Reliability Design of Fender Systemsand Mooring Facilities    Shigeru Ueda    Seigi Yamase      Tatsuhiko Okada        ...
Preface   Review of fender design    Reliability design method    Appropriate confidence level ,    safety factor , and...
Fender   Absorb ship’s berthing energy and   reduce berthing impact force                                       3
Tanker ship and Fender   60         Tanker Ship vs. Fender                                                        ESSO PAC...
600                          500                                    SUC1000HRHRe a c tion Fo rc e (k                     N...
National Oil Stockpiling Kamigotoh Base                                      6
Ed     Ship‘s Berthing Energy          1     E d = Mv C m C e C s C c             2          2     Ed : ship s berthing en...
Deterministic Method (conventional)   Maximum or Standard Ship size: Mass of ship    Design approach velocity : observed...
Approach Velocity                    9
X = PX ・       Confidence 50% a                                                                                           ...
Probability Distribution Function (Regression for any Confidence Level)                                                   ...
VirtualDT) ) Velocity  Eccentricity FactorX mDT   =-0.0873   Approach Factor   =1.326)) )Mass   =-0.477   =-3.772b beVb bC...
Load-Deflection Characteristics of Rubber Fender                                   Fender Performance Curve               ...
Energy Absorption of Fender                               M eansurement Value                    Normal Distribution      ...
FIRST ORDER RELIABILITY DESIGN METHOD AND                      THE SAFETY INDEX  Target Safety Index and Partial Safety Fa...
PROBABILITY DISTRIBUTION FUNCTION AND            THE PROBABILITY OF FAILURE        Generally it is difficult to calculate...
Sensitive factorSensitive factor for approach velocity is most influentialSensitive factor for ship size (DWT) is also inf...
Table 3. Partial Safety Factor    Fender is designed in accordance with the current design method    and its energy absorp...
MONTE-CARLO      SIMULATION    Monte-Carlo Simulation was done by use of     probability density distribution functions  ...
Comparison the Results       by FORM and Monte Carlo Simulation       Table 4. Comparison of the Results       by FORM and...
Comparison the Results by FORM and Monte Carlo SimulationTable 5. Factor for Abnormal Berthing ImpactPIANC2002,     Factor...
SAFETY FACTOR OF ENERGY ABSORPTION                       900                                           3.0                ...
Importance measuring approach velocity at each berth    Approach Velocity is the most important     factor and      it is...
Automatic Berthing System (RTK-GPS)                                      24
CONCLUSIONS    Reliability design method would be established    through intensive effort of field data collection.   Ap...
AcknowledgementThank you very much    for your kind     cooperation!!                      26
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Reliability design of fender systems5(h24.2.7)

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Arrangementet Fender Design 7.2.2012

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Reliability design of fender systems5(h24.2.7)

  1. 1. Reliability Design of Fender Systemsand Mooring Facilities  Shigeru Ueda  Seigi Yamase  Tatsuhiko Okada 1
  2. 2. Preface Review of fender design Reliability design method Appropriate confidence level , safety factor , and probability of failure Conclusion and recommendation 2
  3. 3. Fender Absorb ship’s berthing energy and reduce berthing impact force 3
  4. 4. Tanker ship and Fender 60 Tanker Ship vs. Fender ESSO PACIFIC (51.6) 50 GLOBTIC TOKYO 48.5) 40 THE OKINOSHIMA MARU( 25.4) 30 THE IDEMITU MARU(20.9) HYPER CELL 20 THE TOKYO MARU( 15.9) SUPER CELL THE TOKYO MARU(13.9) CELL 10 (2.8) 0 CYLINDRICAL SUPER ARCH SUPER M DYNA ARCH 1940 1950 1960 1970 1980 1990 yearIncrease of ship size requires more energy absorption 4
  5. 5. 600 500 SUC1000HRHRe a c tion Fo rc e (k N) 400 300 200 Deflection against Steady force 10% Allowable Deflection 35% 100 Rated Deflection 0 0 10 20 30 40 50 Co m pre s s ion St ra in (%) Figure 3 Load-Deflection Characteristics of Rubber Fender S.   UEDA
  6. 6. National Oil Stockpiling Kamigotoh Base 6
  7. 7. Ed Ship‘s Berthing Energy 1 E d = Mv C m C e C s C c 2 2 Ed : ship s berthing energy (kNm) M : ship mass (displacement in ton) v : approach velocity (m/s) Cm : virtual mass factor Ce : eccentricity factor Cs : softness factor Cc : berth cofigulaton factor 7
  8. 8. Deterministic Method (conventional) Maximum or Standard Ship size: Mass of ship Design approach velocity : observed data ex: design approach velocity of some berth ;20cm/s maximum observed approach velocity was 13cm/s among 788 sets of data Virtual mass fcator, eccentricity factor : analysis       Where, each factor is dealt equally weighted.        But, approach velocity have greater influence to 8 the
  9. 9. Approach Velocity 9
  10. 10. X = PX ・ Confidence 50% a Confidence 95% 200000 DWT Confidence 75% 0. 250 Confidence 90% DT = PDT ⋅ DWT 0.957 Vb = PVb ⋅ DWT −0.338 0. 200 PDT Vb ( m/s ) 1 50000 PVb μ=2.131   σ=0.156 0. 1 50 μ=2.040   σ=0.714DT 1 00000 0. 1 00 50000 0. 050 0 0. 000 0 20000 40000 60000 80000 1 00000 1 20000 0 1 0000 20000 30000 40000 50000 DWT DWT 2. 2 0. 60 2. 1 0. 55 2. 0 1. 9CM Ce 0. 50 1. 8 CM = PCM ⋅ DWT 0.022 Ce = PCe ⋅ DWT 0.015 1. 7 0. 45 1. 6 PCM PCe 1. 5 μ=1.491   σ=0.054 0. 40 μ=0.621   σ=0.019 0 20000 40000 60000 80000 1 00000 1 20000 0 20000 40000 60000 80000 1 00000 1 20000 DWT DWT 10
  11. 11. Probability Distribution Function (Regression for any Confidence Level) Confidence 10 Confidence 75% Probability of exceedance 50% ln(DWT) 0 5 0 10Table 1.Relation between Normalized Variable and Confidence Level  . ln(Factor for Berthing Energy) Confidenntial Level 50% 75% 90% 95% Normal Value 0 0.647 1.283 1.645 11
  12. 12. VirtualDT) ) Velocity Eccentricity FactorX mDT =-0.0873 Approach Factor =1.326)) )Mass =-0.477 =-3.772b beVb bCe bCm mAbebm =0.655 =3.843 =0.754 Displacement =0.399((Vb lnln(Ce lnlnVB(Cm Ab Table 2.Regression of Variables Vs toDWT by Akakura((( by Yamase by Moriya Table 2.Regression of Variables vs DWT Variables Regression Formula and 95% Confidence Value µX σX Displacement Regression ln(DT ) = Pln ( DT ) + 0.953 ⋅ ln( DWT ) µ DT =0.754 by Akakura ( DT ) 95% confidence ln(DT ) = 0.874 + 0.953 ⋅ ln(DWT ) σ DT =0.073 Approach Velocity Regression ln(Vb ) = Pln ( Vb ) − 0.338 ⋅ ln( DWT ) µVb =0.655 by Moriya ( Vb ) 95% confidence ln(Vb ) = 1.215 − 0.338 ⋅ ln( DWT ) σ Vb =0.340 Approach Velocity Regression ln(Vb ) = Pln ( Vb ) − 0.419 ⋅ ln( DWT ) µVb =1.326 by Yamase ( Vb ) N port 95% confidence ln(Vb ) = 2.531 − 0.419 ⋅ ln( DWT ) σ Vb =0.733 Approach Velocity Regression ln(Vb ) = Pln ( VB ) + 0.128 ⋅ ln( DWT ) µVb =-3.772 by Yamase ( Vb ) M port 95% confidence ln(Vb ) = −2.987 + 0.128 ⋅ ln( DWT ) σ Vb =0.477 Virtual Mass Factor Regression ln(C m ) = Pln ( Cm ) + 0.022 ⋅ ln(DWT ) µCm =0.399 by Akakura ( C m ) 95% confidence ln(Cm ) = 0.445 + 0.022 ⋅ ln( DWT ) σ Cm =0.036 Eccentricity Factor Regression ln(C e ) = Pln ( Ce ) − 0.015 ⋅ ln( DWT ) µCe =-0.477 by Akakura ( Ce ) 95% confidence ln( DT ) = −0.427 − 0.015 ⋅ ln( DWT ) σ Ce =0.030 Approach Velocity Regression ln( Ab ) = Pln ( Ab ) − 0.590 ⋅ ln( DWT ) µ Ab =3.843 by Yamase ( Ab ) N port 95% confidence ln( Ab ) = 6.023 − 0.590 ⋅ ln( DWT ) σ Ab =1.325 Approach Velocity Regression ln( Ab ) = Pln ( Ab ) − 0.047 ⋅ ln( DWT ) µ Ab =-0.0873 by Yamase ( Ab ) M port 95% confidence ln( Ab ) = 1.8453 − 0.0470 ⋅ ln( DWT ) σ Ab =1.1748 12
  13. 13. Load-Deflection Characteristics of Rubber Fender Fender Performance Curve 1.2 2.4 Ma vimu m Re a c t io n Fo rc e 1.0 2.0 Reaction Force Absorption 0.8 1.6 Energy 0.6 Ma x umu m 1.2 En e rgy Abs o rpt o in 0.4 0.8 0.2 0.4 0.0 0.0 0 10 20 30 40 50 60 70 Compression strain (% ) 13
  14. 14. Energy Absorption of Fender M eansurement Value Normal Distribution 15 μ Z=0.997 σ Z=0.031Frequency 10 5 0 0.96 1 .00 1 .04 1 .08 0.90 0.92 0.94 0.98 1 .02 1 .06 1 .1 0 Factor Z Example of   fender performance distribution 14
  15. 15. FIRST ORDER RELIABILITY DESIGN METHOD AND THE SAFETY INDEX Target Safety Index and Partial Safety Factor Nagao, Okada and Ueda (2003) applied the First Order Reliability Method to fender design for berthing ship (G = γ Z ⋅ Z k ⋅ Ecat − 1 / 2 ⋅ γ PDT ⋅ PDTk ⋅ γ PVb ⋅ PVbk ) 2 ⋅ γ PCM ⋅ PCM k ⋅ γ PCe ⋅ PCek ⋅ ( γ DWT ⋅ DWTk ) 0.288 The partial safety factor of each item related to the ship berthing .energy µX γ X = (1 − α X β T V X ) i Xk αis the sensitive factor of the variable   Χ ∑ σ X ≅ ∑ (α X σ X ) 2 ∑ (α X ) 2 = 1.0 15
  16. 16. PROBABILITY DISTRIBUTION FUNCTION AND THE PROBABILITY OF FAILURE  Generally it is difficult to calculate the probability of failure p f precisely.  It is important for the reliability design to establish the allowable probability of failure or target P fa, , safety index β T .  The probability of failure p f is calculated by the following equation. β z − µz p f = 1 − ∫ φ ( s )ds s= σz −∞ Where, φ (s ) is the standard normal distribution. Monte-Carlo simulation method is employed to calculate the probability of failure p f . Comparison is made beween MSC and FORM. 16
  17. 17. Sensitive factorSensitive factor for approach velocity is most influentialSensitive factor for ship size (DWT) is also influential s hi p s i z e sensitive factor α X DWT Z P DT P Vb P CM P Ce DWT 10,000 -0.267 15,000 -0.233 0.044 -0.103 -0.961 -0.051 -0.044 20,000 -0.275 35,000 -0.194 17
  18. 18. Table 3. Partial Safety Factor Fender is designed in accordance with the current design method and its energy absorption is 317kNm for the 35,000 container ship. μ X σX VX α X β T γ X β TO γ XO Z 0.997 0.031 0.031 0.044 0.997 0.996 P DT 2.131 0.156 0.073 - 0.103 1.017 1.020 P Vb 2.040 0.714 0.350 - 0.961 1.741 1.875 2.203 2.600 P Cm 1.491 0.054 0.036 - 0.051 1.004 1.005 Pce 0.621 0.019 0.030 - 0.044 1.033 1.003DWT(35,000) 30265 15117 0.499 - 0.194 1.214 1.252 γ : partial safety factorThis is a instance and is not be applicable to a ll berth 18
  19. 19. MONTE-CARLO SIMULATION Monte-Carlo Simulation was done by use of probability density distribution functions mentioned above. The probability of failure is given by following equation. q Pf ≅ N , Where, q : the number of trails when the performance function becomes zero and or negative       N : number of trials. 19
  20. 20. Comparison the Results by FORM and Monte Carlo Simulation Table 4. Comparison of the Results by FORM and Monte Carlo simulation. p f γ FORM 1.613 0.0147 MCS 1.644 0.0168Where , γ is the ratio of required energy absorptionto meet the failure probability against a fenderdesigned by conventional method for a 35,000container ship to absorp 317kNm.(95% confidence level ) 20
  21. 21. Comparison the Results by FORM and Monte Carlo SimulationTable 5. Factor for Abnormal Berthing ImpactPIANC2002, Factor for Abnormal Berthing Impact (Cab) -Safety Factor Tanker and Largest 1.25 Bulk Smallest 1.75 Largest 1.5 Container Smallest 2 General Cargo 1.75 Ro-Ro and Ferry 2.0 or 21
  22. 22. SAFETY FACTOR OF ENERGY ABSORPTION 900 3.0 800Absorption of Fender 2.5 700 Required Required Energy Safety Factor 600 2.0 Energy (kNm) 500 Absorption of 1.5 Fender (kNm) 400 300 1.0 200 0.5 100 Safety Factor 0 0.0 Curent 0.01 0.006 0.004 0.002 Design Required Probability of Exceedance Figureure.4 Probability of Failure and the Safety Factor 22
  23. 23. Importance measuring approach velocity at each berth Approach Velocity is the most important factor and it is influenced by following factors Ship size Location and condition of basin (exposed or sheltered) Berthing manoeuvring Tug assistance Use of ship’s thruster 23
  24. 24. Automatic Berthing System (RTK-GPS) 24
  25. 25. CONCLUSIONS Reliability design method would be established through intensive effort of field data collection. Application of numerical simulation method to obtain the probability of failure is useful. Data collection of appraoch velosity is strongly recommended. 25
  26. 26. AcknowledgementThank you very much for your kind cooperation!! 26

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