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 Mechanic

Bhuvaneswari, S.

Hemachandran, R.

Vignashwaran, R.

English

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 Mechanic

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Control Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  5 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  Control Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  6 detection: mKCdNda ).(∆= where a is the crack length, N is the number of cycles, C and m are the Paris 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  The law can be written also as : )log(loglog KmCdNda ∆+=                             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 dNdalog  Phase III High speed of  propagation Phase II Stable propagation Phase I Low speed of propagation  Threshold  ∆Kth Final fracture Kc ( )K∆log  ( )mKCdNda ∆= Control Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  7                                                                   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 These stresses are given by:   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 =σ=σθeRPeRPL 2Control Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  8                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:           ( ) θσpi×= aayK I( ) ICI KeRPaagK ≤×pi××=⇒ .6.0( ) ( )( )23121;factor geometric  theis:6.0with−+=×=eaeaagagaY2)(1 ν−⋅=EJK ICICControl Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  9    ICK : is the tenacity of material (critical stress intensity factor) and is given by:  Note that the factor KI must not exceed the value of KIC .  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 1310.2.5 −=ε=C  The length of the crack is denoted by a with an initial value mm2.00 =a  880=⇒=≤≤NNaeeaaa We have to respect the following ratio:   1001.199.01.0 ≤≤⇒≤≤aeea Take a similar form to  dNda as )()( 21 paa φεφ=&  with: C=ε ;      ( )maaYa pi=φ )()(1   ;     σ∆=p  and  ( )mmpp σ∆==φ )(2  The initial damage is: 0)0( aa =  A recurrent form of crack length gives: 1211 )()( −− +φεφ= iiii apaa And the corresponding degradation is given by: )()( 2111 iiii pDDD φηφ+= −− ( ) )(3for 332 iii ppm θσ∆==φ⇒=   0Morevor aaN −ε=η2)(1 ν−⋅=EJK ICICControl Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  10 00000010011;1 ;   ,0:whereDaDaaaaDdDDDDaaaNnNNNjjNNN+=⇒−====≤≤≤≤≤≤∑=We define the damage fraction by: 0aadadNjj−=                                Therefore, we get the cumulated total damage: 0011 01 aaaaadaaadadDNiNijjij Njijji−=−=−==∑∑∑=== We can easily prove that:  11== ∑=NjjN dD                           Fig. 9: Miner’s law of damage        ni/Ni D 0 1 Failure Reliable Control Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  11 0022011000:are sequencesother  TheaaaDaaaDaaaDaaaDNnnNNN−=−=−=−=M           6. Percept simulation of levels            Fig. 10: Triangular simulation of internal pressure     Table :1 Statistical Characteristics of Each Pressure Mode Pressure mode Mean of ip  ( ip in  MPa) C.o.v. of  ip  in  % Law High (mode 1) 8 10 % Triangular Middle (mode 2) 5 10% Triangular Low (mode 3) 3 10% Triangular Control Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  12   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  Control Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  13   Fig. 12:  Degradation evolution for mode 2     Fig. 13:  Degradation evolution for mode 3 Control Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  14                   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.  Control Theory and Informatics  www.iiste.org ISSN 2224-5774 (print) ISSN 2225-0492 (online) Vol 2, No.2, 2012  15 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.  This academic article was published by The International Institute for Science, Technology and Education (IISTE).  The IISTE is a pioneer in the Open Access Publishing service based in the U.S. and Europe.  The aim of the institute is Accelerating Global Knowledge Sharing.  More information about the publisher can be found in the IISTE’s homepage:  http://www.iiste.org  The IISTE is currently hosting more than 30 peer-reviewed academic journals and collaborating with academic institutions around the world.   Prospective authors of IISTE journals can find the submission instruction on the following page: http://www.iiste.org/Journals/ The IISTE editorial team promises to the review and publish all the qualified submissions in a fast manner. All the journals articles are available online to the readers all over the world without financial, legal, or technical barriers other than those inseparable from gaining access to the internet itself. Printed version of the journals is also available upon request of readers and authors.  IISTE Knowledge Sharing Partners EBSCO, Index Copernicus, Ulrich's Periodicals Directory, JournalTOCS, PKP Open Archives Harvester, Bielefeld Academic Search Engine, Elektronische Zeitschriftenbibliothek EZB, Open J-Gate, OCLC WorldCat, Universe Digtial Library , NewJour, Google Scholar   

Neural Network Precept Diagnosis on Petrochemical Pipelines for Quality Maintenance

Innovative Systems Design and Engineering     www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 3, No 1, 2012  61  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  detection: mKCdNda ).(∆= where a is the crack length, N is the number of cycles, C and m are the Paris 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  Innovative Systems Design and Engineering     www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 3, No 1, 2012  62  - The short physical cracks that serve to increase the speed of propagation  The law can be written also as : )log(loglog KmCdNda ∆+=                             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                                                                  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 dNdalog  Phase III High speed of  propagation Phase II Stable propagation Phase I Low speed of propagation  Threshold  ∆Kth Final fracture Kc ( )K∆log  ( )mKCdNda ∆=  Innovative Systems Design and Engineering     www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 3, No 1, 2012  63  circumferential (hoop stress) σθ and longitudinal stresses (axial stress) σL           Fig. 5: Axial stresses and Hoop stresses in cylindrical pipelines These stresses are given by:   which are perpendicular to maximal stressesσθ, that means The critical cracks are those 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                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.                =σ=σθeRPeRPL 2Innovative Systems Design and Engineering     www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 3, No 1, 2012  64   Fig. 8: Non-uniform distribution of stresses near the crack  The stress intensity factor is given [6] by:              ICK : is the tenacity of material (critical stress intensity factor) and is given by:  Note that the factor KI must not exceed the value of KIC .  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 1310.2.5 −=ε=C  The length of the crack is denoted by a with an initial value mm2.00 =a  880=⇒=≤≤NNaeeaaa We have to respect the following ratio:   1001.199.01.0 ≤≤⇒≤≤aeea Take a similar form to  dNda as )()( 21 paa φεφ=&  with: C=ε ;      ( )maaYa pi=φ )()(1   ;     σ∆=p  and  ( )mmpp σ∆==φ )(2  The initial damage is: 0)0( aa =  A recurrent form of crack length gives: 1211 )()( −− +φεφ= iiii apaa And the corresponding degradation is given by: )()( 2111 iiii pDDD φηφ+= −− ( ) )(3for 332 iii ppm θσ∆==φ⇒=  ( ) θσpi×= aayK I( ) ICI KeRPaagK ≤×pi××=⇒ .6.0( ) ( )( )23121;factor geometric  theis:6.0with−+=×=eaeaagagaY2)(1 ν−⋅=EJK ICIC0Morevor aaN −ε=η2)(1 ν−⋅=EJK ICICInnovative Systems Design and Engineering     www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 3, No 1, 2012  65  00000010011;1 ;   ,0:whereDaDaaaaDdDDDDaaaNnNNNjjNNN+=⇒−====≤≤≤≤≤≤∑=0022011000:are sequencesother  TheaaaDaaaDaaaDaaaDNnnNNN−=−=−=−=M We define the damage fraction by: 0aadadNjj−=                                Therefore, we get the cumulated total damage: 0011 01 aaaaadaaadadDNiNijjij Njijji−=−=−==∑∑∑=== We can easily prove that:  11== ∑=NjjN dD                           Fig. 9: Miner’s law of damage                   ni/Ni D 0 1 Failure Reliable Innovative Systems Design and Engineering     www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 3, No 1, 2012  66  6. Percept simulation of levels            Fig. 10: Triangular simulation of internal pressure     Table :1 Statistical Characteristics of Each Pressure Mode   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.  Pressure mode Mean of ip  ( ip in  MPa) C.o.v. of  ip  in  % Law High (mode 1) 8 10 % Triangular Middle (mode 2) 5 10% Triangular Low (mode 3) 3 10% Triangular Innovative Systems Design and Engineering     www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 3, No 1, 2012  67   Fig. 11:  Degradation evolution for mode 1    Fig. 12:  Degradation evolution for mode 2   Innovative Systems Design and Engineering     www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 3, No 1, 2012  68    Fig. 13:  Degradation evolution for mode 3                   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 Innovative Systems Design and Engineering     www.iiste.org ISSN 2222-1727 (Paper) ISSN 2222-2871 (Online) Vol 3, No 1, 2012  69  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.  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.    This academic article was published by The International Institute for Science, Technology and Education (IISTE).  The IISTE is a pioneer in the Open Access Publishing service based in the U.S. and Europe.  The aim of the institute is Accelerating Global Knowledge Sharing.  More information about the publisher can be found in the IISTE’s homepage:  http://www.iiste.org  The IISTE is currently hosting more than 30 peer-reviewed academic journals and collaborating with academic institutions around the world.   Prospective authors of IISTE journals can find the submission instruction on the following page: http://www.iiste.org/Journals/ The IISTE editorial team promises to the review and publish all the qualified submissions in a fast manner. All the journals articles are available online to the readers all over the world without financial, legal, or technical barriers other than those inseparable from gaining access to the internet itself. Printed version of the journals is also available upon request of readers and authors.  IISTE Knowledge Sharing Partners EBSCO, Index Copernicus, Ulrich's Periodicals Directory, JournalTOCS, PKP Open Archives Harvester, Bielefeld Academic Search Engine, Elektronische Zeitschriftenbibliothek EZB, Open J-Gate, OCLC WorldCat, Universe Digtial Library , NewJour, Google Scholar   

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Neural Network Precept Diagnosis on Petrochemical Pipelines for Quality Maintenance

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