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"Probabilistic decision basis and objectives for inspection planning and optimization" presented at IALCCE2018

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Marine and offshore engineering has long been challenged with the problem of structural integrity management (SIM) for assets such as ships and offshore platforms due to the harsh marine environments, where cyclic loading and corrosion are persistent threats to structural integrity. SIM for such assets is further complicated by the very large number of welded plates and joints, for which condition surveys by inspections and structural health monitoring become a difficult and expensive task. Structural integrity of such assets is also influenced by uncertainties associated with materials, loading characteristics, fatigue degradation model and inspection method, which have to be accounted for. Therefore, managing these uncertainties and optimizing the inspection and repair activities are relevant to improvements in SIM. This paper addresses probabilistic inspection planning and optimization by comparative analysis for a typical fatigue-prone structural detail based on reliability, life cycle cost (LCC) and value of inspection information (VoI). With the objective of clarifying the differences between the theoretical basis and objectives for probabilistic inspection optimization, three maintenance strategies for the structural detail are proposed and studied. It is found that different optimal inspection times are obtained with the objectives of reliability maximization, LCC minimization and VoI maximization. Also, planned inspection and repair can help to achieve higher reliability with fewer repairs than repair without inspection (i.e. time-based replacement). If the cost of unit inspection and repair is not negligible compared with failure consequence, it is suggested to employ the optimization objective of life cycle cost minimization, which considers the costs of SIM. The paper proposes a simple approach for quantifying the VoI, based on life cycle cost analysis for the three maintenance strategies. It is concluded that the VoI is relevant to both the optimal maintenance decision with and without inspection.

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"Probabilistic decision basis and objectives for inspection planning and optimization" presented at IALCCE2018

  1. 1. Reducing Uncertainty in Structural Safety Special Session SS6 Ghent, Belgium 28-31 October 2018
  2. 2. Guang Zou, Kian Banisoleiman and Arturo González Probabilistic decision basis and objectives for inspection planning and optimization
  3. 3. Fatigue cracks & failures • Hot-spot areas • Consequences • Operational safety • Uncertainties • Life cycle costs
  4. 4. Engineering decisions against fatigue
  5. 5. Aim of this research • The role of inspection in reliability and cost management • Influences of different decision basis & objectives on integrity management 1. Fatigue & fracture reliability 2. Life cycle costs 3. Value of information (VoI) Maintenance Strategies Case 1 Do Nothing Case 2 Repair (or replacement) Case 3 Inspection before repair
  6. 6. Case study For simplicity, schedule one maintenance intervention
  7. 7. Probabilistic physical model 𝑑𝑎 𝑑𝑁 = 𝐶∆𝐾 𝑚 , ∆𝐾𝑡ℎ ≤ ∆𝐾 ≤ 𝐾 𝑚𝑎𝑡 ∆𝐾 = ∆𝜎𝑌 𝑎 𝜋𝑎 𝑁 𝑃 = 1 𝜋 Τ𝑚 2 𝐶∆𝜎 𝑚 න 𝑎0 𝑎 𝑐 𝑑𝑎 𝑎 Τ𝑚 2 𝑌 𝑎 𝑚 ∆𝑎 𝑡 = 𝜋 Τ𝑚 2 𝐶∆𝜎 𝑚 න 0 𝑁 𝑡 𝑎 Τ𝑚 2 𝑌 𝑎 𝑚 𝑑𝑁 Variable Distribution Unit Mean Standard Deviation 𝑎0 Exponential mm 0.04 0.04 log10 𝐶 Normal [N, mm] -12.74 0.11 𝐵 Normal - 1.00 0.15
  8. 8. Probabilistic inspection modelling • Crack characteristics • Instrumentation reliability • The environment • Inspection procedure • Human factors 𝑃𝑜𝐷 𝑎 = 𝐹 𝑎 = 1 − exp − Τ𝑎 𝐸 𝑎 𝑑 𝑃𝑜𝐷 𝑎 = ቊ 0 𝑎 < 𝐸 𝑎 𝑑 1 𝑎 ≥ 𝐸 𝑎 𝑑 For Magnetic Particle Inspection, 𝑎 𝑑 = 0.89 mm
  9. 9. Maintenance strategy and repair effect The time, criterion or condition to carry out repair? (time-based & condition-based maintenance) In case of repair, what’s the repair effect on a structural details? (crack dimension returns to initial state) • Drilling a stop hole • Welding • Welding plus post-weld treatment • Replacement • Grinding
  10. 10. Fracture reliability 𝑀 𝑡 = 𝑎 𝑐 − 𝑎 𝑡 𝑃𝑓 𝑡 = 𝑃 𝑀 𝑡 < 0 𝛽 𝑡 = −Φ−1 𝑃𝑓 𝑡 Maintenance Strategies Case 1 Do Nothing Case 2 Repair (or replacement) Case 3 Inspection before repair Failure Survival Inspection & no detection Detection & Repair Event Tree Analysis for Case 3
  11. 11. Probabilistic maintenance optimization
  12. 12. Decrease of reliability with service year (case 1) Maintenance Strategies Case 1 Do Nothing Case 2 Repair (or replacement) Case 3 Inspection before repair Reliability index at end of service life of 1.1
  13. 13. Decrease of reliability with service year (case 2) Maintenance Strategies Case 1 Do Nothing Case 2 Repair (or replacement) Case 3 Inspection before repair Reliability index at end of service life varies depending on the time of the intervention tr = 8 tr = 10 tr = 14
  14. 14. Decrease of reliability with service year (case 3) Maintenance Strategies Case 1 Do Nothing Case 2 Repair (or replacement) Case 3 Inspection before repair Reliability index at end of service life varies depending on the time of the intervention tr = 8 tr = 9 tr = 14
  15. 15. Reliability index at end of service life Maintenance Strategies Case 1 Do Nothing Case 2 Repair (or replacement) Case 3 Inspection before repair There is an optimal intervention time achieving maximum reliability. For case 3, it is 9 years, and for case 2, it is 10 years. There are ranges when one strategy outperforms the other 128
  16. 16. Life cycle costs The costs for operational integrity management - Costs of inspections, repairs and failure The time of analysis and decision is the beginning of service The costs are variables, and subjected to uncertainties - expected values of costs Average annual discounting rate 𝑟 𝐿𝐶𝐶 = 𝐶𝐼 + 𝐶 𝑅 + 𝐶 𝐹 𝐶𝐼 = ෍ 𝑘=1 𝑁 𝐼 𝑃𝑖𝑛𝑠𝑝 𝑘 ∙ 𝐶𝑖𝑛𝑠𝑝 𝑘 ∙ 1 1 + 𝑟 𝑡𝑖 𝑘 𝐶 𝑅 = ෍ 𝑘=1 𝑁 𝑅 𝑃𝑟𝑒𝑝 𝑘 ∙ 𝐶𝑟𝑒𝑝 𝑘 ∙ 1 1 + 𝑟 𝑡 𝑟 𝑘 𝐶 𝐹 = 𝑃𝑓 𝑁 ∙ 𝐶𝑓𝑎𝑖𝑙∙ 1 1 + 𝑟 𝑇
  17. 17. Life cycle costs Maintenance Strategies Case 1 Do Nothing Case 2 Repair (or replacement) Case 3 Inspection before repair 𝐿𝐶𝐶 = 𝐶𝐼 + 𝐶 𝑅 + 𝐶 𝐹 Planned inspection or repair maintenance interventions can reduce LCC if planned at appropriate times Optimal inspection/repair times for maximum reliability and minimum LCC may differ
  18. 18. Failure Risk and Maintenance Costs Maintenance Strategies Case 1 Do Nothing Case 2 Repair (or replacement) Case 3 Inspection before repair Maintenance costs decrease slightly for case 2, but increase dramatically for case 3 with intervention time Failure risk for case 3 is lower than for case 2 for an intervention time between 8 and 12 years
  19. 19. Value Of Inspection Information Information contributes to uncertainty reduction and improvement of decision, but comes at a cost. VoI quantification facilitates rational Inspection optimization and decision-making. VoI calculation: 𝑉 = 𝑈𝑖 − 𝑈0 Optimal decision while adopting inspection Optimal decision without inspection 𝑉 = min 𝐿𝐶𝐶𝑐𝑎𝑠𝑒1, 𝐿𝐶𝐶𝑐𝑎𝑠𝑒2 − min 𝐿𝐶𝐶𝑐𝑎𝑠𝑒1, 𝐿𝐶𝐶𝑐𝑎𝑠𝑒2, 𝐿𝐶𝐶𝑐𝑎𝑠𝑒3
  20. 20. Value of information (VoI) 4 177 Maintenance Strategies Case 1 Do Nothing Case 2 Repair (or replacement) Case 3 Inspection before repair 𝑉 = min 𝐿𝐶𝐶𝑐𝑎𝑠𝑒1, 𝐿𝐶𝐶𝑐𝑎𝑠𝑒2 − min 𝐿𝐶𝐶𝑐𝑎𝑠𝑒1, 𝐿𝐶𝐶𝑐𝑎𝑠𝑒2, 𝐿𝐶𝐶𝑐𝑎𝑠𝑒3 The VoI can be zero for inspections scheduled in the beginning and at the end of service life VoI decreases after year 7
  21. 21. Conclusions • Reliability Optimization: Condition-based maintenance can sometimes achieve higher reliability with fewer repairs than repair without inspection in time-based maintenance. • Life Cycle Cost Optimization: The optimal inspection time by cost- based optimization takes place earlier than by reliability-based optimization. As the inspection and repair costs become smaller compared to failure consequence, then both optimal times get closer. • Value of Information Optimization: The VoI can be zero when inspection system and activity is not properly devised and scheduled. Although the VoI can be calculated based on life cycle costs, the inspection times by VoI-based and cost-based optimization can be different.
  22. 22. The TRUSS ITN project (http://trussitn.eu) has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 642453 Thanks for your attention

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