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Effect of whipping on ship fatigue- Gaussian VS non-Gaussian modelling

Effect of whipping on ship fatigue- Gaussian VS non-Gaussian modelling. Wengang Mao, Igor Rychlik. Measurement data. Full-scale measurements of mid-section during half year 14 voyages: 7 EU-US and 7 US – EU Rainflow (RFC) fatigue estimation as a reference

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Effect of whipping on ship fatigue- Gaussian VS non-Gaussian modelling

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  1. Effect of whipping on ship fatigue-Gaussian VS non-Gaussian modelling Wengang Mao, Igor Rychlik

  2. Measurement data • Full-scale measurements of mid-section during half year • 14 voyages: 7 EU-US and 7 US – EU • Rainflow (RFC) fatigue estimation as a reference • Total fatigue = wave induced fatigue (WF) + whipping fatigue (HF) Measurement location Measured voyaged in the North Atlantic during 0.5 year Investigated vessel and the measurement location

  3. Scope of the project • From full-scale measurements: • Our definition of whipping; • How much fatigue is contributed from whipping; • Investigation of Narrow band approximation (NBA) and Non-Gaussian contributions. • General methodology (NBA) for the ship fatigue design • Non-Gaussian effect on extreme responses • Discussions

  4. RFC analysis of measure stresses Overview of fatigue estimation Spikes Winter voyages Measured stresses during one voyage (2 weeks) Summer voyages Standard deviation of responses in each individual sea state Fatigue estimated for different voyages (RFC) Fatigue in Winter from EU to US (Important); Measurement errors should be cleaned Large sea states for further investigation Small sea states only contribute 3.7% fatigue damage Fatigue difference due to removing small response

  5. Our definition of whipping Spectrum Whipping: High frequency response Separated signal with wave frequency & high frequency Whipping Definition: Total response = Wave induced + Whipping Wave induced response: fz [0, 2] [rad/s] Whipping response:fz [2, 8] [rad/s] Measurement noise: fz> 8rad/s

  6. Investigation of whipping Wave induced response Whipping induced energy: Three peaks of measured spectrum; Last peak is treated as measurement noise; Whipping ratio = Average whipping ratio is less than 3%. Whipping response Normalized spectrums of response in a voyage

  7. Whipping effect on Fatigue Whipping contribution to total fatigue damage Fatigue components Fatigue components based on measurements Wave induced fatigue (WF): 72%, Whipping contributed fatigue (HF): 24%, Some other contributions: 4%.

  8. Gaussian assumption Non-Gaussian responses (whipping) contribute 24% of total fatigue! Simulated Gaussian process Non-Gaussian effect on fatigue: Simulated process (the same spectrum); Largest fatigue difference 5%; Identical average fatigue Gaussian model is available for applications. Balanced between whipping contribution (30%) and NBA conservative part (33%); For long-term fatigue estimation, NBA maybe a good choice!

  9. Gaussian model and NBA NBA for Gaussian response • fz frequency of the mean level Strongly effected by noise (cut-frequency) • hs Significant stress range (energy) Energy of ship response 3%: (less influenced by whipping!) hs stress range little influenced by whipping! No measurement available  Numerical analysis (linear). Hσ()– RAOs (transfer function)

  10. A new simple fatigue model • hs based on hydrodynamic numerical analysis Hs – significant wave height Tz – crossing period of waves U0 – ship forward speed  – heading angle Polar diagram of the constant C (linear relation between hs and Hs) in terms of the ship speed U (radial direction) and the heading angle (hoop direction).

  11. Model for fz • fz model (encountered wave frequency) Vibration period of  2 seconds fz is strongly influenced by whipping (measurement) fz is computed by linear numerical analysis: fz(waveship) Approximated by the encountered wave frequency:fz(mod) fz comparison by different approaches Vibration of ship beam model (Hogging) • Linear numerical underestimate fz; • Expected value of fz computed from model is close to fz.

  12. Estimation of Safety index Total fatigue damage during one voyage Δt– time interval of one stationary sea state vs – ship forward speed i – ship heading angle Hs – significant wave height • The model works well for the measurement: • Errors for this ship are below 30%.; • Errors are smeared out when compute the total damage; • The proposed model depends on Hs.

  13. Gaussian assumption for Extreme prediction Rice’s formula for Gaussian crossings: Up-crossing rate of one stationary period (30min) Up-crossing rate of half a year period Crossing of half a year interval: E[Nhy+(X100)]=3.6*10-4

  14. Discussions • Whipping contributed fatigue 30% • Whipping induced average energy 3% • hs can be computed by linear analysis • Simple NB fatigue model works well wrt RFC • Gaussian assumption will lead to large underestimation of extreme response

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