This document summarizes a research paper about using neural networks to develop a prognostic model for predicting fatigue damage in petrochemical pipelines. The researchers propose using Paris' law and Miner's law to model crack propagation and cumulative damage. They develop a recurrent neural network model to predict crack length over time under different pressure levels. Simulation results show the model can estimate remaining lifetime under three pressure modes, with lifetimes of around 115 hours for high pressure, 160 hours for middle pressure, and 240 hours for low pressure. The neural network approach allows prognosis of pipeline condition to aid quality maintenance in petrochemical industries.
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In this paper we introduce an approach to increase density of field-effect hetero transistors framework a three-stage
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Abstract
1. Description of singular Lagrangian theories by using a
Clairaut-type version of the Hamiltonian formalism.
2. Formulation of a some kind of a nonabelian gauge theory, such
that “nonabelianity” appears due to the Poisson bracket in the
physical phase space.
3. Partial Hamiltonian formalism.
4. Introducing a new (non-Lie) bracket.
5. Equivalence of a classical singular Lagrangian theory to the
multi-time classical dynamics.
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with required configuration should be manufactured. After the manufacture required areas of the heterostructures should be doped by diffusion or ion implantation. The doping should be finished by optimized annealing of dopant and/or radiation defects.
Abstract
1. Description of singular Lagrangian theories by using a
Clairaut-type version of the Hamiltonian formalism.
2. Formulation of a some kind of a nonabelian gauge theory, such
that “nonabelianity” appears due to the Poisson bracket in the
physical phase space.
3. Partial Hamiltonian formalism.
4. Introducing a new (non-Lie) bracket.
5. Equivalence of a classical singular Lagrangian theory to the
multi-time classical dynamics.
The International Journal of Engineering and Science (IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Talk given at Cambridge DAMTP on Friday, 20 June 2008. Describes recent work on understanding what is necessary to embed accelerating cosmology in higher-dimensional theory.
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We analyzed mass and heat transport during manufacturing field-effect heterotransistors with several sources to decrease their dimensions. Framework the result of manufacturing it is necessary to manufacture heterostructure with specific configuration. After that it is necessary to dope required areas of the heterostructure by diffusion or ion implantation to manufacture the required type of conductivity (p or n). After
the doping it is necessary to do optimize annealing. We introduce an analytical approach to prognosis mass
and heat transport during technological processes. Using the approach leads to take into account nonlinearity of mass and heat transport and variation in space and time (at one time) physical parameters of these processes
An approach to decrease dimentions of logicalijcsa
In this paper we consider manufacturing logical elements with function AND-NOT based on bipolar transistors.Based on recently considered approach to decrease dimensions of solid state electronic devices with the same time increasing of their performance we introduce an approach to decrease dimensions of transistors and p-n-junctions, which became a part of the logical element. Framework the approach a heterostructure
with required configuration should be manufactured. After the manufacture required areas of the heterostructures should be doped by diffusion or ion implantation. The doping should be finished by optimized annealing of dopant and/or radiation defects.
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11.neural network precept diagnosis on petrochemical pipelines for quality maintenance
1. Control Theory and Informatics www.iiste.org
ISSN 2224-5774 (print) ISSN 2225-0492 (online)
Vol 2, No.2, 2012
Neural Network Precept Diagnosis on Petrochemical Pipelines
for Quality Maintenance
S.Bhuvaneswari1* R.Hemachandran2 R.Vignashwaran3
1. Reader, Department of Computer Science, Pondicherry University, Karaikal Campus, Karaikal
2. Faculty, N.I.T, Puducherry
3. Scholar, Department of Computer Science, Amrita University, Coimbatore
* E-mail of the corresponding author: booni_67@yahoo.co.in
Abstract
Pipeline tubes are part of vital mechanical systems largely used in petrochemical industries. They serve to
transport natural gases or liquids. They are cylindrical tubes and are submitted to the risks of corrosion due
to high PH concentrations of the transported liquids in addition to fatigue cracks. Due to the nature of their
function, they are subject to the alternation of pressure-depression along the time, initiating therefore in the
tubes’ body micro-cracks that can propagate abruptly to lead to failure by fatigue. On to the diagnostic
study for the issue the development of this prognostic process employing neural network for such systems
bounds to the scope of quality maintenance.
Keywords: Percept, Simulated results, Fluid Mechanics
1. Introduction
The pipelines tubes are manufactured as cylindrical tubes of radius R and thickness e. The failure by
fatigue is caused by the fluctuation of pressure-depression along the time t ( 0 ≤ P ≤ P0). These pipelines are
unfortunately usually designed for ultimate limits states (resistance).To be more realistic, a prognostic
model is proposed here based on analytic laws of degradation by fatigue (Paris’ law) in addition to the
cumulative law of damage (Miner’s law).This prognostic model is crucial in petrochemical industries for
the reason of favorable economic and availability consequences on the exploitation cost .
Fig. 1: Internal pressure diagram.
2. Paris Law
The Paris’ law allows determining the propagation speed of the cracks da/ dN at the time of their
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2. Control Theory and Informatics www.iiste.org
ISSN 2224-5774 (print) ISSN 2225-0492 (online)
Vol 2, No.2, 2012
da
detection: = C.(∆K ) m where a is the crack length, N is the number of cycles, C and m are the Paris
dN
constants, and ∆K is the stress intensity factor.
We can distinguish:
- The long cracks that obey to Paris law
- The short cracks that serve to decrease the speed of propagation
- The short physical cracks that serve to increase the speed of propagation
da
The law can be written also as :
log = log C + m log(∆K )
dN
da
log
dN
Phase I
Phase II Final fracture
Low speed of
Stable Kc
propagation
propagation
Phase III
High speed of
propagation
da
= C (∆K )
m
dN
log (∆K )
Threshold
∆Kth
Fig. 2: The three phases of cracks growth, Paris’ law.
3. Pipelines under Pressure
A tube is considered thin when its thickness is of the order of one tenth of its radius: e ≤R/10
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Vol 2, No.2, 2012
Fig. 3: Cylindrical pipelines
Fig. 4: Stress type distribution
4. State of Stresses
Te tubes are cylindrical shells of revolution. when thin tubes of radius r and of thickness e are under
internal pressure p, the state of stresses is membrane-like under bending loads. the membrane stresses are
circumferential (hoop stress) σθ and longitudinal stresses (axial stress) σL
Fig. 5: Axial stresses and Hoop stresses in cylindrical pipelines
PR
σ θ = e
PR
These stresses are given by: σ L =
2e
The critical cracks are those which are perpendicular to maximal stressesσθ, that means longitudinal
cracks which are parallel to the axis of the tube. A crack is of depth a or of length a, if we measure in the
direction of the tube thickness e. Normally the ratio a/e is within the following range: 0.1 ≤ a/e ≤0.99
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Vol 2, No.2, 2012
Fig. 6: Crack length in radial view
Fig. 7: Cracked pipeline section
The stress intensity factor KI represents the effect of stress concentration in the presence of a flat crack.
Fig. 8: Non-uniform distribution of stresses near the crack
The stress intensity factor is given [6] by:
K I = y (a ) × πa σ θ
⇒ K I = 0.6 × g (a )× πa × P.
R
≤ K IC
e
with Y (a ) = 0.6 × g (a ) : is the geometric factor ;
a
1 + 2
g (a ) = e J IC ⋅ E
3 K IC =
a 2 1 − (ν ) 2
1 − 8
e
5. Control Theory and Informatics www.iiste.org
ISSN 2224-5774 (print) ISSN 2225-0492 (online)
Vol 2, No.2, 2012
K IC : is the tenacity of material (critical stress intensity factor) and is given by:
J IC ⋅ E
Note that the factor KI must not exceed the value of KIC . K IC =
1 − (ν ) 2
5. Proposed Percept Model
Consider a pipeline of radius R = 240 mm and of thickness e = 8 mm transporting natural gases, the
parameters related to materials and to the environment are taken as being equal to
: [5] m= 3 et C = ε = 5.2.10 −13
e e
The length of the crack is denoted by a with an initial value a 0 = 0.2 mm a0 ≤ a ≤ a N = ⇒ =8
8 aN
We have to respect the following ratio:
a e
0 .1 ≤ ≤ 0.99 ⇒ 1.01 ≤ ≤ 10
e a
Take a similar form to
da
as a = εφ 1 ( a ) φ 2 ( p )
&
dN
with: ε = C ; (
φ1 (a) = Y (a ) π a ) m
; p = ∆σ and
φ 2 ( p) = p m = (∆σ)m
The initial damage is: a(0) = a0
A recurrent form of crack length gives:
a i = εφ1 ( a i −1 ) φ 2 ( p i ) + a i −1
And the corresponding degradation is given by:
Di = Di −1 + ηφ1 ( Di −1 )φ 2 ( pi )
for m = 3 ⇒ φ 2 ( p i ) = p i3 = (∆ σ θ i )3
ε
Morevor η =
a N − a0
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da j
dj =
We define the damage fraction by:
aN − a0
Therefore, we get the cumulated total damage:
i
i i da j
∑ da j ai
j =1
Di = ∑ d j = ∑ = =
j =1 j =1 a N − a0 a N − a0 a N − a0
N
DN = ∑ d j = 1
We can easily prove that:
j =1
D
Failure
1
Reliable
ni/Ni
0
Fig. 9: Miner’s law of damage
where :
0 ≤ n ≤ N , a0 ≤ a ≤ a N ;
N
D0 ≤ D ≤ 1 = D N ; D N = ∑ d j = 1
j =1
a0 D a
D0 = ⇒ a0 = 0 N
a N − a0 1 + D0
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The other sequences are :
a0
D0 =
a N − a0
a1
D1 =
a N − a0
a2
D2 =
a N − a0
M
an
Dn =
a N − a0
6. Percept simulation of levels
Fig. 10: Triangular simulation of internal pressure
Table :1 Statistical Characteristics of Each Pressure Mode
Mean of p i
Pressure mode C.o.v. of p i in % Law
( p i in MPa)
High (mode 1) 8 10 % Triangular
Middle (mode 2) 5 10% Triangular
Low (mode 3) 3 10% Triangular
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Vol 2, No.2, 2012
We study three levels of maximal pressures in pipelines which are: 3 MPa, 5 MPa, and 8 MPa that are
repeated within a specific interval of time T=8 hours. At each level, we deduce the degradation trajectory D
in terms of time or in terms of the number of cycles N.
The failure by fatigue is obtained for a certain critical number of cycles: pressure-depression or for a certain
time period. Therefore, the lifetime of the pipeline for each level of maximal pressure is deduced at D=1.
7. Results and Discussion on Simulation
The Monte Carlo one level percept simulations for 1000 times for the pipeline system and under the 3
modes of internal pressure (high, middle and low) gives the degradation trajectory which are represented in
the following 3 figures.
Fig. 11: Degradation evolution for mode 1
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ISSN 2224-5774 (print) ISSN 2225-0492 (online)
Vol 2, No.2, 2012
Fig. 12: Degradation evolution for mode 2
Fig. 13: Degradation evolution for mode 3
13
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ISSN 2224-5774 (print) ISSN 2225-0492 (online)
Vol 2, No.2, 2012
Fig. 14: Degradation evolution for All three modes
We deduce from the percept interrogation that the pipeline lifetime is nearly 115 hours for mode 1 (high
pressure), nearly 160 hours for mode 2 (middle pressure), and nearly 240 hours for mode 3 (low pressure).
From these curves, we can see that our prognostic model, using analytic laws, gives the remaining lifetime
of pipelines at any instant.
8. Conclusion and Scope for Future Work
The percept neural network sustains in predicting the life time effectiveness on field efficiency for the
radial pipelines by which the user is able to read the rear and bear happenings on fluid mechanics in
industries. The study also helps in predicting the sustainability feature of turbines in heavy alloy plants
which could be scope for the work in future.
References
G. Vachtsevanos, F. Lewis, M. Roemer, A. Hess, B. Wu, Intelligent Fault Diagnosis and Prognosis
for Engineering Systems, John Wiley & Sons, Inc., 2006, ch. 5,6 and 7.
J. Lemaitre and J. Chaboche, Mechanics of Solid Materials. New York: Cambridge University Press,
1990.
M. Langon, Introduction a la Fatigue et Mécanique de la Rupture, Centre d’essais aéronautique de
Toulouse, ENSICA April,1999
K. El-Tawil, S. Kadry, Fatigue Stochastique des Systèmes Mécaniques Basée sur la Technique de
Transformation Probabiliste, internal report, Lebanese University, grant research program, 2010
J. Lemaitre, R. Desmorat, Engineering Damage Mechanics, New York: Springer-Verlag, 2005, ch. 6.
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11. Control Theory and Informatics www.iiste.org
ISSN 2224-5774 (print) ISSN 2225-0492 (online)
Vol 2, No.2, 2012
K. El-Tawil, A. Abou Jaoude and S. Kadry, “Life time estimation under probabilistic fatigue of
cracked plates for multiple limit states”, ICNAAM, 2009.
K. El-Tawil, Mécanique Aléatoire et Fiabilité, cours de master2r mécanique, Ecole doctorale des
sciences et technologies EDST Université libanaise, Beyrouth 2004
A. Abou Jaoude, K. El-Tawil, S. Kadry, H. Noura and M. Ouladsine, ”Analytic prognostic model for
a dynamic system”, European Conference of Control, 2010, submitted for publication.
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