A nonlinear Kernel-based adaptive learning-by-examples method for robust NDT/NDE of conductive tubes

ABSTRACT

In this work, the real-time non-destructive testing and evaluation (NDT/NDE) of faulty conductive tubes from eddy current (EC) measurements is addressed and solved in a computationally efficient way by means of an innovative learning-by-examples (LBE) methodology. More specifically, the estimation of the descriptors of a defect embedded within the cylindrical structure under test (SUT) is yielded by combining a non-linear feature extraction technique with an adaptive sampling strategy able to uniformly explore the arising feature space. Predictions are then performed during the on-line testing phase by means of a support vector regression (SVR). Representative results from a numerical/experimental validation are reported to assess the effectiveness of the proposed approach also in comparison with competitive state-of-the-art approaches.

KEYWORDS:

• Non-destructive testing and evaluation
• inverse problems
• inverse scattering
• Eddy currents
• learning-by-examples techniques
• Kernel orthogonal partial least squares
• output space filling
• support vector regression
• conductive tubes

Acknowledgments

A. Massa wishes to thank E. Vico for her never-ending support and help.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 KOPLS is the Kernel version of the orthogonal PLS (OPLS), an improved version of the original PLS providing optimal performances in multi-linear regression and higher compression ratios of the original input variables [41,42,47].

2 It is worth remarking that the $2K$ EC measured features are represented by the real and imaginary parts of the coil impedance variation collected at K scanning locations ${\mathbf{r}}_k\in V_1$, $k=1,\dots ,K$.

3 It should be observed that both feature extraction and predictor exploited in the proposed LBE methodology are based on the Kernel trick to properly cope with the non-linearity of the underlying I/O relationship.

4 It should be pointed out that ${\underset{\_}{\underset{\_}{T}}}_0$ is the only term in (10(10) ${\underset{\_}{\underset{\_}{\mathrm{\Psi }}}}_0={\underset{\_}{\underset{\_}{T}}}_0{\underset{\_}{\underset{\_}{S}}}_0+{\underset{\_}{\underset{\_}{\mathcal{T}}}}_0{\underset{\_}{\underset{\_}{\mathcal{S}}}}_0+{\underset{\_}{\underset{\_}{O}}}_0$(10) ) actually needed for the successive steps, since it contains the extracted features used to compute ${\tilde{\mathrm{\Phi }}}^{-1}\{\cdot \}$. For such a reason, only the part of the KOPLS algorithm devoted at the computation of such a matrix is kept in this work.

5 The presence of the measurement noise has been modeled by adding to the synthetically-generated EC data an additive white Gaussian noise with signal-to-noise ratio (SNRs) defined as in [34].

6 Since the defect is modeled as a volumetric region Ω made of air, its complex permittivity is approximated to ${\epsilon }_c\left(\mathbf{r}\right)\approx 0$.

7 It is worth noticing that, even though the orthogonal features do not carry – by definition – information on the SUT, the choice of their number, A, influences the computation of the J predictive features (see Appendix 3) and it must be calibrated for an effective and reliable application of the whole KOPLS-OSF/SVR.

8 Please notice that the number of predictive features belongs to the range $1\le J\le Q$ (see Appendix 3).

Additional information

Funding

This work has been partially supported by the Italian Ministry of Foreign Affairs and International Cooperation, Directorate General for Cultural and Economic Promotion and Innovation within the SNATCH Project (2017–2019) and by the Italian Ministry of Education, University, and Research within the Program “Smart cities and communities and Social Innovation” (CUP: E44G14000060008) for the Project “WATERTECH – Smart Community per lo Sviluppo e l'Applicazione di Tecnologie di Monitoraggio Innovative per le Reti di Distribuzione Idrica negli usi idropotabili ed agricoli” (Grant no. SCN_00489). Moreover, it benefited from the networking activities carried out within the SIRENA project (2014–2017) funded by DIGITEO (France) under the Call for Chairs 2014; Universidad Carlos III de Madrid Càtedra de Excelencia UC3M-Santander.

Notes on contributors

Marco Salucci

Marco Salucci received the MS degree in Telecommunication Engineering from the University of Trento, Italy, in 2011, and the PhD degree from the International Doctoral School in Information and Communication Technology, Trento in 2014. From December 2014 to November 2016, he was a Post Doc Researcher at CentraleSupélec, in Gif-sur-Yvette, France. From December 2016 to September 2017 he was a Post Doc Researcher at the Commissariat à l'énergie atomique et aux énergies alternatives (CEA), in Gif-sur-Yvette, France. He is currently a Researcher at the Department of Information Engineering and Computer Science (DISI) at the University of Trento, Italy, and a member of the ELEDIA Research Center. Dr Salucci is a Member of the IEEE Antennas and Propagation Society and he was a Member of the COST Action TU1208 “Civil Engineering Applications of Ground Penetrating Radar”. He serves as a reviewer for different international journals including IEEE Transactions on Antennas and Propagation, IEEE Antennas and Wireless Propagation Letters, IEEE Journal on Multiscale and Multiphysics Computational Techniques, and IET Microwaves, Antennas & Propagation. His research activities are mainly concerned with inverse scattering, GPR microwave imaging techniques, antenna synthesis, and computational electromagnetics with focus on System-by-Design methodologies integrating optimization techniques and Learning-by-Example methods for real-world applications.

Nicola Anselmi

Nicola Anselmi received the Master's Degree in Telecommunication Engineering from the University of Trento, Italy, in 2012, and the PhD degree from the International Doctoral School in Information and Communication Technology, Trento, Italy, in 2018. From 2012 he is a member of the ELEDIA Research Center and from 2014 of the IEEE Antennas and Propagation Society, serving as a reviewer for different international journals including IEEE Transactions on Antennas and Propagation, IEEE Antennas and Wireless Propagation Letters, and IET on Microwaves, Antennas & Propagation. In 2016 Dr Anselmi has been the recipient of the “Giorgio Barzilai” award for Young Researchers by the Italian Electromagnetic Society (SIEM). His research activities are mainly focused on synthesis methods for unconventional antenna array architectures, tolerance analysis of antenna systems, and electromagnetic inverse scattering techniques, with interest on compressive sensing methodologies for microwave imaging applications.

Giacomo Oliveri

Giacomo Oliveri received the BS and MS degrees in Telecommunications Engineering and the PhD degree in Space Sciences and Engineering from the University of Genoa, Italy, in 2003, 2005, and 2009, respectively. He is currently an Associate Professor at the Department of Information Engineering and Computer Science (University of Trento) and a member of the ELEDIA Research Center. Moreover, he is Adjunct Professor at CentraleSupélec and member of the Laboratoire des signaux et systèmes (L2S)@CentraleSupèlec Gif-sur-Yvette (France). He has been a visiting researcher at L2S in 2012, 2013, and 2015, and he has been an Invited Associate Professor at the University of Paris Sud, France, in 2014. He is author/co-author of over 330 peer-reviewed papers on international journals and conferences. His research work is mainly focused on electromagnetic direct and inverse problems, system-by-design and metamaterials, and antenna array synthesis. Prof. Oliveri serves as an Associate Editor of the IEEE Antennas and Wireless Propagation Letters, the IEEE Journal on Multiscale and Multiphysics Computational Techniques, the International Journal of Antennas and Propagation, the International Journal of Distributed Sensor Networks, and the Microwave Processing journal. He is a Senior Member of the IEEE, and the Chair of the IEEE AP/ED/MTT North Italy Chapter.

Paolo Rocca

Paolo Rocca received the MS degree in Telecommunications Engineering from the University of Trento in 2005 (summa cum laude) and the PhD degree in Information and Communication Technologies from the same University in 2008. He is currently Associate Professor at the Department of Information Engineering and Computer Science (University of Trento) and a member of the ELEDIA Research Center. In April 2017, Prof. Rocca received the National Scientific Qualification for the position of Full Professor. Prof. Rocca is the author/co-author of over 300 peer-reviewed papers on international journals and conferences. He has been a visiting PhD student at the Pennsylvania State University (USA), at the University Mediterranea of Reggio Calabria (Italy), and a visiting researcher at the Laboratoire des Signaux et Systèmes (L2S@ Supèlec, France) in 2012 and 2013. Moreover, he has been an Invited Professor at the University of Paris Sud (France) in 2015 and at the University of Rennes 1 (France) in 2017. Prof. Rocca has been awarded from the IEEE Geoscience and Remote Sensing Society and the Italy Section with the best PhD thesis award IEEE-GRS Central Italy Chapter. His main interests are in the framework of artificial intelligence (optimization and machine learning) techniques as applied to electromagnetics, antenna array synthesis and design, and electromagnetic inverse scattering. He served as an Associate Editor of the IEEE Antennas and Wireless Propagation Letters in the period 2011–2016.

Pierre Calmon

Pierre Calmon received the PhD degree in physics from the University of Paris-Sud, Orsay, France, in 1990. He joined the Non Destructive Evaluation Department, French Atomic Energy Commission (CEA) and worked on ultrasonic modeling and array imaging. From 2000 to 2005, he was involved in and coordinated the development of the CIVA NDT simulation and expertise platform. Since 2008, he has been a Research Director with the Non Destructive Evaluation Department, responsible for the core research in nondestructive evaluation. His current main topics of interest concern simulation and its use for enhanced diagnosis and reliability of nondestructive evaluation.

Roberto Miorelli

Roberto Miorelli received the MS degree in telecommunication engineering from the University of Trento, Trento, Italy, in 2008 and the PhD degree in physics from the University of Paris-Sud, Orsay, France, in 2012. Since 2012, he has been a Researcher in electromagnetic modeling with the Non Destructive Testing Department, CEA LIST Institute, Gif-sur-Yvette, France. His research interests include electromagnetics theory and modeling with an emphasis on fast forward solutions to electromagnetic problems via Green function integral-equation-based methods in inhomogeneous media. His professional interests are devoted to electromagnetic nondestructive testing and evaluation problems mainly at the low-frequency regime. Apart from the modeling of forward problems, his research is focused on database and metamodel generation targeting almost real-time inversion procedures and statistical studies.

Christophe Reboud

Christophe Reboud received the degree in mechanical engineering from École Centrale de Nantes, Nantes, France, in 2003 and the PhD degree in electrical engineering from the University of Paris-Sud, Orsay, France, in 2006. Since 2012, he has been the Head of the Electromagnetic Modeling Laboratory, Non Destructive Testing Department, CEA LIST Institute, Gif-surYvette, France. He then joined CEA and worked as a Research Engineer, specializing in low-frequency electromagnetic modeling for nondestructive testing applications. His research interests are focused on simulation tools for electromagnetic and X-ray nondestructive testing applications, inverse problems, and statistical tools. Dr Reboud is part of the scientific committee of the International Workshop on Electromagnetic Nondestructive Evaluation and of the COFREND association.

Andrea Massa

Andrea Massa (IEEE Fellow, IET Fellow, Electromagnetic Academy Fellow) received the “laurea” degree in Electronic Engineering from the University of Genoa, Genoa, Italy, in 1992 and PhD degree in EECS from the same university in 1996. From 1997 to 1999, he was an Assistant Professor of Electromagnetic Fields at the Department of Biophysical and Electronic Engineering (University of Genoa). From 2001 to 2004, he was an Associate Professor at the University of Trento. Since 2005, he has been a Full Professor of Electromagnetic Fields at the University of Trento, where he currently teaches electromagnetic fields, inverse scattering techniques, antennas and wireless communications, wireless services and devices, and optimization techniques. At present, Prof. Massa is the director of the network of federated laboratories “ELEDIA Research Center” [ELEDIA@UTB in Bandar Seri Begawan (Brunei), ELEDIA@UniCAS in Cassino (Italy), ELEDIA@UESTC in Chengdu (China), ELEDIA@USIL in Lima (Perù), ELEDIA@UniNAGA in Nagasaki (Japan), ELEDIA@L2S in Paris (France), ELEDIA@CTU in Prague (Czech), ELEDIA@AUTH in Tessaloniki (Greece), ELEDIA@UniTN in Trento (Italy), ELEDIA@TSINGHUA in Beijing (China), ELEDIA@Innov'COM in Tunis (Tunisia)]. Moreover, he is Adjunct Professor at Penn State University (USA), Professor at CentraleSupélec (Paris - France), Guest Professor at UESCT (Chengdu - China), and UC3M-Santander Chair of Excellence at the Universidad Carlos III de Madrid (Madrid - Spain). He has been holder of a Senior DIGITEO Chair at L2SCentraleSupélec and CEA LIST in Saclay (France), Visiting Professor at the Missouri University of Science and Technology (USA), the Nagasaki University (Japan), the University of Paris Sud (France), the Kumamoto University (Japan), and the National University of Singapore (Singapore). He has been appointed IEEE AP-S Distinguished Lecturer (2016–2018). Prof. Massa serves as Associate Editor of the IEEE Transaction on Antennas and Propagation and Associate Editor of the International Journal of Microwave and Wireless Technologies and he is member of the Editorial Board of the Journal of Electromagnetic Waves and Applications, a permanent member of the “PIERS Technical Committee” and of the “EuMW Technical Committee”, and a ESoA member. He has been appointed in the Scientific Board of the “Società Italiana di Elettromagnetismo (SIEm)” and elected in the Scientific Board of the Interuniversity National Center for Telecommunications (CNIT). He has been appointed in 2011 by the National Agency for the Evaluation of the University System and National Research (ANVUR) as a member of the Recognized Expert Evaluation Group (Area 09, ‘Industrial and Information Engineering’) for the evaluation of the researches at the Italian University and Research Center for the period 2004–2010. Furthermore, he has been elected as the Italian Member of the Management Committee of the COST Action TU1208 “Civil Engineering Applications of Ground Penetrating Radar”. His research activities are mainly concerned with inverse problems, analysis/synthesis of antenna systems and large arrays, radar systems synthesis and signal processing, cross-layer optimization and planning of wireless/RF systems, semantic wireless technologies, system-by-design and material-by-design (metamaterials and reconfigurable-materials), and theory/applications of optimization techniques to engineering problems (tele-communications, medicine, and biology). Prof. Massa published more than 700 scientific publications (partial list available at: http://eledia.science.unitn.it/index.php/ricerca/pubblicazioni) among which about 300 on international journals and more than 450 in international conferences where he presented more than 150 invited contributions. He has organized more than 70 scientific sessions in international conferences and has participated to several technological projects in the European framework (20 EU Projects) as well as at the national and local levels with national agencies (more than 150 Projects/Grants).