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THE SOCIETY OF NAVAL ARCHITECTS AND MARINE ENGINEERS
601 Pavonia Avenue, Sulte400, Jeraey City, Naw Jers@y 0730S USA
# Paper presenkd at the Marine Si-uclural lnsp~tion, Maintenan~ and MonitonngSym@um
%eratcm NauonalHotel,Arhnglnn,Vlrgima,March 1E19, 191
Parametric Evaluation of Marine Structural Life
Expectancy Using a Reliability-Based Methodology
B.M. A ub, University of Maryland, College Park, Ma~land
G.J. W~te, U.S. Naval Academy, Annapolis, Maryland
ABSTRACT
The estimation life
ofan absolute expectancy a k these two failure f the
modes was determined or
complex a
process nd theresults areexpected ohave
t forward ofthefour
bottomplating boatclasses.
large
relatively levels ofuncertainty. s
Inthis tudy, a
parametric analysis structural
sensitivity -of life Many factorsaffectthestructural ofa boat.
life
expectanq due tovariation inseveral variables that s type,
They includetructural operational profile,
t
includeheSize oftheplating panel, hickness,
t details,
structural loads,inspection maintenance,
and
operational failure
profile, criteria loading.
and designmethods, safety
factors, and
corrosion,
was
conditions performed. The sensitivity ofthe environmental Thesefactors
factors. havefour of
types
life
structural expectancy oftheforward bottomplating uncertaintynamely,physical statistical
randotrmess,
tovariations inthese w
parametersas evaluated. briefA and modeluncertainties, A
andvagueness.llcanbe
comparative analysis undertakenetweenthree
was b b structural
addressedy a reliability-based life
patroloats.
different b The study limited
k tothe assessmentmethodology.
forward
critical and
bottomplating takes into account
thedifferences inmaterial, dimensions,
plate STRUCTURAL LIFEEXPECTANCYASSESSMENT
operationalprofile, and o
structure loadingfthevessels.
A methodology or life
f structural assessment was
Two failure modes,plasticplate deformation and
developed. he methodology s
T i based on probabilistic
wereconsidered a novel
fatigue, and approach to
analysis using reliability concepts and the statistics of
corrosionandwastage was included.
extremes. The rnethodolo~ results in the probability of
INTRODUCTION
failure of the boat structural system according to the
identified failure modes as a function of time, i.e.,
The estimationofanabsolute ifexpectancy a
l e is structural life. The results can be interpreted as the
complex processnd theresults
a areexpected ohave
t cumulative probability distribution funtiion (CDF) of
relatively levels
large ofuncertainty.Inthis study,a structural life. Due to the unknown level of statistical
methodology or
f structural expectanq
life was correlation between failure modes, limits or bounds on
developed,validated calibrated the
and using the CDF of the structural life the structural system were
performance ecordsftheCape-Class
r o patroloat.
b established. The limits correspond to the extreme cases
The estimationofstructural expectanq
life canbe of fully correlated and independent failure modes. An
basedon selected failure
modes.Allpossible failure interactive computer program was developed to
modes oftheIsland, Heritage,Pointand Cape-Class perform these calculations that allows parametric
patroloats
b wereidentified. mostcritical
The failure sensitivity analysis of structural life due to variations in
modes,basedon experiences oftheU.S.CoastGuard several .variables.
and thefundamentals ofnaval architecture(9to24),
t
were determinedobe plate plastic
deformation and reliabili~
Structural methodsfordetermining
the
fatigue(3,7,16,20).
A novel approach toincludelate
p eract (numen”cal value) of probability of failure of a
corrosionandwastage was developed asa component structural component or system according to a specified
ofthemethodology. tructural expectanq
S life basedon performance function can be classified into two types,
closed-form solutions and simulation-based techniques.
Consider the following performance function:
Z = g(Xl, X2,.... Xn) (1)
B-1
where the Xi’s are the basic random variables. Equation Prob. of Failure (CDF of Ufe)
1 defines the failure surface, such that failure occurs I.00E+~ I I I I
where g(.) <O. The probability of failure can be “ ~.*
1.00E-02
determined by solving the following integral:
1.00E-04 u c8wa4c.
.......
Pf = J J... J f~(xl,..., Xn) dxl dxz ...dx~ (2) 1.00E-06 +M911dw
Rm
1.00E-08 1- 1
where f~ is the joint probability density function (PDF)
051015202530
of X = {Xl, X2,,..., Xn} and the integration is ,.
performed over the region where g(.) <O. Strtiotural Ufe (Years)
,.
In closed-form solutions, Equation 2 is evaluated Figure 1. .Comparative Results for Failure in Plate
making use of the probabilistic characteristics of the Deformation
basic random variables. This can be done if the joint
The details of the methodology that was used in
PDF of the basic random variables is known and the
this study were described in detail by Ayy_ub,et al
integral of Equation 1 can be evaluated. In many
(5,6,7,8). Example results are comparatively shown in
practical problems, these conditions cannot be met.
Figures 1 and 2 for the Point, Cape and Island-Class
patrol boats.
In the classical use of the simulation-based
methods, all the b~ic random variables are randomly
Prob. of Failure (CDF of Life)
generated and Equation 1 is evaluated. Failures are
then counted depending on the sign of Equation 1. The
probability of faihtre is estimated as the ratio of the
number-of failures to the total number of simulation
cycles. Therefore, the smaller the probability of failure
is, the larger the needed number of simulation cycles to 1.00E-08
estimate the probability of failure within an acceptable 1.OOE-10
level of statistical error. In additiou direct simulation
051015202530
requires binmy definition of failure according to the
limit state equation. The level of computational effort Structural life (Years)
in this method is relatively small. The fundamentals of
Figure 2. Comparative Results for Failure in Fatigue . ___
this method are available in several references
(1,2,4,25,26,27).
PARAMETRIC ANALYSIS
The et%ciency of simulation can be largely
A parametric analysis
sensitivity ofthedeveloped
improved by using variance reduction techniques.
modelwas performed theIsland-Class
analytical on
However, the level of computational effort is increased.
b
patroloat.Inorder toperform a
theanalysis,
One of the commonly used methods is conditional
set for
reference ofvalues theanalytical model
expectation combined with antithetic variates variance
n T is
parameterseedstobe defined.hisset usedto
reduction techniques (VKl%) for structural reliability
v for t e
assignalues all heparametersxcept the
assessment (li2i25). These methods were determined parameterbeing The
investigated. value ofthe
to be highly efficien~ and converge to the correct
parameterunderinvestigation isvanedtocover a
probability of failure in a relatively small number of
range, nd the’variation
selected a oftheestimated
simulation t’ycles. The methods are mathematically
life
structural expectanq accordingtothetwo failure
simple, do not require large spaces of computer
p
modes due tothis arametric is
variationplotted. T’he
memog’ and,”therefore, can be programmed on small
set selected
reference is all
suchthat theparameters re a
micro- and personal computers. A menu-driven
atthenormallevels ofthestrength, a
loading nd
computer program, “R4SCS, Eeliability_Asessment of
operationalprofile The reference of
characteristics. set
Structural components and systems,” was developed
w
parametersill”be i
defhie~ nthepaper.”
based on these methods by Ayyub and White in 1988.
Lnthis study, conditional expectation with antithetic The parameters that are considered in this
variates ~T were used for determining the sensitivity analysis iriclude the simulation cycles, size of
probabilities of-failure. the plating panel, thiclmess of the plating, operational
profile; number of operational hours per year, loading
profile, fatigue details, arid plate failure criteria. The
selected parameters are summarized in Table 1. The
R-2
sensitivity of the structural life expectancy of the respectively, yield in statistically accurate results.
forward bottom plating to variations in these Therefore, these numbers of simulation qcle were
parameters was ev~uated. The evaluation was selected and used in all the program runs in this study.
..
performed for both the plastic plate deformation and ~$ : The plate thickness of the
fatigue failure modes. The treatment and presentation forward bottom plating of the Island-Class patrol boat
of the MO failure modes were maintained separate in was varied from its current value of 0.161 in (7#) plate
order to keep track of the .sensitivi~” of each failure to 0.171 in (7.5#), 0.224 in (9#) and 0.236 in (10#)
mode to the variation ii the parametric values. The plate sizes. Based on the results as shown in Figures 3-a
resulting probabilities of failure as a function of time and 3-b, the structural life”expectanq of the forward
are summarized in fi~res that correspond to the bottom plating of the Island-Class patrol boat in this
reference case and the takes with each v~ed critical failure mode can significantly be improved by
parameter. increasing the plate thickness to 7.5# or 9#. The effect
Table 1 Definition of Parameters of plate thickness vahation on fatigue life expectan~ of
the critical k t
region minimal, herefore, war-not
Plate Figure considered.
Parameter Deformation. Fatigue Number
Prob,of Failure(CDFof Life}
1
O.MO1
L
1E= u 7# plate
b
lE-12 + 7S# plate
Plate size x Not
shown lE-16
Wastage x 4 1E-20 I
Annual use x x 5-a &5- 051015202S30
b Structuralhfe (Years)
Plate failure x 6&7
Figure 3-a. Effect of Plate Thickness on Pf
criteria
Speed and sea x Not Plate Deformation for the Island-Class
—,..
state combinations shown
Prob.of Failure(CDFof Life)
Percent use in x Not 1E4
combination 8 shown
1E-50
Fatigue loading x 8
cycles 1E.w , s * Plate
Fatigue local x 9-4 9-b
1E-7o u 10# Plate
details & 9-c K
1E30
Results
1E-90
051015 a2s33
In this sectio~ the results of the parametric
StructuralLife (Years)
analysis are summarized. A brief discussion of the
results is provided. These results can be used to study Figure 3-b. Effect of Plate Thickness on Pf
the effects of future design changes. Plate Deformation for the Island-Class
1.Simulation CWles: In order to select the least
3. Plate Aspect Ratio: The current aspect ratio of
number of simulation qcles that gives results with a plate in the forward bottom part of the boat is 2. This
acceptable levels of statistical’ accuracy, the resulting aspect ratio is based on the plate size, length x width, of
failure probabilities for the analytical model were 23.5 in x 11.75 in. In this analysis, the aspect ratio was
determined as a function of the number of simulation changed to, 1, which corresponds to change in the plate
cycles. The statistical accuracy is measured in terms of
size tcr 11.75 in x 11.75 in. The structural life expectanq
the convergence of the estimated probability of failure
of the forward bottom plating of the Island-Class patrol
and the magnirude of its coefficient of variation (COV).
boat in this critical failure mode can sigtilcantly be
The selected numbers of simulation qcle is based on
improved by reducing the plate size. It will be shown
satisfying the convergence criterion and maintaining a
that this approach is more effective than increasing the
level of COV less that 0.1. By inspecting the resulting
plate thickness. The effect of this change on fatigue is
figures, 2000 simulation cycles and 500 simulation qcles
in the form of igcreming the number of fatigue details.
for plastic plate deformation and fatigue failure modes,
B-3
However, since the failures of fatigue detail are Prob. of Failure(CDF-of tie)
considered to:be statistically highly correlated, the ,,
I.00E+OO
effect of this change on fatigue life expectanq is s WJhm
rninimall: 1.00E-02
u 1210hfa
1 .WE-04 ~
~ ~: The probabilities of +=hm
failure in plastic plate deformation were estimated for a 1.oaEa -
~ XHXlhm
mean value of wastage rate of O, 1, 1.5 and 2 mpy. ~
1.00E-08 G
Unquestionably the inclusion of a wastage allowance in 051015202530
the strutitural xpectanq
lifee model is for
vital a
realistic prediction life. However, the model is
of Structural Ltie (Years)
slightlysensitive to the selection of the plate wastage
rate within the range,l to 2 mpy as shown in Figure 4. Figure 5-b. Effect of hnual Use on Pf for Point-CIMs
.!
In this study, a wastage rate of 1 mpy WaSused.
5. Annual Use : The.current average annual use
.,--
Prob.of FailurafCDFof Life) of the Island-Class patrol boat is 2167 hours/year.
1 w
:mE-+ These results are based on varying the annual use from
1.mE42 2167 to 1500 and 3000 hours/year. The effect of
s 1.0 mpy
increasing the annual use of a boat is greater on fatigue
1.mE-w u 2:0 mpy than plastic plate deformation structural life expectarq’.
1.mE-m q 1.5 mpy However, the analytical model is slightly sensitive to the
selection of the average value of annual use.
1WE-OS q Ompy
l.mE-lo
6. Plate Failure Criteri z The plate ”failure criteria
051015 ~25~ are defined by mainly two parameters, the deformation
StructuralLife Wears) ratio wp/th and the total number of failed plates within
the critical region np/Np. The effect of variation in
Figure 4. Effect of Plate Wastage orI Pf for Island-Class
these parameters on structural life expectancy is studied
in this section.
The effect of plate wastage on fatigue life
expectanq is in the form of slightly shifting the location “-.
a. Deformation Ratio. The deformation ratio
of the neutral axis of the cross section at the fatigue
wp/th for the Island-Class patrol boat was .
.. __J,’
details. The effect of this neutral axis location change selected to take the value of at least 3. The
on the structural life e~ectancy of fatigue details is
effect of varying this ratio on the probability of
relatively small. It-can be shown that after 30 years with
failure in plastic plate deformation is shown in
a plate wastage rate of 1 mpy, this effect results in
Figure 6. In this figure, the ratio takes” the values
detail-stress transfer function values that are 10 to 20%
of 2.5, 3.0 and 3.5. Evidently, structural life
less than the case of nowastage allowance. expectancy breed on plastic plate deformation is
sensitive to variations in this parameter.
Prob.of Failure(CDFof Me)
However, this ratio was carefully selected to take
the value 3 in the reference cases for the Island
and Heritage’Class patrol boats based on the
model calibration process.
.
‘.,
b. Ml mber of Plates. The total number of failed
plates within the critical region np/Np for the
:- Island:Class patril boat was set to take the value
0“ 5.1015 ~25W of at least 6/28~” The effect of varying this
StructuralUfa ~ears) “’ criterion onihe probability of failure in plastic
plate deformation is shown in Figure 7. The
Figure 5-a.’ Effect of Annual Use on Pf for Island-Class criterion was changed to take the values of 3/28,
,. 6/28 and 9/28: Evidently, structural life
expectanq” based on”plastic plate deformation is
sensitive to this’ parameter. However, this
criterionwti carefiilly”selected to take the value
.,: 6/28 in the reference case for the Island-Class
patrol boat based on”the current practices of the
U.S. Coast Guard.
,,.
B-4
m
Prob.of Fallwe (CDFof Life) 1402, 1600 and 1800 cycles/hour. Clearly, structural life
l.mE+m expectanq based on fatigue is slightly sensitive to
-1
p
vahatiominthisarameter+
1.~E@
u Ratio= 3.0
I
Prob.of F~ilura(CDFof Ufe)
1.mE44 U Ratio= 3.5
I
“m’” ~
s 1402c@as
E
1,WEUS
1.mE47
u l~CFISS
1.mE48
0510 15.2025W q l~C@es
StructuralLfe (Years) 1,mEm
O l~+es
Figure 6. Effect of Plate Deformation on Pf 1,mEJ9 1
05101 sm2524Y
7. Sf3eelSea State: As was discussed by Ayyub et
d StructuralUfe ~wars)
al (7,8), combination 8 of the speed and sea state Figure 8. Effect of Fatigue Laading Cycles on Pf
condition represents the most critical case of the Fwb, of Fnilure[CDFof We)
operational profile. This case corresponds to the
medium speed and high sea state. It results in
~
“m’”
significant values for the probabilities of failure in I
1,mE47
plastic plate deformation. For other speed/sea state
combinations, the resulting probabilities of failure are
insignificant virtually zero. 1.m’-os
7s mtailw
X!!_!
Prob.of Failure(CDFof life)
1 1.mE-m ‘ 1
0510152025 S2
0.01 Strumml Ufe Wears)
s Fail 6 out of 2S
Figure 9-a. Effect of Local Fatigue Detail on Pf for the
“, O.ml u Fail 9 out of 2S
Island-Class
+ Fail 3 out of 28
O.ml 10. Fatimse Local Details: According to this study
and other previous studies (5,7,8), fatigue local detail 36
o.~i was determined to be the most critical one in the
o ’57 10 15, m 25 W
forward bottom plating of the Island-Clam patrol boat.
StructuralUfe (Ymrs)
The effect of eliminating this detail and using in its
Figure 7. Effwt of Number of Failed Plates on Pf place local fatigue detail 4 in the form of a continuous
weld “between the longitudinal and the shell on the
8. Percent Use in SDeed/ Sea State Case 8: The structural life expectanq in fatigue is shown in Figure 9-
effeet of varying the percent use in the spe’ed/sea state a. Obviously, structural life expectanq based on fatigue
combination that corresponds to case 8 on thk cati be greatly improved by using local fatigue detail 4 in
probabilities of failure in plastic plate deformation will place of local fatigue detail 36. Similar results are
be discussed. This case corresponds to the medium shown for the Point-Class in Figures 9-b and 9-c.
speed and high sea state. The percent use is considered Prob. of Failure (CDF of Me)
to take the values 0.5, 1, 1.5 %. Evidently, structural life
r
I.00E+m
expectanq based on pl=tic plate deformation is 1.00E41 q Mail 33
moderately sensitive- to variations in this parameter. IJbtailms
1.00E-02
The magnitude of this parameter was selected based orI
1.tiE43 I * btail lm
a survey that was sent to operators of the Island-Class
L-
1.00E-04 o WI 10M
patrol boats.
1.00E-05 A oataiI s
9+ Fatim e hadin~ Cvcle$: Based on the study 1.00E-06
performed by Ayyub and White in 1988 on the Island- 05 10 15 20 25 30
Class patrol boat, the number of fatigue loading cycles
Structural Life (Ymirs)
was determined to be on the average 1402 qcles/hour
based on the strain time-history records. The effect of Figure 9-b. Effect of Local Fatigue Detail on Pf for the
varying this number on the probabilities of failure in Point-Class
“, fatigue is shown in Figure 8s in this figure are 1200,
B-5
Prob, of Failure (CDF of Life) Two”failure modes, plastic plate deformation and
I.00E+OO fatigue, were considered and a novel-approach to
corrosion and wastage wak included.
u“
1.00E432 s mlml4
..
1.00E-04 u Mtail 39
REFERENCES
+ Mail 49 .._
1.00E-06
0 IMail 51 1. Ang,A-H-S. and W.H.Tang,(1983),Probability
1.00E4)8 L-l
Concepts in Engineeri~ Planning and Desi~, Vol. 2-
I.00E-10 Decisiou Risk and Reliability. John Wiley and
0 5 10 15 20 25 30 Sons, New York.
Structural Lie (years) 2. Ayyub, B.M., and A Haldar, (1984), “Practical
Structural Reliability Techniques; .loumal of
Figure 9-c. Effect of Local Fatigue Detail on Pf for the
Structural Engineering,Anerican Society of Civil
Point-Class Engineers, Vol. 110, No. 8, Paper No. 19062, August
1984, pp. 1707-1724.
SUMMARY AND CONCLUSIONS
3. Ayyub, B.M., “and G.J. White, (1987), “Reliability
Analysis of the Island-Class Patrol Boat; Repoti
The estimation of an absolute life expectancy is a
Submitted to U.S. Coast Guard R&D Center, Avery
complex process and the results are expected to have
Point, August 19S7:
relatively large levels of uncertain~. In this s~dy, a
4. Ayyub, B. M., and G.J. White, (1987) “Reliability-
parametric sensitivity hnalysis of structural life
Conditional Partial Safety Factors; Journal of
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StructuralEngineering, herican Society of Civil
include the size of.the plati~g panel, thickness,
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February 1987, pp.279-294.
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5. Ayyub, B.M., G.J. White, and E.S. Purcell, (1989)
structural life expectanq of the forward bottom plating
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6. Ayyub, B.M., and G.J. White, (1988), “Life
different patrol boats. The study is limited to the
%pectanq A.sessmeqt “and Durability of the Island-
critical forward bottom plating and takes into account
Class Patrol Boat Hull ”Structure,” Report Submitted ““-
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-,
n Expectanq Assessment of Patrol Boat Bottom
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B-6
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B-7
