Bayesian synthesis for simulation‐based generation of probability of detection (PoD) curves

HighlightsBayesian approach for PoD curves using reduced number of experimental trials and cases.Framework for data‐level combination of simulation and experimental results.Demonstration of approach for ultrasonic inspection of backwall‐breaking notches.Extension to PoD for complex defects using simulated data of canonical defects. ABSTRACT This paper examines the feasibility of using Bayesian synthesis to reduce the number of experimental cases and trials required for generation of probability of detection (PoD) curves. A Bayesian framework is developed for the data‐level combination of experimental and simulated datasets, in the context of the inspection of back‐wall breaking notches in metallic samples by bulk ultrasonic shear waves. PoD curves generated using the proposed approach, where results from a reduced number of experimental defect cases and trials are used in combination with simulated datasets, are shown to compare well with those from the conventional approach using a large number of experiments. Finally, the framework is also shown to be versatile for generating PoD curves for complex defects (illustrated through the example of an inclined notch) using simulations for canonical defects (vertical notches).

[1]  Daniel Kanzler,et al.  Bayesian Approach for the Evaluation of the Reliability of Non-Destructive Testing Methods: Combination of Data from Artificial and Real Defects , 2012 .

[2]  Xavier Artusi,et al.  Model-based POD study of manual ultrasound inspection and sensitivity analysis using metamodel , 2016 .

[3]  Scott R. Eliason.  Maximum likelihood estimation: Logic and practice. , 1994 .

[4]  R. Bruce Thompson.  A BAYESIAN APPROACH TO THE INVERSION OF NDE AND SHM DATA , 2010 .

[5]  P. Calmon,et al.  The Use of Simulation in POD Curves Estimation: An Overview of the IIW Best Practices Proposal , 2016 .

[6]  Eniq Tgr,et al.  ENIQ TGR TECHNICAL DOCUMENT PROBABILITY OF DETECTION CURVES: STATISTICAL BEST-PRACTICES , 2010 .

[7]  T. Jayakumar,et al.  Use of acoustic emission and ultrasonic techniques for monitoring crack initiation/growth during ratcheting studies on 304LN stainless steel straight pipe , 2014 .

[8]  Nicolas Dominguez,et al.  POD evaluation using simulation: A phased array UT case on a complex geometry part , 2014 .

[9]  J. V. Bradley.  Distribution-Free Statistical Tests , 1968 .

[10]  D. V. Leemans,et al.  Bayesian approaches to using field test data in determining the probability of detection , 2004 .

[12]  E. Leskelä,et al.  Probability of Detection Simulations for Ultrasonic Pulse-echo Testing , 2012 .

[13]  Jennifer E. Michaels,et al.  An Ultrasonic Angle Beam Method for in situ Sizing of Fastener Hole Cracks , 2006 .

[14]  F. Jenson,et al.  A Bayesian approach for the determination of POD curves from empirical data merged with simulation results , 2013 .

[15]  Prabhu Rajagopal,et al.  On the use of absorbing layers to simulate the propagation of elastic waves in unbounded isotropic media using commercially available Finite Element packages , 2012 .

[16]  P. Calmon,et al.  Simulation supported POD curves for automated ultrasonic testing of pipeline girth welds , 2014, Welding in the World.

[17]  A. Karpelson.  Probability of Detection and Uncertainty of Measurement during Ultrasonic Inspection of CANDU Reactor Pressure Tubes , 2015 .

[18]  R. Bruce Thompson.  A UNIFIED APPROACH TO THE MODEL‐ASSISTED DETERMINATION OF PROBABILITY OF DETECTION , 2008 .

[19]  P. Calmon,et al.  SIMULATION BASED POD EVALUATION OF NDI TECHNIQUES , 2010 .

[20]  Lina Tidström,et al.  Estimation of Probabilities of Detection for Cracks in Pipes in Swedish Nuclear Power Plants , 2004 .

[21]  Seldis Thomas.  ENIQ Recommended Practice 10 - Personnel Qualification - ENIQ report no 38 , 2010 .

[22]  M. S. Mohammed,et al.  Probability of detection simulations to study the influence of surface roughness on the reliability of ultrasonic testing system , 2014, Russian journal of nondestructive testing.

[23]  Anil K. Bera,et al.  A test for normality of observations and regression residuals , 1987 .

[24]  M. Kendall.  Probability and Statistical Inference , 1956, Nature.

[25]  S. Biwa,et al.  Influence of axle-wheel interface on ultrasonic testing of fatigue cracks in wheelset. , 2013, Ultrasonics.

[26]  Håkan Wirdelius,et al.  Simulation Based Validation of the Detection Capacity of an Ultrasonic Inspection Procedure , 2012 .

[27]  Jeremy S. Knopp,et al.  Evaluation of probability of detection (POD) studies with multiple explanatory variables , 2016 .

[28]  S. Cantini,et al.  Advanced ultrasonic “Probability of Detection” curves for designing in-service inspection intervals , 2016 .

[29]  Michael J. S. Lowe,et al.  TOWARDS IMPROVED FINITE ELEMENT MODELLING OF THE INTERACTION OF ELASTIC WAVES WITH COMPLEX DEFECT GEOMETRIES , 2009 .

[30]  Krishnan Balasubramaniam,et al.  On a framework for generating PoD curves assisted by numerical simulations , 2015 .

[31]  William Q. Meeker,et al.  Physical Model-Assisted Probability of Detection of Flaws in Titanium Forgings Using Ultrasonic Nondestructive Evaluation , 2014, Technometrics.

[32]  John C. Aldrin,et al.  Demonstration of model-assisted probability of detection evaluation methodology for eddy current nondestructive evaluation , 2012 .

[33]  Krishnan Balasubramaniam,et al.  Finite Element Simulations to Predict Probability of Detection (PoD) Curves for Ultrasonic Inspection of Nuclear Components , 2014 .

[34]  N. Dominguez,et al.  SIMULATION SUPPORTED POD: METHODOLOGY AND HFET VALIDATION CASE , 2011 .

[35]  P. J. Green,et al.  Probability and Statistical Inference , 1978 .

[36]  L. W. Schmerr Jr..  Fundamentals of Ultrasonic Nondestructive Evaluation: A Modeling Approach , 2016 .

[37]  Bertrand Iooss,et al.  Model Assisted Probability of Detection Curves: New Statistical Tools and Progressive Methodology , 2016, Journal of Nondestructive Evaluation.

[38]  S. C. Gupta,et al.  Fundamentals Of Mathematical Statistics , 1972 .