© WZL/Fraunhofer IPT Peak Detection Methods for Ultrasonic Thickness Measurements Presentation by Arno Rehbein Aachen,

Seite 2© WZL/Fraunhofer IPT Outline Introduction to Ultrasonic Testing 1 Motivation 2 The Signal Processing Chain 3 Peak Detection Methods 4 Conclusion and Outlook 5

Seite 3© WZL/Fraunhofer IPT Nondestructive Testing (NDT) using Ultrasonics Sonic waves of high frequency (20kHz - 2GHz) are used for nondestructive inspection of parts Piezoelectric transducer that acts as transmitter and receiver generates ultrasonic waves A short pulse is emitted and passes through the coupling liquid into the inspected object At each surface, a part of the pulse is reflected and travels back to the receiver By continuously sampling the amplitude of the received signals, a visual representation over time is obtained (A-Image) The squirter is moved along the surface for automated inspection Thickness measurement is performed by evaluating the distance between reflections Ultrasonic Squirter

Seite 4© WZL/Fraunhofer IPT Traveling Path of an Ultrasonic Signal over Time - Illustration t t Received signal (A-Image)Workpiece FrontsideBackside

Seite 5© WZL/Fraunhofer IPT Outline Introduction to Ultrasonic Testing 1 Motivation 2 The Signal Processing Chain 3 Peak Detection Methods 4 Conclusion and Outlook 5

Seite 6© WZL/Fraunhofer IPT Insonic – Industrial Application for Thickness Measurements Ultrasonic thickness measurements in an industrial environment Peak detection based on Multiscale Wavelet Decomposition Results not sufficiently robust Implementation uses too much knowledge of the measurement setup Objective: Find new peak detection method with higher reliability and reusability

Seite 7© WZL/Fraunhofer IPT The problem of peak position determination

Seite 8© WZL/Fraunhofer IPT Outline Introduction to Ultrasonic Testing 1 Motivation 2 The Signal Processing Chain 3 Peak Detection Methods 4 Conclusion and Outlook 5

Seite 9© WZL/Fraunhofer IPT Signal Processing Chain A-ImagePreprocessingPeak Detection Thickness calculation Postprocessing A-Image is obtained through sampling hardware limited in speed and resolution Noise is introduced by natural or electomagnetic sources, remove through averaging / median / wavelet filtering Compensation of attenuation, if required Employ peak detection to identify backside echoes Increase peak position resolution through interpolation (single sample ~ 0.12mm) Average peak distances to obtain one thickness value per A-Image Use statistical or smoothing procedures to remove outliers

Seite 10© WZL/Fraunhofer IPT Possible Signal Modifications for Peak Detection Consider rectified signal |s| or |s²| Use envelope of rectified signal Simplified signal leads to simplified detection methods These modifications have shown to improve or accelerate the detection process [1]

Seite 11© WZL/Fraunhofer IPT Outline Introduction to Ultrasonic Testing 1 Motivation 2 The Signal Processing Chain 3 Peak Detection Methods 4 Conclusion and Outlook 5

Seite 12© WZL/Fraunhofer IPT Peak Detection Methods - Overview Threshold Values (+) Fast, easy to implement (-) Highly unreliable Template Matching (+) Precise (-) Choice of template F0 Estimation (+) Successful in other areas (-) Multiples of correct value Wavelet Decomposition (+) Fast, precise (-) Result postprocessing Model-Based Estimation (+) Equals physical model (-) Computational expensive Simplified M.B. Estimation (+) Simple model (-) Untested

Seite 13© WZL/Fraunhofer IPT Peak Detection through Thresholds [1] Selection of maxima/minima not possible Threshold value outside of standard noise deviation Problem: Single noise spikes Solution 1: Test for multiple threshold values Solution 2: Use a sliding window Solution 3: Zero Crossings as Threshold Requires previous knowledge of peak shape

Seite 14© WZL/Fraunhofer IPT Peak Detection through Template Matching [1,2] Correlate template t with signal s, compute least squares error: Peak is found, if error is below pre-defined threshold Reduce computational amount through preselection of areas and by employing Fourier Transform Use first backside peak as template, if no other available Faster: One Bit Correlation (Elmer & Schweinzer, [2])

Seite 15© WZL/Fraunhofer IPT Fundamental Frequency Estimation (f0 Estimation) [3] Determine the underlying frequency f 0 (fundamental frequency) Wavelength corrsponds to two times the distance Correlate downsampled signal with itself Use results to identify cross correlation on real signal Postprocessing to remove multiples of wavelength

Seite 16© WZL/Fraunhofer IPT Decompose signal of length 2 n into n scales Identify the first set of echoes on coarse scale Use coefficients on finer scale to identify peaks Choice of scale is critical, evaluate multiple scales Criteria: Number of peaks found and equidistance of peaks Practical experience shows: Still not reliable enough Decomposition of full signal into various scales mDecomposition of first set of echoesFail of peak detection because of wrong scale Multiscale Wavelet Decomposition (DWT) [4,5]

Seite 17© WZL/Fraunhofer IPT Model-Based Estimation of Ultrasonic Echoes [6] Define a model based on physical properties of pulse Set of five parameters:  - bandwidth factor  - arrival time f c - center frequency  - phase  - amplitude Model of single peak Model of signal with addend v(t) for noise   fcfc  

Seite 18© WZL/Fraunhofer IPT Model-Based Estimation of Ultrasonic Echoes [6] Algorithm for estimation of parameters (x: actual signal) Converges within 25 steps for well-chosen parameters Expensive, lots of matrix-multiplications We only need  Other parameters should remain near-constant

Seite 19© WZL/Fraunhofer IPT Model-Based Estimation (Simplified) Use a simpler model: Gaussian-shape model Only two parameters,  and   corresponds to peak position Perform iteration through Gauss-Newton algorithm

Seite 20© WZL/Fraunhofer IPT Outline Introduction to Ultrasonic Testing 1 Motivation 2 The Signal Processing Chain 3 Conclusion and Outlook 5 Peak Detection Methods 4

Seite 21© WZL/Fraunhofer IPT Conclusion and Outlook Over the years, various peak detection methods have been developed and used (with more or less success) Requirement of reusability Requirement of precision Near-realtime requirement What is the best method ? Use real world data and find out! Thanks. Any Questions?

Seite 22© WZL/Fraunhofer IPT References 1. Barshan, Billur: Fast processing techniques for accurate ultrasonic range measurements. Measurement Science and Technology 11, pp. 45–50, Institute of Physics Publishing, UK (2000) 2. Elmer, H., Schweinzer, H.: Performance Considerations of Ultrasonic Distance Measurement with Well Defined Properties. In: Journal of Physics: Conference Series 13, 7th International Symposium on Measurement Technology and Intelligent Instruments. (2005) 3. Talkin, David: A Robust Algorithm for Pitch Tracking (RAPT). In: Speech Coding and Synthesis, Chap. 14, Elsevier Science (1995) 4. Mallat, Stephane G.: A Theory for Multiresolution Signal Decomposition: The Wavelet Representation. IEEE Transactions On Pattern Analysis And Machine Intelligence, Vol. 11, No. 7 (1989) 5. Wulf, Christian: Numerische Analyse digitalisierter Ultraschallsignale zur automatisierten Impuls- Echo-Laufzeitbestimmung. Studienarbeit. Lehrstuhl für Fertigungsmeßtechnik und Qualitätsmanagement RTWH Aachen, Germany (2000) 6. Demirli, R., Saniie, J.: Model-Based Estimation of Ultrasonic Echoes Part I & II. In: IEEE Transactions On Ultrasonics, Ferroelectrics And Frequency Control, Vol. 48, No. 3 (2001)

Seite 23© WZL/Fraunhofer IPT Backup

Seite 24© WZL/Fraunhofer IPT Wavelets Decomposition - Introduction ‚Small waves‘ that integrate to zero Well localized in frequency and time Analyze signal through dilations (scales) and translations of the mother wavelet Discrete Wavelet Transform (DWT) in O(n), can be performed in closed form We obtain a fully reconstructable representation of our signal Haar WaveletDaub4 WaveletDaub20 Wavelet

Seite 25© WZL/Fraunhofer IPT Volumetric Nondestructive Testing 90 mm 50 mm 100 mm B-Scan-stack