the link and then summed along
with the other inputs to the node. For further details
concerning the operation of neural networks, the reader
is directed to (Haykin, 1994), and for recursive neural
networks to (Falter, et al., 1997~.
A recursive neural network has feedback; the
output vector is used as additional inputs to the
network at the next time step. For the first time step,
when no outputs are available, these inputs are filled
with initial conditions. The time step at each iteration
represents a step in dimensionless time, /\t'. Time is
rendered dimensionless using the ship's length and its
speed computed from the preceding iteration; thus, the
dimensionless time step represents a fraction of the
time required for the flow to travel the length of the
hull. The neural network is stepped at a constant rate
in dimensionless time through each maneuver. Thus,
Predicted an input vector at the dimensionless time, t', produces
Output Vector the output vector at t' + /\ t', where
t'+At'= t'+ ~ ,) and At'= O.09 . (2)
Because ship speed, U(t'), varies while length, L, is
constant, the spacing between samples, At, must vary
in order that the dimensionless time step, At', remain
constant at the chosen value of 0.09.
The network described here has 56 inputs.
Each hidden layer contains 54 nodes, and each of these
nodes uses a bias. The output layer consists of 6 nodes,
and does not use bias units. The network contains 118
computational nodes and a total of 6608 weights and
biases. The input vector, described in detail below,
1 consists of a series of forces and moments which act on
the vehicle, and the network then predicts at each time
step dimensionless forms of the six state variables:
three linear velocity components u, v, and w, and three
OCR for page 227
mgular velocity componem. -, q End ~ Specifically,
the outputs are defined as
u'(t'+At')= ( (,) ), x'mdw'similar
'(t'+.~t') = P(t +6t ) L, q' md r'similar
These velocity predictions are then used to compute at
each time step the remaming kinematic variables
described in Table 1: h secto y components, Euler
mgles md accelerations
The 56 conhibutions that to m the input
vector are described as follow Sewn basic force md
moment te ms describe the influence of the conhol
inputs md of time-dependent flow held effects: thrust
from two propeller., F.,, md 7;,,,, lit fiom two
deflected rudder, L,, md Lid,, tw restoring
moments resultmg fiom disturbances in pitch md
roll, K, md M,, md a Munk moment acting on the
hull, NAOMI These temms are developed fiom
knowledge of the controls: propeller rotation speeds
md rudder deflection mgles, geomet y of the vehicle,
md from output variables which are recursed md made
available to the inputs A detailed description of these
sew n inputs is reserved for the next section
Additional inputs are obtamed by retaining
past values of the sewn basic inputs This gives the
netw rk memo y of the force md moment hi to y
acting on the vehicle md pe mits the netw rk to learn
of my delay that cm occur between the mplication of
the force or moment md the re ponse of the vehicle
One past value hom each of fLe tw propeller thmst
tffms is retained to provide tw additional inputs For
each of the remainmg 5 basic mputs, 7 past values are
retained as additional mputs The number of past
values to keep is chosen empirically md mpea~ to be
a f nction of the fi equency response of fLe vehicle in
this case the netw rk is given infommation about past
events for a penod of time requu ed for the flow about
the vehicle to h avel a dist mce of 0 63L
Recursed ouqputs fiom the prior time step are
used as six additional contributions to fLe input wctm
Fu the more, the ouqput vectorhom one previous time
step is retamed md made available as six additional
inputs Knowledge of fLe output velocities for tw
successive time teps pemmits fLe netw rk to implicitly
lean about the accele~tions of fLe vehicle A
summary of the w~rious contributions that make up the
input vector is provided below m Table 2, md attention
is next duected to a detailed ~pl mation of fLe seven
basic force md moment inputs
Input Des~ription T b puts
[,,,(t'),T,,~(t' At') 2
:,(t),~,(t' At') 2
L,,(t), L,,~(t At ), . ., L,,~(t 7At ) 6
L~,(t ), L~,(t At ), . ., L~,(t 7At ) 6
K,(t ), K,(t At), . ., K,(t 7At) 6
M,(t),M,(t At), . . ,M,(t 7At)
NAo~(t) NAo~(t At),. .,NA^,,(t 7At) 6
u'(t'),v'(t'),w'(t),p'(t'),q'(t),r'(t) 6
u'(t' At'),v'(t' At'),w'(t' At'), 6
p(t' At'),q'(t' At),r'(t' At)
Total 56
Table 2 Summary of netw rk inputs
FORCE AND MOMENT INPUTS
Neural netw rks have m am~ing ability to
identify md t~ck nonlmear beEwior linking a set of
mputs to a set of outputs This innate ability c m be
f ther mgmented, however, by carefully const cting
physically motiw~ted mput md output variables that
fo m a well-posed problem For this ta k, inputs to fLe
neural netw rk were cast m the fo m of forces md
moments actmg on fLe vehicle: thrust hom fLe
propell~ss, lifl fiom deflected rudders, re tormg
moments resultmg fiom di turbames in pitch md roll
md a Munk moment acting on fLe hull These tffms
were fashioned from the basic control w~riables:
propell~s rotation speeds, n, md n:; md mdder
deflection mgles: 5r, md 5q Also available for fLe
deEnition of fLe input te ms ae ouqput variables hom
fLe previous time tep, which are recu~ed md made
accessible to the input side of fLe netw rk in this
m mner a t e simulation is prese~ved as only fLe
control hi tories md initial conditions of the whicle
are requned to m the simulation The followmg
pa~grmhs describe fLe creation of each of the input
te ms
The h~t tw mputs to fLe netw rk are fErust
fiom the staboard a~d po t propelle~, re pectively A
dimensional malysis ~ewis, 1968) relates propell~s
fEru t coeff'cient, Cr. to Froude numbe' Fr, advame
mtio, ~/, cavitation number, t, md Reynolds number,
Fe as follows:
OCR for page 228
CT = f (Fr, J. a, Re) ~
(4)
where CT = T/0.5PD2UA, Fr = gD/UA, J = UA/nD,
CT = (PPV )/0 5P UA ~ Re = UA D/V, UA is the
advance speed of the propeller, D is the propeller
diameter and PA is the vapor pressure of the fluid. An
approximation to this relationship may be found by
considering only the primary dependence of the thrust
coefficient upon the advance ratio. Expressing the
thrust coefficient in the more convenient form,
KT = T/p n2D4, a linear dependence upon J forms a
useful approximation (Fossen, 1994), and may be
stated as
KT = C1 + C2 J
Thrust may then be determined from
T= pD4KT(J)|n|n,
and the approximation becomes
(5)
(6)
T = C1 P D4 |n|n+C2 P D3 |n|UA . (7)
The advance speed of the propeller is related
to ship speed by means of the wake fraction, Wf, and is
written as UA = (1 - Wf ) U. where Wf ~ 0.1 to 0.4.
Furthermore, the presence of a hull-propeller
interaction increases the resistance of the hull, or
conversely, decreases thrust; therefore, T should be
replaced by T(1 - t), where t ~ 0.05 to 0.2 . Using
these expressions, the thrust approximation may be
written as
~ . ~ {1 i., ~
Ship2 -- KTvsJ
0.200 ~ ~
0.190 . \
0.180 \
0.170 ~W
KT 0 ~ 50
0.140
0.130
0.120
0.110
0.100
0.750
0.800
0.850 0.900 0.950 1.000
J
p2.
Fig. 6 Measured KT VS. J for Shi
Star
Port
The coefficients c1 and c2 for each propeller for
Ship 2 were taken from the fits to the data. These
values and those estimated for Ship 1 are given in
Table 3.
~ cl-star
Ship 1 1 0.600
Ship2 1 0.553
c2 -Star
-0.400
-0.472
l c1 -Port
0.600
_ 0.533 .
Table 3 Coefficients c1 and c2.
3
-0.400
-0.460
Because the rudders are located aft of the
propellers for these vehicles, a deflected rudder will
interact with the propeller slipstream and reduce the
overall thrust imparted to the vehicle (Soding, 19984.
The drag is given by
Tprop =c~ pD4<,J In|n+C2 p DO ~ JInIu <84 ~ ~
where the prop subscript is used to differentiate this
basic propeller thrust from a reduction term to be
discussed in a later paragraph.
The propeller rotation speeds from the current
time step and ship speed from the previous time step
are used in Eq. 8 to generate the thrust approximation.
Actual values for p and D were used and reasonable
estimates of Wf=0.2 and t=0.1 were made. The
coefficients c1 and c2 were estimated for Ship 1. For
Ship 2, thrust measurements were available for each of
the maneuvers. For this case KT and J (computed
using ship speed) were calculated for each point of the
steady state portion preceding execution of the
maneuver and then averaged. Plotting a point for each
of the circle and overshoot maneuvers for Ship 2
revealed the trends shown in Fig. 6.
T = T (1 - cos dr) 1 + . `(9)
rud prop ~ ~
At a given time step, Eq. 8 is calculated which in turn
allows a value for CT to be computed. Then, the
reduction described by Eq. 9 may be determined, and
the resultant thrust generated by the propellers may be
computed from
T - T - T
prop rud
(10)
This final expression was used to approximate the
thrust imparted to the vehicle from the starboard and
port propellers and represents the first two inputs to the
neural network. The reader should note that although
an attempt to produce reasonable coefficients for the
thrust expressions was made, any errors in the
coefficients will be accounted for by the network
during training.
The next two inputs to the network are lift
forces generated by the starboard and port rudders,
OCR for page 229
re pectively The lid force is mproximated a the
supemosition of tw contabutions: lid on the rudder in
the absence of a propeller, md m additiona ii t mput
resulting from deflection of fLe propell~s slipstream
(Sodmg, 1996) To describe the h~t contabution, a ii t
coeffcient is required md is deEned a
C~ = L/O 5p U. A,,,' Soding then mproxima es the
ii t on a rudder a
Cz=~(A)() sm~+sm~|sm~|cos~, (11)
dcr :~
where cr is m mgle of ata k This fo mula uses the
exa t lid gradient for a fLin foil in tw -dimensiona
potentia flow given by
(dCt) =2~
md then decrea es it by a reduction fa tor which is a
function of rudder a pect raio fha atempts to conect
for deviaions hom tw -dimensionaity it is deEned
r(A) = ~:
(12)
(13)
The mdder apect raio, A, may be found fiom
A=h2/A,,,~, where h is rudder height md A,,,' is
rudder a ea
To compute the lih from Eq 11, one requnes
the loca mgle of ata k a fLe rudd~s This qu mtity
wa caculaedhom
tr=5r ta i| ~+,L
U,~
When ah mwerse velocity component, x, or m mgula
velocity of yaw, r, is pres:~t, the simple result tha
mgle of ata k equas rudder mgle must be conected
The qu mtity L, is fLe a la di t mce h om fLe center of
gra ity to the rudder pivot The d:mmmaor
represents the longitudma speed in the wake of the
vehicle multiplied by m ampliEca ion fa tor due to the
propeller
Soding e timaed fLe additiona ii t on a
rudder fiom m upstream propeller fiom moment m
themv The mmoximaionisfoundfiom
(14)
where L,,,~ is giwn by Eq ll solved for ii t, namely
L,,,~ =p U,5~ [2~r(A)sm~+sin~| sin~| cos~]
(17)
Summaizmg, a a given time step, fLe mgle
of atak is computed from Eq 14 requaing rudd~s
mgle, recmsed vaues of h msve~e velocity, yaw
mgula velocity md ship speed, md a vaue for Cr
computed dming fLe thrust caculaions The ii t on the
mdder is fLen computed from fLe sum of Eqs 15&17,
md fLese caculaions a~e pe fo med for fLe ta~boa d
md po t mdders md fo m fLe next tw inputs to fLe
netw rk
b addition to fLe propulsion a d steermg
mputs tw nghting moment inputs ae provided to
a count for di turb mces m roll md pitch A st dy of
meta entac stability reveas fha fLe nghting am m
ea h ca e is propo tiona to the dist mce fi om the center
of g~vity to a point know a the trmsverse or
longitudina meta enter; fLis meta entric height is
denoted OMr or OM~ The product of the moment
am md fLe weight of the whicle creaes a couple
which a ts to restore fLe vehicle to its undist rbed
onenta ion These moments may be mproxima ed by
K, = pgva sin~
M, = pg VOM~sin9
where V is volumetric displa ement amd ~ md 9 a~e
mgles of roll md pitch, respectively The meta enh ic
height is commonly decomposed into a differ:me
between fLe distmce hom the center of buoymcy to
fLe meta ente' BMr or BM~, md fLe di t mce from
fLe c:~ter of buoymcy to the center of g avity, BO
Fu the more, B md B may be mproximaed
for mal roll mdpitch motions by Ir/V ad l~/V,
where Ir md 1~ a e moments of me tia of the wetted
po tion of the vehicle about the h mswrse or
long itu din a c enterl me , re p e ct iw Iy U pp er b omm ds on
fLese moments formost ships saisfy Ir < yl2B3L md
1~ < Ih2BL3, where B is the beam md L is the ov~sal
length of the vehicle Repla ing fLe f~ction wifh a
const mt, the restoring moments may fLen be w itten a
(Ig)
ulem y l ne dpp! UXmidUm ms IUUnU ~ mn
L~=~,,sindr |1+~ (15) K = pgV( r BO)sm~
Therefore, the tota ii t on the mdder is found a V
L = L,,,/ + L~, (16)
(19)
OCR for page 230
This info mation, when available, cm be explicitly
provided, md file network will attempt to lean the
unknow const mts cr md cat naturally during
tminmg Altennatively, the simpler expressions
K, = C,smq1 md M, = C, sm 9, (20)
may be used, again allowing the netw rk to dete mine
the unknots constmts
These restoring moments were implemented
in the latter to m Roll md pitch mgles at the currant
time step were obtained by adv mcing previous roll md
pitch mgles using
( U )
( U )
The derivatives ~ md 9 are obtamed by using
recursed mgular velocities A, q md r md previously
computed ro 11 md pitch s gles fi om the equations
~=p+tm9`,(rcos~`,+qsin~`,)
9=qcos~,, rsm~,,
p=sin'( V)
A y needed con tmt required to improw file
approximation of Eq 24 c m be detemmined by file
netw rk during training
The sewn basic inputs to file netw rk have
now been defined They consist of the fErust fi om each
propeller, the lifl trom each deflected Odder, restoring
moments to di turbames m roll md pitch End a Mu k
moment acting on file hull of the vessel With file
description of file architecture of the neural netwodk
now complete, attention is du ected to the procedure by
which the netwodk was h amed
(21) TRAINING PROCEDURE
(22)
The fmal basic input to the neural netw rk is a
moment which acts on the hull of file vehicle (Munk,
1920) Consideration of a body moving through a
pe Sect fluid End creating a potential flow reveals That
fluid pressure acting on file hull will produce a net
moment on the vehicle A real fluid with viscosity md
deviation trom a potential flow inhoduces
modifications but does not substmtially chmge the
resulting moment The magnitude md direction of the
moment depend on file square of file velocity of the
vehicle md on the position of the vessel relative to the
direction of motion For a so face ship oriented with
m mgle of d i t, p, relative to its du e tion of motion,
the moment is given by
LAOS = P U2(Vr V,) r pcos p, (23)
equal to file added mass when the vehicle is oriented at
p = 0° End p = 90, respectively For elongated
bodies such as a ship, V, t V md V, t 0
Therefore, the moment may reasonably be
mproxr red by
LAOS = pVU: sm pcos p
(24)
The implementation of fLis moment as m input to the
netw dk requires ship speed md a recm sed value of the
t msveee velocity, x, in order to compute p given by
(25)
As discussed in m earlier section, mfo mation
presented to file inputs of a neural network is modified
as it flow through file network by the presence of file
weights md by file nonlinear outputs of each of file
various nodes until it aTives at the output layers of file
netw rk Thus, at each time step, m input vector
produces a predicted output Actor, this is Glen
compared to file actual (target) ouqput vector
dete mined fiom the data The difference between file
target md predicted ouqput Vectors is a measure of the
enor of the prediction The process by which file
netw rk is iteratively presented with m input vector m
o der to produce outputs that are Glen compared wish a
desired output vector is know as traming The
pumose of traming is to gradually modify the weights
between the nodes in o der to reduce the enor on
subsequent itontiuns in other w rd., the neural
netw rk learns how to reproduce the conect mswex
When the emu has been minimi ed, haming is halted,
md the result mt colle tion of weights that have been
e tablished among file mmy co reckons m file
netw rk represent the knowledge stored m file trained
neural net Therefore, a haming algorithm is required
to detemmine the eno5 between the predicted ouqputs
md file desired target values md to act on this
mfo mation to modify file weights until file or is
reduced to a minimum The mo t commonly used
haming algonthm, Ed the one employed here, is
called backpropagation which is a gradient descent
algorithm The collection of input md conespondmg
target output vectors comprise a training set, md these
data are requu ed to prepare the netw rk for f this use
Data hles containmg time hi tories of tactical cacle
md bon ontal over hoot m reuse. to med file
haming sets
A ter file neural netw rk has been successfully
hamed, the weights are no longer modified md remain
hoed At this point the netw rk may be presumed with
m input vector similar to the input Actors m file
OCR for page 231
training set (that is, drawn from the same parameter
space), and it will then produce a predicted output
vector. This ability to generalize, that is, to produce
reasonable outputs for inputs not encountered in
training is what allows neural networks to be used as
simulation tools. To test the ability of the network to
generalize, a subset of the available data files must be
set aside and not used for training. These validation
data files then demonstrate the predictive capabilities
of the network.
Three neural networks were trained in this
manner to predict Ship 1 tactical circles, Ship 2 tactical
circles and Ship 2 overshoots. In each case about 80%
of the data files comprised the training set with 20% set
aside as validation files. The networks were initially
trained for 100,000 epochs, where an epoch is defined
as the presentation of the time series for all inputs and
outputs for all files in the training set. During this
training process, training is paused every 10 epochs,
and the network is tested for its ability to generalize.
To carry this out, all of the files in the training set are
combined with the validation files set aside earlier for
this purpose, and the entire set is presented to the
network. During this generalization phase, the weights
are not modified; the data from the files simply go
through the network to produce predicted outputs and
these are then compared with the measured outputs.
Use of the word output in this context implies any of
the kinematic variables described in Table 1 which are
computed at every time step. The errors are quantified
by computing three error measures at each time step for
each output. These errors are averaged over all of the
outputs and then further averaged over all of the time
steps in the file to produce measures of the
generalization error for each file in this testing set. The
errors are then further averaged over all of the files in
the testing set (training files and validation files) to
produce a measure of the generalization error over the
entire set at this stage of training. The error measures
are the absolute error and the dimensionless quantities:
average angle measure and correlation coefficient. The
average angle measure was developed by the
Maneuvering Certification Board at NSWC and is
similar to a correlation coefficient in that a value of one
represents a perfect prediction and a zero value denotes
a poor prediction. The equations defining these error
measures may be found in (Hess, et al., 19994. After
training has concluded, one examines the error
measures as a function of the number of epochs that
have elapsed. The curves reveal an optimum number
of epochs at which training should have ceased and
where minimum absolute errors and maximums in the
dimensionless measures occur. Periodically during
training, every 100 epochs, the weights are written to a
data file. Neural network training is then restarted, at
the closest epoch for which a weight set was saved, and
continued to the desired optimum stopping epoch.
o
200
180
160
140
120
100
° 80
60
40
20
O
1
0.98
0.96
' 0.94
E 0.92
0.9
0.88
> 0.86
0.84
0.82
0.8
o
. _
-
1
0.98
~ 0.96
,, 0.94
0.92
0.9
~, 0.88
- 0.86
° 0.84
0.82
0.8
0 20000
.
40000 60000 80000 100000
Epochs
AAM vs Epochs
~S~t
0 20000
40000 60000 80000 100000
Epochs
R vs Epochs
0 20000 40000 60000 80000 100000
Epochs
Fig. 7 Evolution of generalization errors
for Ship 2 circles.
An example of the evolution of the
generalization errors over the 100,000 epochs of the
training phase for the network simulation of Ship2
tactical circles may be found in Fig. 7. Of the 18
possible output variables described in Table 1 for
which generalization errors may be computed, 5 were
chosen as critical variables: a, x, y, ~ and tu. The
generalization performance of the network was judged
on the basis of these critical variables for purposes of
choosing the optimum stopping epoch. Because the
relative magnitudes of each of these five variables are
quite different, the averaged absolute error over the
five variables will be a number that largely reflects
errors in x and y, and this may be seen in the absolute
error scale in the top graph of Fig. 7.
OCR for page 232
The stopping epoch for 6 is net wok wa
selected a epoch 81,760 The network wa restated
md Glen hated at this epoch The absolute enor wa
45 1, the average mgle measure wa 0 953 md the
conflation coefficient wa 0 963 At this epoch the
as curie mgle mea ure rem bed its ma imum, md the
absolute en or md file conflation coefficient were ve y
close to flair minimum md ma imum, re pectively
Figure 7 show that fter the flu t 20,000
epochs most of file points on en h plot are clustered in
a relative Iy thin b md This mdicates fhat file solution
is relatively moodh wish smal charges to the 6608
weights md bin es at en h epoch c msmg only minor
fluctuations m enors This wa t e for bodh Ship I
md Ship 2 to tica cu cle simulations with the optimum
solution typicaly mpeamg Stiff 60,000 to 80,000
epochs of homing For the Ship 2 overshoot
simulation, file optimum solution required a somewhat
longer 100,000 to 150,000 epochs of Paining The
emu plots were simile to Fig 7 except fhat the pomts
clustered in a thicker b md This w uld indicate fhat
the evolution town d file optimum solution for the
overshoots wa more difficult with smal charges to
the weights casing lags fluctuations in solution
emu s This topic will be revisited in a la ff section
Summai ing, three neura netw rks were
twined to predict Ship I to tica circles, Ship 2 to tica
circles md Ship 2 overshoots using the procedure
described in d is section The results of these
simulations proved to be quite encouraging md are
detailed next
RESULTS
Beginnmg wish Ship 1, the netw rk wa
twined using 12 to tica circles wish three set a ide for
vaidation Figure 8 depicts Ship I circle hajectones
predicted by file homed netw rk superimposed upon
the a tug trajectories followed by the vehicle in en h
ca e the only info motion provided to the twined
netw dk was fom time hi tories for po t md staboa d
propeller rotation peed md mdder deflection mgles
md the initia conditions of file vehicle Compasing
the top row of the figure are four of the 12 m meuvers
used for homing, md the bottom row contams al 3
vaidation runs The fom homing mns fhat me how
represent a mint re of four different rudder mgles md
thee different mproach speeds Similarly, the
vaidation m meuvers contam three different rudder
mgles md two different apron h peed Notice fhat
tw of the traming cu cles fhat a e show are led t nets
with the of her tw right tub s Solid lines represent the
predictions, md dashed Imes are used for file acted
path in each cane the steady state pats of file
m Feuded =.- Comex md before Execute were
reduced to a length dete mined by t'= I, md only a
po tion of this sh aight path is show
The predictions for file twining cacles are
excellent This is the Bust te t that file netw rk must
pa s if a relation hip bemused file force md moment
inputs md the velocity ouqputs exists, file netw rk must
dete mine this connection if the experiments data is
poor, or the network is improperly to mutated, Glen file
netw rk's pe to m mce on file tminmg data will be
conespondmgly poor Neither is the cage here; file
homed netw rk ha leamed how Ship I pe to ms a
to tica cu cle m meuver That d is is tme is evinced by
file pe to mmce of the netw rk on file vaidation
cacles Recall that file Rand r on runs were ne s er used
to modify file weights during tl Ming, md m this sense,
hwe never before hew seen by the netw rk The
recursive nema netw rk ha been successfully able to
g:~eraize: to make predictions for m meuwrs different
fiom, but simile to, those represented m the tminmg
set in tw out of the three ca es, file most difficult md
nonlinea po tion of the mmeuve' file initia pat of
file t na a represented by the adv mce md h msfer, ha
hew capt red precisely Predictions for the steady
t numg diametffs a e excellent in a I three ca es
To qumtify these statements, averaged enm5
for Ship I to tica circles have been tailed in Table 4
for file ti -e critical Or abler a, x, y, ~ md ~ The
but number in en h cell is m en or averaged over a I
15 m meuvers, wherea the second number is the emu
averaged over file 3 vaidation circles only To give
some percentage emus, file absolute enors were
no maized by the following scares: average steady
peed m the tum of 5 2 m s (17fl/s), a~emtie tunumg
diameter of 651 m (2135O, average peak-to-peak roll
vaiaion of 2 8° md m average total headmg vaiaion
Table 4 Ship I to tica circle en or mea res
avenged over ail m meuvers / avenged over
w~lida ion h ICY only
OCR for page 233
-1 00
100
300
-
E 500
700
900
1100
-1 00
100
300
E 500
700
900
1100
-1 700 -
-1 500 -
-1 300 -
-1100 -
-900 -
-
-700 -
-500
-300
-1 00
100
1 000
-1 00
100
300
-E 500
700-
900
1100
1300 -
it_ 1
.
~ \~~,
-800
-700
-600
-500
-400
-300
-200
-1 00
O
_ 100
i0~ ~
In
-1 00
O
100
200
300
400
500
600
~ It-- ~ I
-
. -
. ~
-50
-00
-350
-300
-250
-200
-1 50
-1 00
-50
O
50
0 400 800 12( 200 500 800 11( 1100 1300 1500 1700 1200 1300 1400 1500 1600 1700
X(m) X(m) X(m) X(m)
) -1 00 -1 00
~ 1~ ~100~10
800 600
500 900 1300 17( 200 600 1000 600 800 1000 1200
X(m) X(m) X(m)
Fig. 8 Ship 1 tactical circles. Top row: training files 3000,3041,3100, and 3070.
Bottom row: validation files 3030,3043, and 3050.
Predictions: solid lines, Measured: dashed lines.
.., 1 ~
1400 1800 2200 2600
X(m)
-200 -
O-
200 -
400 -
600 -
800 -
1 000 -
1200 -
1400 -
_ 1600 -
600 1000 1400 1800 400
X(m)
Fig. 9 Ship 2 tactical circles. Top row: training files 3440,3211,3223, and 3460.
Bottom row: validation files 3111,3201,3310 and 3330.
Predictions: solid lines, Measured: dashed lines.
~_~
\ \:
~
-1 00 - _
100 -
300 -
500 -
700 -
900 -
1100 - .
400 800 1200 1600
X(m)
\ my'
/'
-1 00 --
O- -- 1 1~ 1
200- jj ~ >\
300 - - .,
400 -
500 -
600 -
7800 ~ ~:~
900
1900 2100 2300 2500 2700 294
X(m)
-1 00
~ (~! a00~\
1 300
800 1200 1600 2000 500 900 1300 1700
X(m) X(m)
-900 1
. -800 t
-700 t
-600 t i ~
-500 t ~ Hi,)
-400 t ~ '
Too+ I'm
°L I real I
100
300
500 700 900 1100 1300
-100 r
100 +
Boo t
500 +
7oo t
Boo 1
1400 1600 1800 2000 2200 2400
X(m)
OCR for page 234
E 8 | ~ E 8
6- '. ~ 6-
4- , , , , 1 , ' 4- , , , , , , i
~C~ O - ~ ~ ~ ~ = =
-3 -3
1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 1 ..........
0.5 ~ 0.5
~ O- ~ , s O-
._ -0.5 . ~ -0.5
-1 - 1 1 1 1 1 1 i -1 - i
- 1 Q 50 ~ - ......
300- _ ~ . ~ 300-
100- ~~ ~ 100-
-100- ~ I -100-
12 1 2
E 8 W ~ ~ _ E 8 ~ it=
61 , , - ~ 6
4 4
E 0 2 ~ ' _- ~ ~ 0 6
-1 - , , , , , , , -1 -
_ 001 ' = - ' O ~ ~ - -
E 002 ~ ~ E 0 02 fir
3 -0.03 -0.03
-0.04- ' ' ' ~ ~ ~ i -0.04-
0.08 - -- ~ 0.08 - .... . . .. . . .....
0 04 ~ ~ eL 0.08
-0.12 -0.12
~ W0.011 \ _ ''_= {D0.01~
-0.05 -0.05
of ~ ~ 1 - ~ _
jib 06~ ~ 06;
-0.2 -0.2
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
Time (s) Time (s)
Fig. 10 Ship 2 tactical circle. Left column: training file 3223.
Right column: validation file 3310.
Predictions: solid lines, Measured: dashed lines.
OCR for page 235
so
-20
o
20
40
60
80
100
120
140
-100 r
-50
E 50
-
>~ 100
150
200
it
0 2000
X(m)
\) '-' 1
250 - _
2000 4000
X(m)
-1 00
-50
0
50
100
150
200
250
0 1000 2000
X(m)
0 1000 2000 3000 40t
X(m)
3000
-300 -
-250 -
-200 -
-150 -
-1 00 -
-50 -
O
601 0
1 i"~!
. ~) 1 1
1 Boo 2000
X(m)
-300
-250
-200
-1 50
-1 00
-50
O
3000
! I
I ~
2000
X(m)
Fig. 11 Ship 2 horizontal overshoots. Top row: training files 9002, 9040, 9030, and 9070.
Bottom row: validation files 9060 and 9000.
Predictions: solid lines, Measured: dashed lines.
For Ship 2, the network was trained using 20
tactical circles with 5 set aside for validation, and
Fig. 9 depicts the predicted and actual trajectories. The
top row of the figure contains four of the 20 training
maneuvers, 2 right turns and 2 left turns, and the
bottom row contains 4 of the 5 validation runs. The
four training runs that are shown represent a mixture of
four different rudder angles and four different approach
speeds, and the validation maneuvers consist of three
different rudder angles and three different approach
speeds.
Even though Ship 2 is larger with bigger
propellers and rudders the network again performs
extremely well on the training runs and very good on
the validation runs. Note that the fifth validation run is
of similar quality, and was not shown due to space
limitations.
Var Abs. KIT.
~-
u 0.12/0.18 m/s
x
Y _
\~1 4.4/7.2°
37 9 1 HISS 7 m
',s~/4nom
0.22/ 0.57°
Pet.
1.5/2.3
1 3.5/ 5.2
_ 2.713.7
9.7124.9
_-
0.8/ 1.3 _
Avg. Ang.
0.989/0.984
0.982/0.978
0.967/0.948
0.840/0.523
n oso / n os1
COIT. Coef. |
0.987 /0.968
0.993 /0.984 1
0.995 / 0.990]
0.845 / 0.462
. 1.000 / 1.000
Table 5 Ship 2 tactical circle error measures
averaged over all maneuvers / averaged over
validation runs only.
In three out of the four cases the advance and transfer,
has been predicted extremely well. Predictions for the
steady turning diameter are excellent in all four cases.
The results for Ship 2 are quantified in
Table 5. The first number in each cell is an error
averaged over all 25 maneuvers, whereas the second
number is the error averaged over the 5 validation
circles only. The percentage errors were obtained by
normalizing with: average steady speed in the turn of
7.9 m/s (26ft/s), average turning diameter of 1072 m
(3516ft), average peak-to-peak roll variation of 2.3°
and an average heading variation of 560°.
Figure 10 displays Ship 2 speed, roll, pitch,
heading and the direct neural network outputs: linear
and angular velocity components. The left column of
graphs gives the data for training file 3223 shown in
Fig. 9, whereas the right column depicts graphs for
validation circle 3310. One can see that the data is
predicted almost perfectly for the case of the training
file, and this is typical for all of the training files. For
the validation file, agreement is again very good. In
general, the predictions of v and w during the advance
and transfer phase and especially ~ are the most
difficult quantities to predict.
Ten horizontal overshoot maneuvers were also
available for Ship2. Eight were used to train the
network with two set aside for validation purposes.
OCR for page 236
E 7 ~ ~ E r ;
6: ~ 61 ^~~
5 5
~ ~ ... 3 _ ...
0.4- 04 .............................................................
hi, 0.2- . to 0.2-
`~ -0.2 ~ ~ ~ = ~ ~ ~ ~ ~ I -0.2
-0.4 -0.4
to I ............. ~e
-40 -40
E 7 ~ E 7 it,, I_ =
.... ,., ,,., ,., ,.,, , , ,,,.,., , ,, , .................................... ,,,,, , , , , , ,., , ,,,,,,,,,, ,,, ,,,.-
E ~ \ / : ~ E 0
-0.8 -0.8
0.02- 1 0.02- .......
0.01 ~/ ~ 0.01 ~~ me, =;
3 -0.01- , , , , , , 3 -0.01-
-0.02 -0.02
0.08 ------------------------------------------------------------------------------------------------------------------------------------------------------------------] 0.08 ----------------------------------------------------------------------
'', 000 \ / ~ ~ ~ / <~ =~ 004~ w
-0.08 -0.08
0.03 - .. . ........... .................................................................................................................. ^ 0 03 ...................................................................
:- a' 00 ~ ~ ~ 001t \_/ ~ ~ ~
-0.03 -0.03
_0'5 ~ , ~ =005 ~ \ /
-1 -1
0 100 200 300 400 500 600 0 100 200 300 400 500 600
Time (s) Time (s)
Fig. 12 Ship 2 horizontal overshoot. Left column: training file 9070.
Right column: validation file 9060.
Predictions: solid lines, Measured: dashed lines.
OCR for page 237
The predicted md a blat hajectories ale show in
Fig 11 The top row of the figure contains four of the
eight traming m meuvers, tw begmning with right
tm s md two beginnmg wish led tug S, md file bottom
row contams both validation mns The four homing
runs tha a e show represent a ml ture of two different
rudder checking mgles md two different apron h
speeds, md file w~lidaion m meuwrs consist of tw
different rudder checking a gles md tw different
apron h peed
The honzonta over hoot is a more complex
m meuver Ah m the to tick cacle md yet file netw rk
twined extremely well to file data Small deviations
from the a t a path were typicaly 10 m or less with
the large t deviations of about 20 m This is aso the
ca e for the but of file tw vaidaion m meuvers The
prediction for file second validation run is exceptional
until about 1000 . into the mmeuver ssbere a lager
deviation of about 50 m occurs
The results for Ship 2 overshoots ale listed in
Table6 The but number in each cell is m enor
avenged over al ten mmeuver., wherea the second
number is the emu averaged m al file tw w~lidaion
runs only The percentage emus were obtained by
no mail ing with: average steady speed Isle m the
m meuver of 4 2 m s (13 6fl/s), asrutie Spain period
of 1424 m (4672fl), werage peak-to-peak distmce of
153 m (500fl), asrutie peak-to-peak roll va Ration of
1 2° md m average peak-to-peak heading vaiaion of
41°
Table 6 Ship 2 hori onto over hoot emu mea ures
averaged over al mameuvers / averaged over
vaidaion runs only
Figure 12 illu it lie. Ship 2 peed, roll, pitch,
headmg md file neural netw rk ouqputs: Imea md
mgula velocity components The led column of
grmhs gives the data for over hoot homing Ale 9070
show in Fig 11, whesea the right column depicts
grmhs for validation run 9060 The agreement with
the h Ming da a is excellent, md for file rdlda ion Ale,
the agreement is w y good indeed Examinaion of
Figs I I md 12 show that predictions of the impo t mt
qumtities deEnmg a honzonta or hoot mmeuwr:
red 11, period, overshoot mgle md overshoot time a e
predicted ve y well
The reader Lloyd note tha emus m
predictions trom neural netwodks twined with
emerimenta data cm be no better film the precision
enor i herent m the data To make some estimaes of
detle tion md approal HI speed were compared For file
to tick cycles, file steady peed m the turn varied by
O 1-0 2ms (0 3-0 6fl/s) or 1 4%, the tummg diameter
differed by 30 m (lOOfl) or 3-5% md file peak-to-peak
roll fluctuated by 0 2-0 3° or 10% For file hori onto
overshoots, the e timaed pain period varied by a
much a 150 m (500fl) or 10%, the peak-to-peak
distmce tlnclllred by 15 m (50fl) or 10%, file peak-to-
peak roll clla ged by 0 3-0 5° or 30-50% md the peak-
to-peak heading differed by 1-3° or 2-7/o
CONCLUSIONS
Reckon e neural netw dks homed on to tick
cycle mmeuvffss for tw separate ships were able to
predict speed, tmje to y components md heading wish
enors averaged over al file data of 5% or less When
considering only file vaidaion mmeuwrs, rlm5 for
these variables raged fiom 1-7/o Emus in roll
e timaes were tom 0 2-0 5° for m avenge roll
vaiaion of 2-3° For the more complex overshoot
m meuver the emus were only a little higher Speed,
longit ding haje to y component, x, md headmg
e hibited enors averaged over al file data of 5% or
less, wherea considera ion of ju t file va ida ion
mmeuve5 increased the enors to 10% or less Roll
enors were O 1-0 3° for m average roll vaiaion of
12°
The mo t difficult predictions for file
overshoots were clearly the trmwerse hajecto y
component, y, m integ a qu mtity resultmg prima ily
fiom the t msver-e velocity component, x, md to a
lesser extent, the heading This is a so file likely red on
for file flicker bmd of generali Lion rlr5 a file
solution evolved dating Gaining The effects of wind
on the or hoot mmeuwrs will be felt shongly m
these tw variables a the mmeuwrs are Sways
conducted paalel or mti-paalel to the wind
duection in file case of the cycles, for which
environmental effects could be removed, the networks
pe to med well for these tw va iables Clea Iy glen,
substmtia improvement is likely to result trom file
addition of wind force md moment inputs to the lle r al
netw rk models, md f ture w dk will be directed to
Allis end
Rerlhnv neural netw rks have demon trued
m ability a a robust md acurae mmeuvermg
simulation tool With the f ther addition of
environmental etle ts, the simulation could serve a a
plmt model within m admtive conhol system New
control cmahildies under investigation include
OCR for page 238
OCR for page 240
OCR for page 241
OCR for page 242
Representative terms from entire chapter:
neural netw
tmjecto y following, mmeuver pre-plmnmg amd
improved talon-keeping under adwrse conditions
ACKNOWLEDGEMENTS
The U. S. Offce of Nava Resea ch sponsors
this w rk, a d the program monitor is Dr T
DISCUSSION
J. Fein
Naval Undersea Warfare Center, USA
The neural net is s powerf I interpolator of htr But
by using e timsted force Ed moment models, are
you not i trod cing en or Ed leading to s network
that has the w aknesses of s coefficient model, rasher
th m s neural net based purely m h isls data with
unspecified imput
AUTHOR'S REPLY
To mswer this que non, let us review s f w
details of She simulation technique The Inputs to the
INN model consist of time histories of She conhol
variables Ed She initial condition of She vehicle To
use the hained network, the user provides She
r pared controls dots, Ed s prediction of She motion
of th vehicle is obtained Th control hi tories may
come fr m experimental data, or sltenurtively, the
control histories Ed imtial co diti ms may be moated
by the user to describe s desined maneuver not carried
out experimentally The simplicity Ed flexibility of
this arrmgeme t makes the simulation easy to use
However, She resulti g motion of the vehicle is not
duectly rel.t ed to s rudder deflection Ogle or s
propeller rotation peed but Instead to She lif force
produced by that deflected rudder or to the f u t
produced by the propulsor Therefore, m
intermediate step, as show in Fig I in She p Her, is
required to t msfomm easily pecked input conhol
variables mto She forces Ed moments Nat direct She
motion of She vehicle Dr Fein's q esti m concern
the maimer in which this h msformstion should be
accomplished
This paper computed lorces Ed moments
from nonlinear expressions using empirical or fitted
coefhcients The primary concern here is to define
She shape of the nonlinear force Ed m merit time
histories as opposed to getting scaling factors exactly
correct S sling th force Ed m merit amplitudes or
spplymg s DC offset will not affect th nbi it of the
neural network to identify She relationship between
force Ed m merit Inputs Ed motion outputs; Instead,
it will simply alter She magnit de of She weights Nat
me determined during haming In fact, all of the
naming data must be scaled, using s Imear
t msfcrmsti m, to the domain Ed r mge of She
activation fm tions employed within each node of
the network (see Eq I m the paper) before it c m be
used For example, the complicated expressions for
th righting moments defined m Eq 19 c m be
replacedbyth simpler e pressions
K, = an go Ed M, = smO,
~1)
becmsethe premultiplying coefficie ts simply serve
to scale the smplit de of the simmsoids More
impo tmt h re is to capture the f ndsmental
sinusoidal behavior Ed thorn let th nemal network
determine during haming the correct weight
magnit des to ensme appropriate scaling On the
of her hand, coefficie ts such as c, Ed c: m E 5
adjust the relative level of two contributions to T~,~
Ed Therefore help to define She shme of She resulting
quantity Conecting small deficiencies m these
coefficients is lik Iy to provide s second or r
conection to the predictions at best The ~emarkstle
level of accuracy Greedy obtained demon tmtes His
generallymth 5-10%rmge,seeTstles 4,5 md6)
Fu themmore, She accmacy Nat is ultimately
achievable is conshamed by the precision enor
i herent m She experimental dote used to train the
simulation
A alternative method for estimating ~esultmg lorces
Ed moments from specified control variables is to
employ CFD using pote tisl or FANS codes This
may prove to be s sup rior method Ed has She added
benefit that th geomeby of th vehicle is explicitly
defined during this process Coupling CFD
computttiorr to the front end of s INN simulation
offers th potential for s ye mete to-motion
simulsti m capability The mfhors have already
commenced efforts m His direction as part of mother
effo t Ed work is proceeding
DISCUSSION
T. Ji mg
Versuchs mstalt fur Bi memchfffl m e \, Germ my
In your presentation, you apply partly ve y complete
lorce formulations, for mst me, for prop Her Ed
rudder forces, Ed partly ve y simple fommuls, for
in tance for Mu k's moment My question is what is
impo t mt in mod hng She hyd odynamics by using
the neural network technique? Which details of She
hyd odynsmics me radii v requuedS
AUTHOR'S REPLY
In general, when combuctmg s nemal
h twork, Oh mu ~ UK lude nil Inputs that htse m
i flux e on the outputs that Oh is trying to predict
Id ntifyi 8 the mproprhte inputs c m h n difficult
hsk For example, ff the expression for She Mu k
moment c m be signffi Fitly improved with the
inclusion of free surface effects (as suggested: She
discussi m by V Be tom bel w), th n th output
predictions are likely to improve The level of
improvement will be dictated by the degree to which
th omitted Input i fommati m effects the outputs
The fact that She work reported here achieved c level
of accmacy generally in She 5-10% range (see
Tables 4, 5 Ed 6) Indicates Nat cdditiorul input
i fommation that may be k ki g in th current
simulation is likely to offer only second order
improvements On She of her h Ed, for the hori ontcl
overshoot maneuvers, the abnormally high error in
th h msverse tmjecto y component, y, is m
indication that import mt input i formation is still
missing This is exp cted to improve with She
addition of envuomme till factors (wmd faces) es
described m the paper
DISCUSSION
E Mesbahi
University of New astle, United tom don
Application of Artffflcitl Neural Networks m dynamic
mod ill g, simulation Ed co trol of highly n mime
systems ht. been proved se y successful for c wide
r mge of ind strict applications _' Ming from
unde water remotely operated vehicles to She conhol
Ed monitoring of satellite sy tems Undoubtedly,
marine technology Ed related industries, extending
from prelimirLtry ship design offices to the
sophi ticated ride control ystems, all could benefit
from ANN techniques as c versatile static Ed
dynamic mod Inn platfomm
Authors are to be con mmh~ d on c very concise Ed
w 11 presented pep r Their excellent work clearly
sh ws Shea f 11 appreciation of She physical mles
governing ship motions Recursive nemal network
me used for dynamic mod llmg of ship m moeuvres
Commmt 1: RNNs m provide non-physiccl models
of dynamic ystems; m other words, Heir application
me similar to con- emmn~l sy tem identiflcation
techniques such es L c t Squmes An outst mding
pm t in this pmer is the combirLttion of phase 91
under t mding of the ship motion parameters Ed
RNN methodology Aubhors force the RNN to learn
th functicrurl relati mship betw n ce tam input
parameters, which me cclcubted in "Component
Force Modules", Ed measured "6 DOF State
Variables" (se Fig 1) Once c valid model is
obtained (after s fficient Ed succes ful ttsmi g), it
may be utilized for time-domcm Ed c mseque fly
creeps -d main crurlysis of the ship moti ms
Q cation 1: Could w ignore the "Component Force
Modules" box Ed t y to model She ship motions by
using "E vuommental Wind Ed Waves" Ed
"Control Signals" only? This is closer to c "Black-
Bcx" mod llmg approach where no physics is
implied
Commmt 2: The effect of She en ir mental factors
such es wind sled mfavoumble oce m cunents are
mentioned to close d ffts, hence dust rbmg the ship
m moeuvrmg cacles This is partially confected by m
mtomated procedure I hope this mtomated
procedure looks after both tidal Ed wave Ed wind
d ffts
Question 2 Could we use these two signals, i e
metsured wave Ed wmd, es cdditiorul Inputs into
RNN model Ed do not t y to eliminate unavoidable
d if t in the m moeuvring circles? This may lead to
mod Inn, or in better words, to finding the
functional relationship betw en wave Ed wind signal
Ed unconected ship cacles
Commmt 3: Generalisation cmctility of RNNs are
w 11 described Ed presented Fig 7 clearly sh ws
that contimmous t~ainmg will improve She accmacy of
th model for c particular ship type Nevertheless,
once th haming is stopped, the RNN mod I only
represents c specific ship t pe, shipl or ship' m this
case in other words, model is not c generic model
capable of representing c wider r mge of ships This
is clearly c short oming of She RNN simulation when
compared to conventional mathematiccEphysiccl
mod Ihng of ystems
Q action 3: Fu th r research: Whet would happen if
you mix the ttsming epochs of shipl Ed ship' Ed
train one single RNN? Obviously each set of data
needs to be tagged separately by c m meric
representi g She ship Ember But, is His
generalisation possible et all?
AUTHOR'S REPLY
Question I Th moti m of She vehicle is not
duectly related to c rudder deflection Ogle or c
propeller rotation peed but Instead to She lif force
produced by that deflected rudder or to the f u t
produced by the propulsor Therefore, She
i termedicte step trmsfommmg easily specified Input
co trol variables i to She forces Ed moments Nat
duect fihe motion of the vehicle is requited
How ver, the question is wh ther fihe neural network
c m team this t msformstion or wh ther it must be
explicitly defined The mthors did not tug the
suggested approach in this work
experience with of her probl ms m which both
approaches w re art mpted has show that output
prediction m be improved by including k wn
physical i formation Particularly importmt is to
defme the type of input nonlinearity For example,
for the righting moments, which fundamentally have
s sinusoidal response, the output prediction is likely
to be better by explicitly defumg inputs as ink md
sinO mvend of just as 93 md O
Comment 2 The automated d fft conection
procedure does not requite my k owledge about the
cmse of th d fft it simply conects whatever d fft is
present
Question 2 The mfhors believe that the
m wet to f is q estion is yes Conecting for d fft as
opposed to duectly p~edictmg the motion of the
vehicle executing unconected circles has always
been considered to be s temporary fast step The
inclusion of err nonrnem31 factors Kunently
underway) should make She d if t confection
procedure unnecessary
Comment 3 Th fact that th cunent
modeling sch me recopies s separate INN model for
each ship t pe is disadvantageous How ver,
practically, She time r pared to create s deferent
model for s deferent ship type is minimal if the
experimental dot is available Therefore, the impact
so far has t een minor As described above m the
reply to J. Fein, the mthors are attempts g to inject
geomeby i to She model by coupling CFD
calculations on She fro t end if f is effort is
our e. ful, thorn s single model may be sufficient for
s cuss of ships is s --is s single ship
Question 3 This approach has not been
tried md so the msw r is not k ow The lik I hood
is Nat She solution, if it converges, will represent
neith r ship Minimal geomeby i formation is
includ d it preiem md is used primarily to rend r
variables dnnennonfess
DISCUSSION
V Berbam
Hamburg Ship Model Basin
Gemm my
I co grist late the mthors on their progress
made since the 22 Symposium on Naval
Hyd odynamics Th mfhors r mmd us with Heir
i toasting conh~bution Nat ind ed ship
hyd odynsmics encompasses more th m just CFD md
progress is till possible land thus research
worthwhile) tl so in experimental fluid dynamics The
mfhors succeeded again in presenting then work m s
clear md unpretentious way Nat serves as s good
imtt oduction to She neu ml network technology I hope
the pap r will umpire more colleagues to study md
incorporate neural networks in ship hyd odynsmics
I would lik to add s few references for
nemal network applications in ship hyd odynsmics
Various applications mcludmg the trimar m ship
moti m prediction c m be found in [2] which should
be more widely available th m the 1993 reference [3]
use neural network to predict mdder forces on s new
i tegmted propeller-rudder sy tem [4] mploy neural
networks to derive simple ship d sign e timstes
e pecislly for t gs [6] has developed s commercial
program for the prediction of propeller induced
p~essme pulses accountmg also for cavitatmg
prop Hers [1] use neural networks m co trolling tins
to reduce ship motion where the neural network is
trained on new t 9.. 9.' Apparently neural networks
d if slowly i to th maritime mdu t y but are far
from bemg widely used I would like to invite the
mfhors' comments on why w do not see more
research r employing neural networks md what
could be done to disseminate th technology faster
within the community
On several occasions She hors have
inhoduced mme k owledge about the physics f m in
the previous work presented It the 22 d Symposium
in Wsshmgtoa The pragmatic engineering approach
obviously improves She overall mod Inn
capabilities Coefficients are often simply estimated
by const mts lying m s t pi 91 b mdwifh of ship data
The mfhors ckim that "although m attempt to
produce re tSontble coefhcients for thrust e pressi ms
..95 made, my errors m the coefhcients will be
accou ted for by the network during teaming " This
statement is somewhat mislesdmg Neural nets cm
only yield proper predictions ff all ~elevmt input
variables me supplied This is ack owledged in the
exphrmtion of ~ mm errors due predomi Fitly to
the not yet mod fled i fluence of wmd, but should be
mewed h me sgsm let addition, neural nets map
fm tions on intervals between 0 md I If She set 91
dhtn lie only on 9 tm911 t bmter. al, the Resolute m"
of th spproxim tti m will be .. t t thm ff the whole
interval would be used This should result in higher
enors in She predicti m of She hamed network it is
th refute desirable to t pply as much i formation as
possible or ressonshle to the mod I md reduce the
Chute force" neural net system identification to the
r mlinmg coetllcienrs Wtke fir non, thou t
deducti m coefficients md stability coefhcients like
BMr may be estim tted with more socur y
dep ndmg m ship typ or mam dimensions [5 giv
various empi ical fommuke deriv d by cor~ntiom~l
regression arulysis Using better estimstes here msy
facilitate fhe r msinmg job for the neural nets
Th Mu k moment seems to be p~edicted
quite simply neglectmg the effect of the fiee su face
Ev n within potentisl theo y, the ship will experience
s trim moment md s v rtical fmce due to fhe effect
of fhe free surface These forces will ususlly increse
wifh peed md decresse with wster depfh They msy
be impo t mt in shallow wster ev n st I w speds
Such forces c m be predicted ressorurbly w 11 with
f~ su face potentisl flow codes ~equirmg perhaps
30 mim tes CPU time on is t generstion PCs I would
I kc to mvite s comment on wheth r fhe mthors dem
m extff~sion of th ir model in fhis duection as
worfhwhile or whedher the expected improv ment
would not justify fhe sdded c mplexity in the
spproach
As s frul c mment: Hsv fhe suthors
com idered to validste their nemal network spproach
sgsinst ship model tests under controlled conditions
in towing tmks? Model experiments should then be
much better reproduced ff mdeed the i fluff~ce of
wind is fhe predomi mt factor accounting for errors
m model
I Lmt, DA, Mook, DT, VmLAnd6ngham, HP
md Nsyfeh, A H "Roll reduction m ships by m nas
of activ fim conholed by s neural network", Ship
Techmology Research 47, 2000, pp 79-S9
2 Mestshi, E md Atlar, M "Adifcisl Nemal
Networks: Applicsti ms in Marme Design md
Modelli g", I h~term~tiorurl Co ference on
Comuuter Aunlicstions md formstion Techmolo~v
in fhe Marine industries, COMPIT'2000, Potsdsm,
2000, pp 276-291
3 Mestshi, E md Koushm, K '?mpaical
PredLction Medhods for Rudder Porces of s Nov I
I tegmted Propeller-Rudder Sy t m", OCEANS'9S.
IEE OES Co ference, Nice, 199S, pp 532-537
4 Mesbahi, E md Berbam, V "Empaical Design
Pormuke using A tificial Neural Nets", I
Internatiom~l Co fe~ence on Comuuter Aunlicstions
md formstion Techmolo~v in the Marine industries.
COMPIT'2000, Potsdsm, 2000, pp 292-301
5 5 hmeekdubh, H md Bertmm, V "Shiu Desien for
Efficiencv md E onomv", Butterworfh &
Hememarm, O ford, ISBN 0750641339, 199S
6Koushm, K "Prediction of Propeller h~duced
Pressme Pulses Usmg Adffiical Neural Networks", ",
I Intemstiorul Co fe~ence on Computer
Aunlicstions md I formstion Techmolo~v m fhe
Marine Indushies. COMPIT'2000, Potsdsm, 2000,
pp 24g-254
AUTHOR'S REPLY
Comment I Nemal networks are I kely to
bee me more widely used withm fhe maritime
commmmity if fhey c m be show to be successf I md
if they c m demonstmte fnat they p~esent s istle
slterrutiv to e istmg techmiques A large f~action of
ext mt neural network ~esearch ~eported in fhe
literst re has beff~ concem d with ~demic
questions regarding textbook problems ss opposed to
explormg spplied problems See fhe literst re ~eview
by Psller, 1996 Inmessed spplicstion of neural
networks to spplied problems is likely to slleviste
bodh concems
Comment 2 The mthors sgree thst the
inclusion of relevmt physical i formstion to ~educe
fhe level of brute force sy tem identfficstion fnat
must be performed by fhe neural network is desimble
How v r, efforts to better estimste those coefficients
fnat me~ely scale th amplitud of th input me not
r quned ss descobed m the ~eply to J. Peia An
sdditiorurl example of such s scaling coefficient is the
thust reduction coefficient ss impleme ted m E 5
Us mg better e stimste s for fho se coefhcients fna t
determine fhe shope of the input time histories, such
ss wake coefficient, msy mdeed improve the ~esults
somewhst
Comment 3 The use of CPD codes to
mgment or duectly perfomm the calculstion of fmce
md moment inputs is m excelle t sugge tion fnat has
been considered Initisl sttempts to couple CPD
calcubtions wifh the RNN simulstion me underway
ss part of mother project
Comment 4 The mthors hav comid red
usmg ship model te ts to validste fhe nemal network
spproach We are sttempting to id ntffy sppropriste
exp rimental dsta thst co tsms enough messured
varistles to be usef I for fhis purpose
REFERENCE
Psller, W. E md 5 h eck, 5 J. "Neural Networks:
Applicstions md Opport nities m Aero mtics",
Pro~'ess m Aerosuace Sciff~ces, Vol 32, No 5,
1 996
