Peter Hammersberg, Gert Persson, Håkan Wirdelius Emulation of POD curves from synthetic data of phased array ultrasound testing Peter Hammersberg, Gert Persson, Håkan Wirdelius

Variations in NDT responses is the sum of variations from many sources Dominates and difficult to estimate makes general modeling difficult

…makes NDT modeling lag Design Evolution Trial & Error Empirical Mathematical Statistical Deterministic (Factors of Safety) Stochastic (Risk Quantified) Random Experimentation Experience-based Systematic Experimentation Graphical Approaches Physics-based Analytical Models Nominal Solutions Physics-based System Simulations Robust Solutions Provided by GE Aircraft Engine Division

NDE capability by POD Response Defect size Signal magnitude Probability of detection (POD) a â Experiments or simulation

Mathematical modelling of UT simSUNDT The simSUNDT program (freeware) consists of a Windows®-based pre-processor and postprocessor The simSUNDT enables simulations of the entire ultrasonic testing situation. The model is completely three-dimensional though the simulated component is two-dimensional simSUNDT uses as a mathematical kernel, UTDefect, that employs various integral transforms and integral equation techniques Model of ultrasonic backscattering due to grain growth in a welded region The result can be read by a number of commercial analysis software Reduce number of test pieces and synthetic defects

Development of simulation model Phased array UT E.A. Ginzel1 and D. Stewart2 , PHOTO-ELASTIC VISUALISATION OF PHASED ARRAY ULTRASONIC PULSES IN SOLIDS, Proc WCNDT 2004

Development of simulation model gj =g0+jDg p(r) g0 A0 A1 A2 A-1 A-2 xl Figur 2 Phased array UT Simulation time 5-15 minutes per run

Experimental verification of the model Dimensions of used test specimen (12%Cr Steel) 20 40 60 10 80 300 5 Side-Drilled Holes 6 Flat- Bottom Holes all f = 2.4 mm 35 5 Depth 20, 40 and 60 Depth 10, 30 and 50

Experimental verification of the model

Procedure for synthetic data based POD The inspection objectives Nondestructive Testing (NDT). UT, ET, RT UT, ET, RT (technique, method) Nondestructive Evaluation (NDE). UT, ET, RT Hit/Miss (procedure, calibration) The NDT procedure Essential parameters: x0 = a x1 x2 ... xn Technical Justification: x1 ±D x1 and x2 ±D x2 and ... xn ±D xn and

Problem POD curves need to capture experimental variation from many sources: Many variables > 10 Many simulations amount of simulation runs grow very quickly Emulation of model simulators by computer experiments using experimental design Simulator Real world Emulator

Calibration of simulation model to experimental data collection Simulation Control factors, Ci Responses: Input Signal M SimsuNDT Y = f(x)= f(M,Ci,Ni) Measured phased array signal amplitude (dB) Diameter: 3mm Depth: 15-75mm Ref depth: cali. 55mm (0db) Intended Output Signal Y Delta= 0 [5,75mm] Calibrate simulation to follow measurements for defect size 3mm for all defect depth Noise Parameters Ni (Uncontrollable Sources of Variation) Variation in settings and input mtrl Measurement variations Piece-to-Piece variation Side hole variations Equipment between & over time Simulation model Operator usage Environment System interaction Unintended Output (Error State) Deviation between measurements and simulations

Work path – predictive modeling Simulation control factors Locked at Reason for locking Computer experimental stage Factor unit low high Focal plane mm 20 500 Change scenario Screening in three steps with fractional design of experiements Focal adjustment % -20 minor impact on both responses Couple ant 0,05 0,4 0,2 Sound velocity tranvers (T) mm/s 5404 6604 6004 Sound velocity tranvers (S) 2979 3641 3310 Frequence MHz 4 6 5,75 Set to minimise difference between measure and simulated signal amplitude (delta=0) for the defect depth range tested - calibration of simulation Full factorial design of experiments Band width 3 5 Sensor length 11 22 Defect depth 15 75 Control factors for emulation of the simulation by predictive modelling: meta-modelling Amplitude damping Angle ° 41 49 Sensor elements # 2

Make simulator follow real world variations with simulation factors with limited physical meaning Keep flat

Emulation of simulator by experimental design - 2 order model 47 simulations Adding defect characteristic: Defect Diameter

Emulation of simulated signal amplitude (meta-model)

Response surface Sim signal vs defect size and depth

Emulation of signal response variation Monte-Carlo estimation of 5000 points per setting (<1sec) (compared to simulation 5-15 minutes per point)

Example of Probability of detection Detectability limit -6 [dB] Defect depth: 65 mm Defect diameter: 1,5 mm POD: 17,58 %

POD Example of emulated POD curves from synthetic data of phased array ultrasound testing Detection threshold: -6dB from reference defect

Conclusion simSUNDT has the possibility to simulate Phase Array, and is experimentally verified for the current setup Emulation of the simulation model by meta-modeling allow parameter studies of variability such as POD Calculation time ~1:10000 Complicated physical simulation models may need emulation by computer experiments, including Gaussian Process emulators, for example: Signal amplitude – multi-parameter regression sufficient (shown) Signal response angle – require higher level stochastic modeling (not shown since no POD relevance)

Deliverables Publication: G. Persson and H. Wirdelius, “Recent survey and application of the simSUNDT software”, Proc. Review of Progress in Quantitative Nondestructive Evaluation, Kingston, 2009. H. Wirdelius and G. Persson, ”Simulation based validation of the detection capacity of an ultrasonic inspection procedure”, accepted abstract, International Symposium On Fatigue Design & Material Defects, Trondheim, 2011. H. Wirdelius, P. Hammersberg and G. Persson, ”Predictive modeling of POD curves”. Integrity and quality assessment by NDE (IqNDE). The PICASSO project (EU) - imProved reliabIlity inspeCtion of Aeronautic structure through Simulation Supported POD (6M€)

Future plans Experimental validation of a more realistic situation with artificial fatigue cracks (EDM notches). Compare experimentally based POD curves with corresponding emulated from synthetic data. Include higher level stochastic modeling into the emulator.