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3-D Defect Profile Reconstruction from Magnetic Flux Leakage Signatures Using Wavelet Basis Function Neural Networks Kyungtae Hwang Iowa State University

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3-D Defect Profile Reconstruction from Magnetic Flux Leakage Signatures Using Wavelet Basis Function Neural Networks Kyungtae Hwang Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 2000 3-D defect profile reconstruction from magnetic flux leakage signatures using wavelet basis function neural networks Kyungtae Hwang Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Electrical and Electronics Commons Recommended Citation Hwang, Kyungtae, "3-D defect profile reconstruction from magnetic flux leakage signatures using wavelet basis function neural networks " (2000). Retrospective Theses and Dissertations. 13907. https://lib.dr.iastate.edu/rtd/13907 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has t>een reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author dkl not send UMI a complete manuscript arxJ there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overiaps. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black arxl white photographic prints are available for any photographs or illustrations appearing in tills copy for an additional charge. Contact UMI directiy to order. Bell & Howell Informatton and Learning 300 North Zeeb Road. Ann Arbor, Ml 48106-1346 USA 800-521-0600 « 3-D defect profile reconstruction from magnetic flux leakage signatures using wavelet basis function neural networks by Kyungtae Hwang A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Electrical Engineering (Communications and Signal Processing) Major Professor: Satish S. Udpa Iowa State University Ames, Iowa 2000 Copyright @ Kyungtae Hwang, 2000. All rights reserved. UMI Number 9962823 UMI' UMI Microfomfi9962823 Copyright 2000 by Bell & Howell Infomnation and Leaming Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Leaming Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 ii Graduate College Iowa State University This is to certify that the Doctoral dissertation of Kyungtae Hwang has met the dissertation requirements of Iowa State University Signature was redacted for privacy. Committee Member Signature was redacted for privacy. ^ Committee Member Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Committee Member Signature was redacted for privacy. Major Professor Signature was redacted for privacy. Signature was redacted for privacy. For thf^jraduate College iii TABLE OF CONTENTS ACKNOWLEDGEMENTS xi ABSTRACT xii CHAPTER 1 INTRODUCTION 1 Inspection of Gas Pipeline 1 Defect Characterization 4 NDE and Neural Networks 5 Motivation 6 Objective 8 Dissertation Outline 9 CHAPTER 2 MAGNETIC FLUX LEAKAGE METHODS 10 CHAPTER 3 WAVELETS AND MULTIRESOLUTION DECOM­ POSITION 19 Wavelet Transform 19 Multiresolution Decomposition 22 CHAPTER 4 NEURAL NETWORKS 25 Introduction 25 Radial Basis Function Neural Networks 27 Wavelet Basis Function Neural Networks 32 iv CHAPTER 5 METHODS 38 Basis Functions 38 Training 39 Center 39 Support 43 Weights 43 Procedure 47 Neural Networks With A Priori Information 49 Approach 49 A Priori Information 51 CHAPTER 6 IMPLEMENTATION RESULTS 60 Simulation Data 60 Data Generation 60 Density Dependence 63 Noise Effect 63 Circumferential Component 66 Experimental Magnetic Flux Leakage Signatures 68 Data Preparation 68 Data Set I 70 Data Set II 85 Data Set III 86 CHAPTER? CONCLUSIONS Ill BIBLIOGRAPHY 112 LIST OF FIGURES Figure 1.1 Natural gas pipeline system in USA 1 Figure 1.2 Schematic diagram of a gas pipeline inspection system 2 Figure 1.3 MFL signal interpretation scheme 3 Figure 1.4 Screen shot of MFL interpretation software 7 Figure 1.5 Mapping from an MFL signal to a 3-D defect profile 7 Figure 2.1 Magnetic characterization of billet material (Modified from Ref. [24]). Figure 2.2 Magnetic characterization of billet material (Reproduced from Ref. [24]) 11 Figure 2.3 Leakage flux predictions obtained using Forster's model (Repro­ duced from Ref. [26]) 12 Figure 2.4 Leakage flux line with partial slot (Reproduced from Ref. [26]). 13 Figure 2.5 MFL signal on the experimental defect showing demagnetization. 14 Figure 2.6 Zatsepin and Shcherbinin model (Reproduced from Ref. [28]). 15 Figure 2.7 Leakage field profiles for various defects [29] 16 Figure 2.8 Leakage flux line with partial slot 18 Figure 3.1 Basis function resolution in the time-frequency plane 20 Figure 3.2 Several different families of wavelets 21 Figure 3.3 Function approximation using multiresolution analysis (IEEE Trans­ actions on Pattern Analysis and Machine Intelligence, Mallat, 1989) 23 vi Figure 4.1 Model of a neuron 26 Figure 4.2 Architecture of a radial basis function network 27 Figure 4.3 Architecture of a wavelet basis function neural network 33 Figure 4.4 Decomposition using a inultiresolution analysis 36 Figure 5.1 Basis functions for a wavelet basis function neural network. ... 40 Figure 5.2 Location of basis functions based on dyadic selection 42 Figure 5.3 Calculation of support 43 Figure 5.4 Parallel neural networks 46 Figure 5.5 The training procedure for a radial VVBF neural network 48 Figure 5.6 Overall scheme of a neural network with a priori information. 50 Figure 5.7 Architecture of a neural network with a bias 50 Figure 5.8 Particle in a force field 51 Figure 5.9 Boundary extraction on a natural corrosion 52 Figure 5.10 Distance calculation between two saddle points 53 Figure 5.11 Boundary representation 54 Figure 5.12 Polygonal boundary. 55 Figure 5.13 Effect of Fourier descriptors by moving an origin 56 Figure 5.14 Normalized central moments 59 Figure 6.1 Geometry of the defect profile used in the simulation study. ... 61 Figure 6.2 Typical MFL signal generated by a FEM model 62 Figure 6.3 Effect of increasing the number of resolutions on the prediction results. Figure shows upside-down view of the defect for clarity.. 64 Figure 6.4 Comparison of squared error obtained between dense and sparse data sets 65 Figure 6.5 Squared error obtained when a noisy data set is used as input. 66 vii Figure 6.6 Squared error obtained when both axial and circumferential com­ ponents are employed compared to result obtained using a single component only with (a) 2 resolutions and (b) 3 resolutions. 67 Figure 6.7 Photograph of a typical machined defect 68 Figure 6.8 (a) Geometry of a defect profile used in the analysis, (b) Typical defect profile after zero padding 69 Figure 6.9 Typical signals contained in data set I and II. Signals are obtained from a 3" x 3" x 50% deep x 45° angle defect 71 Figure 6.10 Typical signals contained in data set II and III. Signals are ob­ tained from a 6" x 1" x 20% deep x 45° angle defect 72 Figure 6.11 Differences between training and test signals 74 Figure 6.12 Squared errors obtained as a function of number of resolutions for each defect type 75 Figure 6.13 Effect of pruning centers 75 Figure 6.14 Effect of changing the number of resolutions for a 50% deep, 3" X 3", 45° angle defect profile (true: —, predicted: —) 77 Figure 6.15 Effect of changing the number of resolutions for a 50% deep, 6" X 1", 23° angle defect profile (true: —, predicted: —) 78 Figure 6.16 Effect of changing the number of resolutions for a 50% deep, 6" X 3", 23° angle defect profile (true: —, predicted: —) 79 6.17 Three dimensional cutaway view of true and predicted defect profiles for a 50% deep, 3" x 3", 45° angle defect 80 6.18 Three dimensional cutaway view of true and predicted defect profiles for a 50% deep, 6" x 1", 23° angle defect 81 6.19 Three dimensional cutaway view of true and predicted defect profilesfor a 50% deep, 6" x 3", 23° angle defect 82 Figure 6.20 Boundary extracted from 2-D MFL images 84 viii Figure 6.21 Boundaxj' extracted from 2-D edge images 88 Figure 6.22 Boundaries extracted from edge images 89 Figure 6.23 Comparison of true vs. actual depth estimates obtained with training (o) and test data (*) 89 Figure 6.24 Performance improvement obtained when a length is employed as a priori information. (Positive value implies the error obtained without using a prion information is greater than the error ob­ tained when a priori information is used.) 90 Figure 6.25 Effect of a priori information on prediction results for a 50% deep, 6" x 3" defect profile (true: —. predicted: —) 91 Figure 6.26 Effect of a priori information on prediction results for a 50% deep, 6" x 1" defect profile (true; —, predicted: —) 92 Figure 6.27 Effect on preprocessing on the signal 93 Figure 6.28 Data distribution of 50% deep defects 95 Figure 6.29 Estimation of length by measuring the distance between two lower saddle points 96 Figure 6.30 Performance improvement obtained when a length is employed as a priori information.
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