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Spatial dependence of Receiver Operating Characteristic curves for Risk Based Inspection of corroded structures: application to on-pile wharf
... Les secteurs les plus avancés dans cette utilisation sont les secteurs maritimes pour lesquels les coûts et les difficultés d'inspection sont des facteurs importants. Les modèles reposent soit sur des statistiques issues de campagnes d'inter- calibration ( Barnouin et al., 1993)), soit sur des hypothèses sur la modélisation par la théorie du signal de données d'inspection ( Schoefs et al., 2007). Plus récemment, on a montré (Rouhan et al., 2003) comment la probabilité de fausse alarme PFA - probabilité de détecter un défaut non existant-influe sur la politique de maintenance. ...
... On suppose ici que le bruit est indépendant de la taille du défaut mesuré, ce qui est le cas lorsque la qualité d'inspection est fortement affectée par les conditions environnantes (visibilité, difficulté d'accès et de mise en oeuvre, etc..). Cette hypothèse a été validée à partir d'une campagne de mesures dans le secteur portuaire ( Schoefs et al., 2007). ...
... The building of sample of noise (see equation (6)) allows plotting the scatter diagram of figure 18: it is clearly shown that there is no correlation between the noise and the real size of loss of thickness [33]. Thus we suppose that the noise is mainly governed by the inspected area (tidal or underwater zones). ...
... 12 Evolution of −log(L(φ)) for PC order p = 2 and p = 3; noise at z 1 = +2m. 3213 Noise and of loss of thickness fitting with polynomial chaos for several orders p; z 1 = +2m.33 14 Noise and of loss of thickness fitting with polynomial chaos for several orders p;z 6 = −1m.34 ...
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.
... . the radius d NDT equals the performance index (NDT-PI) (distance between the BPP and the ROC curve) (Schoefs and Cle´mentCle´ment 2004, Schoefs et al. 2007, 2008a); . the a NDT is the angle between axis (PFA ¼ 0) and the line (BPP, NDT-BPP). ...
Owners of structures and infrastructure base their maintenance decision schemes mainly on structural integrity assessment and consequence analysis. The major inputs come from information collected by inspections employing non-destructive or destructive tools. Uncertainties and errors of measurement can lead to bad decisions but these effects are rarely integrated into the decision making process. Risk Based Inspection (RBI) provides the basics for optimizing the maintenance plans of existing structures while ensuring satisfactory safety and availability of the structure during its service life. This basis depends both on computation of reliability index and probabilistic modeling of inspection results. Probabilistic modeling of inspection results leads to specifying the Probability of Detection (PoD), the Probability of False Alarms (PFA) and the Receiver Operating Characteristics (ROC) curve that are usually considered as key parameters in RBI. Under these circumstances the comparison of Non destructive Testing (NDT) tools in terms of cost/benefit is difficult to be established as well as the method for optimizing a given technique. This paper starts from the αδ method that gives a new performance indicator in this context, and apply it to the field of inspection of steel harbor structures, after a detailed analysis of uncertainties during corrosion assessment by ultrasonic measurements.
... Since corrosion on a steel pile is usually associated with a significant change of colour (Tsushima et al. 1997) of the affected location, image processing based techniques can be successfully used (Tsushima et al. 1997, Pakrashi et al. 2007) for the detection and quantification of the corroded region. Such image processing technique based information also forms a basis of probabilistically identifying the efficiency of the technique itself through the use of Receiver Operating Characteristics (ROC) ( Schoefs et al. 2007) which plots the Probability of Detection (PoD) versus the Probability of False Alarm (PFA). The POD is defined as the probability of correcting identifying a damage when it exists, while the PFA is defined as the probability of identifying a damage when there is not any. ...
... The αδ method lies on the characterization of ROC curves by the Polar coordinates of the Best Performance Point of the NDT tool (NDT-BPP). This point corresponds on the ROC curve to the minimal distance between the curve and the best performance point BPP of coordinates (PFA = 0, PoD = 1) [4] NDT-BPP is defined by: ...
Owners of civil infrastructures base their maintenance decisions schemes mainly both on structural integrity assessment and consequence analysis. Some inputs come from information collected by non-destructive or destructive tools. Uncertainties and noise of measurements can lead to bad decisions but are rarely integrated into the process of decision. Nowadays, Risk Based Inspection (RBI) provides the basic concepts for optimizing the maintenance plans of existing structures while insuring a good safety and availability conditions during service life of structures. In this paper, concepts are applied on a steel sheet pile seawall submitted to uniform corrosion where spatio-temporal dependence of performance of ROC (Receiver Operating Characteristic) curves is studied. Résumé Les gestionnaires d'infrastructures de génie civil basent leurs schémas décisionnels de maintenance essentiellement à partir de l'évaluation de l'intégrité structurale des ouvrages et de l'analyse des conséquences en cas de défaillance. Certaines données d'entrée proviennent de contrôles destructifs ou non destructifs. Les incertitudes et le bruit sur les mesures peuvent conduire à de mauvaises décisions mais sont rarement pris en compte dans les processus de décision. Actuellement, les méthodes RBI (Risk Based Inspection) donnent les fondamentaux pour aboutir à des plans de maintenance optimisés tout en garantissant la sécurité et la disponibilité des ouvrages en service. Dans cet article, ces concepts sont appliqués à un quai constitué par un rideau de palplanches soumis à la corrosion uniforme et la dépendance spatio-temporelle de la performance des courbes ROC (Caractéristique Opérationnelle du Récepteur) est étudiée.
Inspection by non-destructive testing techniques of existing structures is not perfect and it has become a common practice to model their reliability in terms of receiver operating characteristic (ROC) curves. This paper suggests a method of building ROC curves in case of random fields of defects on a structure by using polynomial chaos decomposition. Knowledge of spatial distribution of defects allows a reliability analysis to be performed. When selecting stochastic finite element analysis to solve this problem, the format is the same as the one chosen for modelling inspections results. The paper shows how to link these quantities (ie. reliability and inspection results) in a risk analysis by using polynomial chaos decomposition as a common language.
Clément A., Boéro J., Schoefs F., Memet J.B., "Statistical analysis of corrosion impact for marine structures: overview of French structures in several harbours", Proceeding of 1st International Conference on Applications Heritage and Constructions in Coastal and Marine Environment, (MEDACHS’08), paper #26, 28-30 January 2008, Lisbon (LNEC), Portugal (2008).
Reassessment of existing structures generates a need
for up-dated materials properties. In a lot of cases,
on-site inspections are needed and in some cases
visual inspection is not sufficient. For example Non
Destructive Testing (NDT) tools are required for the
inspection of coastal and marine structures where
marine growth acts as a mask or immersion area
gives harsh condition of inspection. In these fields,
the cost of inspection can be prohibitive and an accurate
description of the on-site performance of
NDT tools must be provided. Inspection of existing
structures by a NDT tool 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 quantities are
generally the main inputs needed by owners of structures
in view to achieve Inspection, Maintenance
and Repair plans (IMR) (Sheils et al., 2008). The assessment
of PoD and PFA is even deduced from inter-
calibration of NDT tools or from the modelling
of the noise and the signal.
Theoretical aspects coming from detection theory
and probabilistic modelling of inspections results in
view to provide inputs in the computation of mathematical
expectation of RBI cost models are described
in Schoefs et al. (2008).
First, let us focus in this paper on the benefit of
the combination of multiple Non-Destructive Testing
(NDT) and the role of expert judgement in this
process. In this case, expert judgement acts at two
levels:
− The knowledge of ageing laws to provide the
probability of defect existence that is needed
when computing likelihood of events that govern
the cost expectation;
− The way to address the decision after obtaining
results from the two inspections.
The process is illustrated for the RBI of steel harbour
structures.
Then, the effect of the shape of ROC curve on the
decision process is highlighted. To this aim, a parametric
study is performed to analyze the influence of
the polar coordinates of the best performance point
of the NDT tool (NDT-BPP) on the expectation of
the cost of detection and the cost of no detection (see
Figure 1). NDT-BPP is defined as the closest point
of the ROC curve to the best performance point BBP
of coordinates (PFA=0 , PoD=1) and the NDT-BPP
polar coordinates are defined by:
− The radius dNDT equal to the performance index
(NDT-PI) (distance between the best performance
point and the ROC curve) (Schoefs, 2007);
− The angle aNDT between axis (PFA=0) and the
line (BBP , NDT-BPP).
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 Receiver Operating Characteristic (ROC) curves. This paper suggests a method of building ROC curves in case of random fields of defects by using polynomial chaos decomposition. Knowledge of spatial distribution of defects allows performing reliability analysis. When selecting stochastic finite element analysis to solve this problem, the format is the same as the one chosen for modeling inspection results. The paper shows how to link these quantities in risk analysis.
The localisation and calibration of damage in a structure are often difficult, time consuming, subjective and error prone. The importance of a simple, fast and relatively inexpensive non-destructive technique (NDT) with reliable measurements is thus greatly felt. The usefulness and the efficiency of any such technique are often affected by environmental conditions. The definition of damage and the subsequent interpretation of the possible consequences due to the damage introduce subjectivity into an NDT technique and affect its performance. It is of great importance in terms of practical application to find out the efficiency of an NDT technique in a probabilistic way for various damage definitions and environmental conditions through the use of receiver operating characteristic (ROC) curves. Such variations of performance of an NDT tool can be predicted through simulation processes, and the test conditions conducive to good detections can be isolated and ranked according to their relative efficiency. This paper considers a camera based image analysis technique to identify, quantify and classify damage in structures at various levels of scale. The general method has been applied to identify the affected areas on aluminium due to pitting corrosion. The method depends on the optical contrast of the corroded region with respect to its surroundings, performs intelligent edge detection through image processing techniques and computes each affected and closed region to predict the total area of the affected part, together with its spatial distribution on a two-dimensional plane. The effects of various environmental factors on the quality of such images are simulated from an original photograph. The objectivity and the amount of available information, quantification and localisation and the extent of pitting corrosion are observed, together with the various constructed ROC curves. The method provides the engineer, the owner of the structure and the end-user of the NDT technique with a tool to assess the performance of the structure in an as-built condition and decide on the appropriateness of a certain NDT, under a given environmental condition and a certain definition of damage. Moreover, it allows the findings of the NDT results to be introduced in the decision chain and risk analysis.
Owners of civil infrastructure base their maintenance decision schemes mainly on both structural integrity assessment and consequence analysis. Some inputs come from information collected by inspections with non-destructive or destructive tools. Uncertainties and errors of measurement can lead to bad decisions but are rarely integrated into the decision process. Currently, risk-based inspection (RBI) provides the basic concepts for optimising the maintenance plans of existing structures while insuring satisfactory safety and availability of the structure during its service life. It relies both on reliability computations and probabilistic modelling of inspection results. This last point leads to introduce the probability of detection and the probability of false alarms that are usually considered as parameters in RBI. However, when data from inter-calibration campaigns are available, the whole receiver operating characteristics curves should be used. Then, the comparison of non-destructive testing tools in terms of cost or benefit is difficult as well as the method for optimising a given technique. This article presents the αβ method that gives a new performance indicator in this context. It is applied to the field of inspection of harbour structures.
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