Non-destructive testing (NDT) methods have been widely used for damage examination and structural maintenance, e.g. detecting and repairing fatigue cracks. In-service inspections help to increase fatigue reliability by providing new information for updating structural failure probability and making decisions on repair. However, these benefits are often compromised by uncertainties associated with inspection methods. Sometimes existing cracks may not be identified, and positive inspection indication may not exist. It is of great interest to consider the influence of inspection uncertainty in maintenance optimization because the benefits and costs of maintenance are affected by inspection decisions (inspection times and methods) which are subjected to inspection uncertainty. However, the influence of inspection uncertainty on maintenance optimization has not been explicitly and adequately covered in the literature. In this paper, the problem has been investigated by probabilistic modelling of the qualities of inspection methods via probability of detection (PoD) functions. A new PoD function has been proposed to characterize the inspection quality when inspection uncertainty is not considered. Optimum inspection decisions are derived with the objective of maximizing lifetime reliability index under two scenarios (considering and not considering inspection uncertainty). The effectiveness of a planned inspection is defined based on the max reliability indexes under the two scenarios. It is shown that the max lifetime reliability index generally decreases when inspection uncertainty is considered. However, inspection uncertainty may have little influence on the lifetime reliability index depending on the planned inspection time. The effectiveness of a planned inspection increases with the decrease of the mean detectable crack size.

1. Workshop
CERI, UCD, Dublin
Wednesday 29th August 2018

2. Guang Zou, Kian Banisoleiman and Arturo
González
On the effectiveness and
uncertainty of inspection methods
for fatigue crack management

3. Fatigue cracks & failures
• Hot-spot areas
• Consequences
• Operational safety
• Uncertainties
• Life cycle costs

4. Engineering decisions against fatigue

5. Structural integrity management

6. Probabilistic maintenance optimization

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

8. Probabilistic inspection modelling
• Crack characteristics
• Instrumentation reliability
• The environments
• 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

9. Maintenance strategy and repair effect
• The time, criterion or condition to carry out repair?
• In case of repair, what’s the repair effect on a structural details?
• Drilling a stop hole
• Welding
• Welding plus post-weld treatment
• Replacement
• Grinding
• Damage size
• Deterioration rate
• Fatigue resistance
• Failure probability

10. Formulation of fatigue reliability
𝑀 𝑡 = 𝑎 𝑐 − 𝑎 𝑡
𝑃𝑓 𝑡 = 𝑃 𝑀 𝑡 < 0
𝛽 𝑡 = −Φ−1
𝑃𝑓 𝑡
𝑃′ 𝑓(𝑡𝑖)= σ 𝑏=1
𝑁 𝑏
𝑃𝑏 ∙ 𝑃𝑓|𝑏
𝛽′ 𝑡𝑖 = −Φ−1
൯𝑃′ 𝑓(𝑡𝑖

11. An illustrative example

12. Results and discussions

13. Conclusions
• Generally, fatigue reliability is lower when inspection uncertainty is considered.
• Fatigue reliability can be higher when inspection uncertainty is considered (the
inspection (by CVI, VI) is scheduled at the early stage of service life)
• Inspective uncertainty has little influence on fatigue reliability when the inspection
is scheduled at the late stage of service life.
• When inspection uncertainty is considered, the effectiveness of an planned
inspection increases with the decrease of the mean detectable crack size.

14. 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