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Abstract
Inspection by non-destructive testing (NDT) techniques of existing structures is not perfect and it has become a common practice to model their reliability in terms of probability of detection (PoD), probability of false alarms (PFA) and receiver operating characteristic (ROC) curves. These results are generally the main inputs needed by owners of structures in order to achieve inspection, maintenance and repair plans (IMR). The assessment of PoD and PFA is even deduced from intercalibration of NDT tools or from the modelling of the noise and the signal. In this last case when the noise and the signal depend on the location on the structure PoD and PFA are spatially dependent. This paper presents how to define PoD and PFA when damage and detection are stochastic fields or spatially dependent. Corrosion of coastal structures in harbours is considered for illustration and ROC curves are deduced. Identification of probability density functions on polynomial chaos is shown to be more suitable than predefined probability distribution functions (pdf) in view of fitting noise and signal plus noise distributions.
Highlights
The actual challenge of the maintenance of a set of structures needs to find the optimum balance between the increasing number of deteriorating structures and the limited funds available for their upkeep [1,2,3,4,5,6,7]
Concepts of probability of detection (PoD), probability of false alarm (PFA) and ROC curves coming from detection theory are very useful tools in order to quantify the quality of non-destructive-techniques
Used for inspection of cracks of offshore structures, they can be applied to corrosion problem in the case of inspection of ships or corroded marine and coastal structures
Summary
The actual challenge of the maintenance of a set of structures (harbours, bridges, etc.) needs to find the optimum balance between the increasing number of deteriorating structures and the limited funds available for their upkeep [1,2,3,4,5,6,7]. For example nondestructive-techniques (NDT) tools are required for the inspection of coastal and marine structures where marine growth acts as a mask or underwater zone gives harsh condition of visual inspection. The concepts of probability of detection (PoD), probability of false alarm (PFA) [11], probability of indication [12,13,14] have been proved to be suitable when performing risk-based-inspection [15,16,17,18] or management of networks [19] They allow introducing the cost/benefit of NDT tools in a complete risk analysis. The way to introduce these concepts as decision aid tools is focused on These definitions are extrapolated in the case of spatially dependent deterioration stochastic processes. Two models of noise are suggested: the first one consists in considering one independent random variable by density of probability PoD level of inspection and the second one consists in gathering data by area which leads to get one independent random variable by zone (tidal zone and underwater zone)
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