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MODELLING ENVIRONMENT AND INFRASTRUCTURE OF SHIPYARD TRANSPORTATION SYSTEMS AND PROCESSES
A. Blokus-Roszkowska, K. Kolowrocki.
Gdynia Maritime University, Gdynia, Poland e-mail: ablokus@am. gdynia.pl
ABSTRACT
In the paper an analytical model of port transportation systems environment and infrastructure influence on their operation processes is constructed and presented in an example of shipyard rope transportation systems in Naval Shipyard in Gdynia. A general semi-markov model of a system operation process is proposed and the methods of its parameters statistical identification are presented. Further, the shipyard rope transportation system and the ship rope elevator operation processes are analyzed and their operation states are defined. A preliminary collection of statistical data necessary to the ship transportation systems' operation processes identification is included.
1 SHIPYARD ROPE TRANSPORTATION SYSTEMS - DESCRIPTION
The ship-rope elevator is used to dock and undock ships coming to the Naval Shipyard in Gdynia for repairs. The elevator is composed of a steel platform-carriage and 10 rope-hosting winches fed by separate electric motors. Motors are equipped in ropes "Bridon" with the diameter 47 mm each rope having a maximum load of 300 tones (Kolowrocki 2002, Kolowrocki et al. 2002). The rope transportation system in the Naval Shipyard in Gdynia is composed of three broaching machines working independently equipped in the steel ropes "Drumet" with the diameter 30 mm. This system is used to transfer ships coming to the shipyard for repairs from platform to the repair post and back from repair post to the platform. The load of steel ropes in the broaching machines is measured as a power consumption of amperage. The maximum of power consumption of broaching machines is 100 Ampere.
Generally all actions taken to the ships coming to the shipyard for repairs can be divided into 5 tasks:
- task 1 - ship docking (rope elevator is working),
- task 2 - ship's transportation to the repair post (rope transportation system is working),
- task 3 - the repair measures (both systems are not working),
- task 4 - ship's transportation to the platform (rope transportation system is working),
- task 5 - ship undocking (rope elevator is working).
Figure 1. The ship at the repair post R1/B1.
First during ship docking the ship settled in special supporting carriages on the platform is raised to the wharf level and then the ship is transferred from the platform with the rope broaching machine on a traverser. Next the ship with the traverser, on which the ship is settled, is shifted in the repair post direction. Then after stretching the ropes from the ship to the broaching machine through some blocs, the ship is transferred from the traverser to the repair post. After some repair measures, the ship is transferred back to the traverser and then on the platform. Finally, during undocking the ship on the platform is moved down to the water. There are nine repair posts, denoted by symbols R1-R9. The first repair post R1 can be lengthening to the post R1/B1 for long ships. There are also available two repair depots denoted by symbols B and D. Generally all kind of repairs can be carried out in any repair post. The repair posts R1 and R2 are equipped in crane. The submarines are repaired in the depot. Additionally large vessels are transferred to the repair post R1/B1. The scheme of the plan of repair post placing is given in Figure 2.
D B v............' , < ___-BROACHIN ^^ BROACHIN ^BROACHIN r G MACHINE NO 3 G MACHINE NO 2 G MACHINE NO 1
= PLATFORM = TRAV ERSER R1 B1
r» ■ ■ ■—
R6 R2
R7 R3
R8 R4
R9 R5
Figure 2. The scheme of the plan of repair post placing.
2 SEMI-MARKOV MODEL OF SYSTEM OPERATION PROCESS
Usually the system environment and infrastructure have either an explicit or implicit strong influence on the system operation process. As a rule some of the initiating environment events and infrastructure conditions define a set of different operation states of the industrial system. Thus, we assume that the system during its operation is operating in v, v e N, different operation states. After this assumptions, we can define the system operation process Z(t), t e< 0,+<»>, with discrete states from the set of states Z = {z1, z 2,..., zv}. If the system operation process Z(t) is semi-markov (Grabski, 2002) with the conditional sojourn times 9bl at the operation states zb when its next operation state is zl, b, l = 1,2,..., v, b ^ l, then it may be described by (Kolowrocki & Soszynska, 2006):
- the vector of probabilities of the system operation process initial states
[ Pb (0)]1xv= [ P1 (0), p 2(0),..., pv (0)],
where
Pb (0) = P(Z(0) = zb) for b = 1,2,...,v,
- the matrix of probabilities of the system operation process transitions between the operation states
P11 P12 ... Plv
[ ] = P21 P22 . . . P2v [Pbl ]vxv =
_Pv1 Pv2 . . . Pvv _
where Pbb = 0 for b = 1,2,..., v,
- the matrix of the system operation process conditional sojourn times 0bl distribution functions
Hu(t)H 12(t)...H^(t)" H 21(t) H 22(t)... H 2v (t)
[Hbl (i)]„v =
Hvl(t ) H v2 (t )... Hvv(t )
where and
Hbl (t) = P(6bl < t) for b, I = 1,2,...,v, b * I,
Hbb (t) = 0 for b = 1,2,..., v.
Under these assumptions, the mean values of the system operation process conditional sojourn times 0bl are given by
Mb, = m,] = 1 tdHM (t), b, l = 1,2,...,v, b * l.
(1)
By the formula for total probability the unconditional distribution functions of the sojourn times 6b of the system operation process Z (t) at the operation states zb, b = 1,2,..., v, are given by
Hb (t) =vPb,Hb, (t), b = 1,2,..., v. (2)
1=1
Hence, the mean values E[9b ] of the system operation process unconditional sojourn times 0b in the particular operation states are given by
Mb = E[db] =vPb,MM , b = 1,2,...,v, (3)
,=1
where Mbl are defined by Equation 1.
Moreover, it is well known (Grabski, 2002) that the limit values of the system operation process transient probabilities at the particular operation states
Pb (t) = P(Z(t) = Zb), t e< 0,+®), b = 1,2,..., v,
are given by
w A A
(4)
nbMb
Pb = lim Pb (t)=
t
b = 1,2,..., v,
i=i
where Mb, b = 1,2,...,v, are defined by Equation 3, whereas the probabilities nb of the vector [nb]1xv satisfy the system of equations
K ] = [nb ][Pbl ] i n = i.
(5)
i=i
Other interesting characteristics of the operation process Z (t) possible to obtain are its total sojourn times 9b in the particular operation states zb, b = 1,2,...,v. It is well known (Grabski, 2002) that the system operation process total sojourn times &b in the particular operation states zb, for sufficiently large operation time 9, have approximately normal distribution with the expected value given by
E[$b] = Pb9, b = 1,2,...,v, (6)
where pb are given by Equation 4.
3 STATISTICAL IDENTIFICATION OF SYSTEM OPERATION PROCESS
In order to estimate parameters of the operation process model the following step should be done (Soszynska, 2006):
- to fix the number of states v of the system operation process Z(t) and to define the operation states z1, z2, ..., zv of the set Z,
- to fix the vector of realizations
K (0)] = K(0), «2(0),..., nv (0)], of the numbers nb (0), b = 1,2,..., v, of the system operation process Z(t) transients in the particular states z, at the initial moment t = 0
- to fix the matrix of realizations
K] =
ni1 ni2 . . . niv n21 n22 . . . n2v
nv1 nv 2 . . . nvv
of the numbers nbl, b,l = 1,2,..., v, of the system operation process Z(t) transitions from the state zb into the state zl during the experiment time ©, - to fix the vector of realizations
[ p(0)] = [ P1 (0), p 2(0),..., pv (0)],
of the initial probabilities pb (0), b = 1,2,..., v, of the system operation process Z(t) transients in the particular states zb at the moment t = 0, according to the formula
Pb (0) =
n(0)
for b = 1,2,..., v,
where
V
n(0) =Z nb (0),
b=1
is the total number of the system operation process Z(t) realisations at t = 0, - to fix the matrix of realisations
Pn P12 ••• Plv
r p l = p21 p22 • • • p2v
vPbu -
_pv1 pv2 • • • pvv
of the transition probabilities pbl, b,l = 1,2v„,v, of the system operation process Z(t) from the operation state zb into the operation state zl during the experiment time ©, according to the formula
n
pbl =for b,l = \,2,..,V, b * l, nb
pbb = 0 for b = 1,2,:;V,
where
V
nb = X nbl , b = 1,2,:;V,
b*l
is the realization of the total number of the system operation process Z (t) transitions from the operation state zb during the experiment time 0,
- to formulate and to verify the hypotheses about the conditional distribution functions Hbl(t) of the system operation process Z(t) sojourn times 0bl, b,l = 1,2v„,v, b * l, in the state zb while the next transition is the state zt on the base of their realizations , k = 1,2,_,nbl during the experiment time 0^
4 SHIPYARD ROPE TRANSPORTATION SYSTEMS PRELIMINARY DATA COLLECTION PRESENTING
The rope transportation system reliability depends strongly on the tonnage of transferred ships and therefore we can divide system's load into six groups:
- without loading,
- loading over 0 up to 500 tonnes,
- loading over 500 up to 1000 tonnes,
- loading over 1000 up to 1500 tonnes,
- loading over 1500 up to 2000 tonnes,
- loading over 2000 up to 2500 tonnes^
The broaching machines in the transportation system are numbered 1, 2, There is used one or there are used two broaching machines depending on weight and length of the ship and on which repair post the ship should be transferred^ There are never used all three broaching machines simultaneously • So, the system under consideration is in order if one or two of the broaching machines are not failed^ Due to this fact we can conclude that it a "1 out of 3" or "2 out of 3" system^ The scheme of the transportation system is given in Figure 3^
Figure 3. The scheme of the transportation system.
With this knowledge during ships' transportation we can distinguish the following situations:
- the ship is transferred using only the broaching machine number 1,
- the ship is transferred using only the broaching machine number 2,
- the ship is transferred using only the broaching machine number 3,
- the ship is transferred using two broaching machines number 1 and 2,
- the ship is transferred using two broaching machines number 1 and 3,
- the ship is transferred using two broaching machines number 2 and 3.
Figure 4. The ship during transportation from the traverser to the repair post R7.
Now we can analyze the ship transportation system in Naval Shipyard in Gdynia taking into account the system operation process and its varying in time reliability structures. Considering the weight and size of the vessel, i.e. the system's loading and the place where the ship is transferred, that has influence on the decision which broaching machines are used, we can distinguish following (v = 25) operation states of the system operation process Z(t):
an operation state z1 - the system is without loading,
an operation state z 2 - loading over 0 up to 500 tonnes and the broaching machine no. 1 is used, an operation state z3 - loading over 0 up to 500 tonnes and the broaching machine 2 is used, an operation state z 4 - loading over 0 up to 500 tonnes and the broaching machine 3 is used, an operation state z5 - loading over 500 up to 1000 tonnes and the broaching machine 1 is used, an operation state z6 - loading over 500 up to 1000 tonnes and the broaching machine 2 is used, an operation state z7 - loading over 500 up to 1000 tonnes and the broaching machine 3 is used, an operation state z8 - loading over 1000 up to 1500 tonnes and the broaching machine 1 is used, an operation state z9 - loading over 1000 up to 1500 tonnes and the broaching machine 2 is used, an operation state z10 - loading over 1000 up to 1500 tonnes and the broaching machine 3 is used, an operation state z11 - loading over 1000 up to 1500 tonnes and the broaching machines 1 and 2 are used,
an operation state z12 - loading over 1000 up to 1500 tonnes and the broaching machines 1 and 3 are used,
an operation state z13 - loading over 1000 up to 1500 tonnes and the broaching machines 2 and 3 are used,
an operation state z14 - loading over 1500 up to 2000 tonnes and the broaching machine 1 is used, an operation state z15 - loading over 1500 up to 2000 tonnes and the broaching machine 2 is used, an operation state z16 - loading over 1500 up to 2000 tonnes and the broaching machine 3 is used, an operation state z17 - loading over 1500 up to 2000 tonnes and the broaching machines 1 and 2 are used,
an operation state z18 - loading over 1500 up to 2000 tonnes and the broaching machines 1 and 3 are used,
an operation state z19 - loading over 1500 up to 2000 tonnes and the broaching machines 2 and 3 are used,
an operation state z 20 - loading over 2000 up to 2500 tonnes and the broaching machine 1 is used, an operation state z 21 - loading over 2000 up to 2500 tonnes and the broaching machine 2 is used, an operation state z 22 - loading over 2000 up to 2500 tonnes and the broaching machine 3 is used, an operation state z 23 - loading over 2000 up to 2500 tonnes and the broaching machines 1 and 2 are used,
an operation state z 24 - loading over 2000 up to 2500 tonnes and the broaching machines 1 and 3 are used,
an operation state z 25 - loading over 2000 up to 2500 tonnes and the broaching machines 2 and 3 are used.
All preliminary defined operation states of the ships' transportation system operation process will be verified in they are necessary in practice after the experiment time i.e. after full identification of ships' transportation system operation process.
For example a vessel with tonnage 1500 tones is dragged first from the platform to the traverser during 3 hours and 15 minutes using broaching machine number 3 and next with the same broaching machine from the traverser to the repair post R4 during 45 minutes, so the system operation process Z (t) is in operation state z10. A vessel with a tonnage 1700 t is transferred using two broaching machines number 1 and 2 from the repair post R1 to the traverser during 1 hour 30
minutes (an operation state z17) and then for about 1 hour from the traverser to the platform using one broaching machine number 1 (an operation state z14).
To identify all parameters of this system operation process the statistical data are still collected as a part of the Poland Singapore Joint Research Project "Safety and Reliability of Complex Industrial Systems and Processes". Preliminary statistical data are given in Tables 1 and 2.
Table 1. Preliminary set of realizations of rope transportation system in Naval Shipyard in Gdynia operation process conditional sojourn times in particular states
Number of realization Ship's tonnage Broaching machine 1 2 3 Operation state Date Start time Time of state duration Start post End post
1 1700 t X X z17 24.02.08 20:00 1h 30m R1/B1 T
2 1700 t X z14 24.02.08 22:10 1h T P
3 1200 t X z10 25.02.08 21:30 2h 30m P R1
4 1500 t X z10 13.03.08 19:25 3h 15m P T
5 1500 t X z10 13.03.08 23:20 45m T R4
6 600 t X z7 20.03.08 09:15 25m R7 T
7 600 t X z7 20.03.08 10:35 30m T B
P - platform, T - traverser, B - depot, R1, R4, R7, R1/B1 - repair posts,
Having given the preliminary statistical data in Table 1 we can begin the statistical identification of the system operation process. We assume that the numbers nbl, b,I = 1,2,...,v,b ^I, of realizations of
the system operation process Z(t) transitions from the state zb into the state zt during the
experiment time © should be equal at least 40. We expect the experiment time to be about 1 year to have fulfilled the above condition. After this period of time the full identification of ships' transportation system operation process will be performed.
At the initial moment t = 0 the system operation process is in the operation state z1 (without loading) and the initial probabilities of the system operation process transients in the particular state at the moment t = 0 are equal
A(0) = 1, pb (0) = 0 for b = 2,3,...,25. After collecting all necessary data during the experiment time we can determine sojourn times 0bl, b,I = 1,2,.,v,b ^ l, of the system operation process Z(t) in the state zb, while the next transition is to the state zl on the base of their realizations d^, k = 1,2,..., nbl, during the experiment time ©. Considering data given in Table 1 we get the preliminary set of realizations of analyzed transportation system's operation process conditional sojourn times 9bl in the state zb, while the next transition is to the state zl:
0\X1 = 4 days 20 hours, 0\71 = 1 hour 30 min., 0n4 = 40 minutes, 024 1 = 1 hour, #j310 = 22 hours 20 minutes, 0301 = 2 hours 30 min., 0410 = 16 days 19 hours 25 min., = 3 hours 15 minutes, 0510 = 40 minutes, 00,1 = 45 minutes, 067 = 6 days 9 hours 10 minutes, 071 = 25 minutes, 077 = 55 minutes, 071 = 30 minutes.
From the specification of the system we can notice that after transferring the ship the system operation process always has to transit to the operation state z1 in which the system is without loading. So the system operation process Z (t) from the operation state z1 can be changed into any
state from z 2 to z 25, and then the system operation process always came back to the operation state z1. Even if after one ship transportation the second ship should be transferred there is needed some time to draw the ropes from the broaching machines to the transferred ship and during this time the analyzed system is without loading. Due to above remarks we conclude that:
0k, = 0 for b, l = 2,k, v, k = 1,2,...
5 SHIP-ROPE ELEVATOR PRELIMINARY DATA COLLECTION PRESENTING
The ship-rope elevator in Naval Shipyard in Gdynia is widely described and analyzed under the assumption that its components are independent in (Kolowrocki, 2002, 2004) and as a system with dependent components in (Blokus-Roszkowska, 2006).
Figure 5. The ship while docking.
Considering the tonnage of the docked and undocked ships by the rope elevator in Naval Shipyard in Gdynia we can divide the system's load, similarly as in the previous ships' transportation system, into six groups and due to fact that the rope elevator system depends mainly on the tonnage of docking ships we can distinguish the following (v = 6) operation states of the rope elevator system operation process:
an operation state z1 an operation state z an operation state z3 an operation state z4 an operation state z5 an operation state z6
- without loading,
- loading over 0 up to 500 tonnes,
- loading over 500 up to 1000 tonnes,
- loading over 1000 up to 1500 tonnes,
- loading over 1500 up to 2000 tonnes,
- loading over 2000 up to 2500 tonnes.
Table 2. Preliminary set of realizations of rope elevator in Naval Shipyard in Gdynia operation process conditional sojourn times in particular states
Lp. Operation state Rope-hosting winches Date Start time Time of state duration Rising Moving down
1 2 3 4 5 6 7 8 9 10
1 z2 X X X X X X X X X X 21.02.08 15:40 25 m X
2 z2 X X X - - X X X X X 21.02.08 16:45 30 m X
3 z5 X X X X X X X X X X 24.02.08 23:50 40 m X
4 z4 X X X X X X X X X X 25.02.08 19:15 40 m X
5 z4 X X X X X X X X X X 25.02.08 20:40 10 m X
6 z2 X X X X X X X X X X 07.03.08 13:55 50 m X
7 z4 X X X X X X X X X X 13.03.08 15:30 1 h 30 m X
8 z4 X X X X X X X X X X 17.03.08 14:00 4 h 15 m X
9 z4 X X X X X X X X X X 19.03.08 02:00 3 h X
Analyzing the data collected in Table 2 we can notice that not always all 10 rope-hosting winches are loaded. This notice will have influence in the further system's reliability analysis on the reliability functions of the ropes in the winches. More precisely, if some winches (i.e. ropes in the winches) are used more often or are more loaded during ships' docking and undocking then these ropes' reliability functions will be worse than reliability functions of the ropes in the winches used less. With this knowledge the rope elevator in the further reliability analysis will be described as a non-homogeneous system.
T R A V E R S E R
the
ship's
bow
10
a control panel
PLATFORM
the
ship's
stern
9
8
7
6
1
2
3
4
5
Figure 6. The scheme of the winches arrangement.
On the basis of the statistical identification of system operation process given in Section 3 we obtain the preliminary set of realizations of the elevator operation process conditional sojourn times 9bl in the state zb, while the next transition is to the state zl: 9 = 1 day 15 hours 40 minutes, 9l21 = 25 minutes, 912 = 40 minutes, 922j = 30 minutes, 635 = 3 days 6 hours 35 minutes, = 40 minutes, 6*14 = 18 hours 45 minutes, 941 = 40 minutes, 9154 = 45 minutes, 9451 = 10 minutes, 912 = 10 days 17 hours 5 minutes, 926j = 50 minutes, 9j4 = 6 days 45 minutes, 9 = 1 hour 30 minutes,
084 = 3 days 21 hours, 041 = 4 hours 15 minutes, 094 = 1 day 7 hours 45 minutes, 0^ = 3 hours.
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