Smart aeronautical structures: development and experimental validation of a structural health monitoring system for damage detection

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(1)UNIVERSIDAD POLITÉCNICA DE MADRID school of aerospace engineering. DOCTORAL THESIS. S M A RT A E R O N A U T I C A L S T R U C T U R E S : D E V E L O P M E N T A N D E X P E R I M E N TA L VA L I D AT I O N O F A S T R U C T U R A L H E A LT H M O N I T O R I N G SYSTEM FOR DAMAGE DETECTION.. by JULIÁN SIERRA-PÉREZ mechanical engineer (m.sc-ing.). January 2014.

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(3) S M A RT A E R O N A U T I C A L S T R U C T U R E S : D E V E L O P M E N T A N D E X P E R I M E N TA L VA L I D AT I O N O F A S T R U C T U R A L H E A LT H MONITORING SYSTEM FOR DAMAGE DETECTION. by julián sierra-pérez. supervised by professor dr. alfredo güemes dr. luis e. mujica. Department of Aerospace Materials and Production School of Aerospace Engineering Universidad Politécnica de Madrid. January 2014.

(4) Julián Sierra-Pérez : SMART AERONAUTICAL STRUCTURES: Development and Experimental Validation of a Structural Health Monitoring System for Damage Detection. © January 2014.

(5) To my beloved wife..

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(7) ABSTRACT. In many engineering fields, the integrity and reliability of the structures are extremely important aspects. They are controlled by the adequate knowledge of existing damages. Typically, achieving the level of knowledge necessary to characterize the structural integrity involves the usage of nondestructive testing techniques. These are often expensive and time consuming. Nowadays, many industries look to increase the reliability of the structures used. By using leading edge techniques it is possible to monitoring these structures and in some cases, detect incipient damage that could trigger catastrophic failures. Unfortunately, as the complexity of the structures, components and systems increases, the risk of damages and failures also increases. At the same time, the detection of such failures and defects becomes more difficult. In recent years, the aerospace industry has done great efforts to integrate the sensors within the structures and, to develop algorithms for determining the structural integrity in real time. The ‘philosophy’ has being called “Structural Health Monitoring” and these structures have been called “smart structures”. These new types of structures integrate materials, sensors, actuators and algorithms to detect, quantify and locate damage within itself. A novel methodology for damage detection in structures is proposed. The methodology is based on strain measurements and consists in the development of strain field pattern recognition techniques. The aforementioned are based on PCA (Principal Component Analysis) and other dimensional reduction techniques. The use of fiber Bragg gratings and distributed sensing as strain sensors is proposed. The methodology have been validated by using laboratory scale tests and real scale tests with complex structures. The effects of the variable load conditions were studied and several experiments were performed for static and dynamic load conditions, demonstrating that the methodology is robust under unknown load conditions.. RESUMEN. En muchas áreas de la ingeniería, la integridad y confiabilidad de las estructuras son aspectos de extrema importancia. Estos son controlados mediante el adecuado conocimiento de danos existentes. Típicamente, alcanzar el nivel de conocimiento necesario que permita caracterizar la integridad estructural implica el uso de técnicas de ensayos no destructivos. Estas técnicas son a menudo costosas y consumen mucho tiempo. En la actualidad, muchas industrias buscan incrementar la confiabilidad de las estructuras que emplean. Mediante el uso de técnicas de última tecnología es posible monitorizar las estructuras y en algunos casos, es factible detectar daños incipientes que pueden desencadenar en fallos catastróficos. Desafortunadamente, a medida que la complejidad de las estructuras, los componentes y sistemas incrementa, el riesgo de la aparición de daños y fallas también incrementa. Al mismo tiempo, la detección de dichas fallas y defectos se torna más compleja. En años recientes, la industria aeroespacial ha realizado grandes esfuerzos para integrar los sensores dentro de las estructuras, además de desarrollar algoritmos que permitan determinar la integridad estructural en tiempo real. Esta filosofía ha sido llamada “Structural Health Monitoring” (o “Monitorización de Salud Estructural” en español) y este tipo de estructuras han recibido el nombre de “Smart Structures” (o “Estructuras Inteligentes” en español). Este nuevo tipo de estruc-. vii.

(8) turas integran materiales, sensores, actuadores y algoritmos para detectar, cuantificar y localizar daños dentro de ellas mismas. Una novedosa metodología para detección de daños en estructuras se propone en este trabajo. La metodología está basada en mediciones de deformación y consiste en desarrollar técnicas de reconocimiento de patrones en el campo de deformaciones. Estas últimas, basadas en PCA (Análisis de Componentes Principales) y otras técnicas de reducción dimensional. Se propone el uso de Redes de difracción de Bragg y medidas distribuidas como sensores de deformación. La metodología se validó mediante pruebas a escala de laboratorio y pruebas a escala real con estructuras complejas. Los efectos de las condiciones de carga variables fueron estudiados y diversos experimentos fueron realizados para condiciones de carga estáticas y dinámicas, demostrando que la metodología es robusta ante condiciones de carga desconocidas.. viii.

(9) P U B L I C AT I O N S. Some ideas and figures have appeared previously in the following publications:. book chapters • A Güemes and J Sierra. New Trends in Structural Health Monitoring, chapter Fiber Optic Sensors, pages 265–316. Springer, 2013. conferences • J Sierra and A Güemes. Detección de daño en materiales compuestos mediante fibra óptica (in spanish). In Actas del IX Congreso Nacional de Materiales Compuestos (in spanish), pages 631–636. Girona, Spain, 2011 • A Güemes, J Sierra, J Rodellar and L Mujica. A robust procedure for Damage detection from strain measurements based on Principal Component Analysis. In 4th Asia-PAcific Workshop on Structural Health Monitoring. Melbourne, Australia, 2012 • J Sierra and A Güemes. Damage detection at an aluminum beam from discrete and continuous strain measurements. In 9th Intenation Workshop on Structural Health Monitoring. Stanford, United States of America, 2013 • J. Sierra, A Güemes, and M Gómez. Sensibilidad de las variaciones en el campo de deformaciones en función de la aparición de daños en palas de aerogeneradores fabricadas en materiales compuestos. In X Congreso Nacional de Materiales Compuestos MATCOM 13. Algeciras, Spain, 2013 • J. Sierra and A Güemes. Damage detection in aerostructures from strain mesurements. In 8th International Aerospace Supply Fair AIRTEC 2013. Frankfurt, Germany, 2013. • J Sierra, A Güemes, E del Olmo and J Pintado. A robust procedure for damage identification in a lattice spacecraft structural element by mean of strain field pattern recognition techniques. In 16th European Conference on Composite Materials. Sevilla, Spain, 2014 • J Sierra, A Güemes and M Gómez. Strain measurements and damage detection in large composite structures by fiber optics sensors. In 16th European Conference on Composite Materials. Sevilla, Spain, 2014 • J Sierra, M-A Torres, G Cabanes, A Güemes, L Mujica and C-P Fritzen. Damage detection in metallic beams from dynamic strain measurements under different load cases by using automatic clustering and pattern recognition techniques. In 7th European Workshop on Structural Health Monitoring. Nante, France, 2014 • J Sierra, M-A Torres, A Güemes, L Mujica and C-P Fritzen. Structural health monitoring of wind turbine blades from distributed strain measurements. In 6th World Conference on Structural Control and Monitoring. Barcelona, Spain, 2014. ix.

(10) • M-A Torres, J Sierra, G Cabanes, A Güemes and C-P Fritzen. A pattern recognition approach for damage detection and temperature compensation in acousto-ultrasonics. In 7th European Workshop on Structural Health Monitoring. Nante, France, 2014 • M-A Torres, J Sierra, J Rodellar and C-P Fritzen. A robust multivariate data-driven modelling approach for damage detection under variable temperature conditions. In 6th World Conference on Structural Control and Monitoring. Barcelona, Spain, 2014 journal papers • J Sierra, A Güemes, and L Mujica. Damage detection by using FBGs and strain field pattern recognition techniques. Smart Materials and Structures, 22:25011–25020, 2013 • A Güemes, J Sierra, J Rodellar, and L Mujica. A robust procedure for damage detection from strain measurements based on principal component analysis. Key Engineering Materials, 558:128–138, 2013. • J Sierra and A Güemes. Damage detection in aerostructures from strain measurements. Aircraft Engineering and Aerospace Technology, 2013 • J Sierra, A Güemes, L Mujica, and M Ruiz. Damage detection in composite materials structures under variable loads conditions by using fiber Bragg gratings and principal component analysis, involving new unfolding and scaling methods. Intelligent Materials Systems and Structures, 2013. x.

(11) Don´t only practice your art, but force your way into its secrets, for it and knowledge can raise men to the divine. — Ludwig van Beethoven. ACKNOWLEDGMENTS. I want to specially express my gratitude to my parents Gloria and Horacio, and to my wife Tatiana for their support, love, encouragement and motivating attitude. Thanks for their patient and understanding during the difficult moments. I have many more things to be thankful for, than I can express in a few lines. I owe them much more that I ever could thank. Without them, it would have been impossible to move forward. Special thanks to Professor Alfredo Güemes from Universidad Politécnica de Madrid for welcoming me in his research group and for his invaluable support, thanks for his wise advices and guidance. Thanks to the nice people in Madrid who helped me and offered me their experience and friendship. Thanks to Professor Luis Mujica from Universtitat Politècnica de Catalunya for his inestimable contributions and teachings. Thanks to Prof. Dr.-Ing. Claus-Peter Fritzen from Universität Siegen for welcoming me in his research group, where, I want to specially thank Dr.-Ing. Miguel Torres for his advice, contributions, help and friendship. Thanks to Professor Guénaël Cabanes from Université Paris-Nord for share with me his work on two-level clustering methods. Thanks to Mrs. Chantal Roldan, Mrs. Mercedes Gómez and Mr. Miguel Murillo from INDRA for their support, help and humanity. Thanks to Dr. Encarna del Olmo from EADS CASA Espacio and to Dr. Malte Frövel from INTA, for share with me experimental results and information for support part of this work.. xi.

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(13) CONTENTS. i introduction 1 introduction 1.1 OUTLINE . . . . . . . . . . . . . 1.2 MOTIVATION . . . . . . . . . . 1.3 OBJECTIVES OF THIS THESIS 1.4 CONTRIBUTIONS . . . . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. ii theoretical background and state of the art 2 structural health monitoring (shm) 2.1 SMART structures . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 An SHM overview . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 SHM in practice . . . . . . . . . . . . . . . . . . . . . . . . . . 3 fiber optic sensors 3.1 Introduction to Fiber Optic Sensors . . . . . . . . . . . . . . . 3.2 Fiber Optic Sensors overview . . . . . . . . . . . . . . . . . . 3.3 Fiber Bragg Gratings (FBGs) . . . . . . . . . . . . . . . . . . . 3.3.1 FBGs manufacturing . . . . . . . . . . . . . . . . . . . . 3.3.2 Mechanical effects . . . . . . . . . . . . . . . . . . . . . 3.3.3 Thermal effects . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Combined effects (mechanical and thermal) . . . . . . 3.3.5 Temperature compensation . . . . . . . . . . . . . . . 3.3.6 Other effects (local strain gradients) . . . . . . . . . . . 3.4 Distributed sensing . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Optical Backscatter Reflectometer (OBR) . . . . . . . . 3.5 Review of FOS-Based Techniques in SHM . . . . . . . . . . . 4 strain field 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Strain theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Strain concentration in the near and far field . . . . . . . . . 4.4 Strain-based damage detection: differential strains . . . . . . 4.5 Review of Strain-Based Techniques in SHM . . . . . . . . . . 5 pattern recognition techniques used in shm 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Artificial Neural Networks (ANN) . . . . . . . . . . . . . . . 5.2.1 Supervised ANN . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Unsupervised ANN . . . . . . . . . . . . . . . . . . . . 5.3 Principal Component Analysis (PCA) . . . . . . . . . . . . . . 5.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Unfolding methods . . . . . . . . . . . . . . . . . . . . 5.3.3 Standardization methods . . . . . . . . . . . . . . . . . 5.3.4 Damage detection indices and thresholds for PCA . . 5.4 Nonlinear Principal Component Analysis (NLPCA) . . . . . 5.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Damage detection indices and thresholds for NLPCA 5.4.3 Non-linearity test for PCA models . . . . . . . . . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . .. 1 3 4 5 5 6 9 11 11 12 14 17 17 18 20 21 21 22 22 22 23 24 25 27 31 31 32 35 36 38 39 39 41 42 44 45 45 50 52 54 58 58 62 65. xiii.

(14) xiv. contents. 5.5 Classification and clustering techniques . . . . . . . . . . 5.5.1 Self-Organizing Maps (SOM) . . . . . . . . . . . . . 5.5.2 Two-Level Clustering methods . . . . . . . . . . . 5.6 Review of Pattern Recognition-Based Techniques in SHM. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. iii damage detection methodology 6 system for monitoring and detection of defects 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Stage 1 (G1): Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Acquisition equipment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Sensors network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 Selection of sensors location in the structure. . . . . . . . . . . . . . . . . 6.2.5 Installation of sensor network into the structure. . . . . . . . . . . . . . . 6.2.6 Experiment design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.7 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Stage 2 (G2): Preclassification and clustering. Optimal Baseline Selection (OBS) 6.3.1 Classification and clustering according to operational variables . . . . . 6.3.2 Classification and clustering with automatic techniques . . . . . . . . . . 6.4 Stage 3 (G3): Unfolding and standardization . . . . . . . . . . . . . . . . . . . . 6.4.1 Multi-load unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Scaling for multi-load unfolding. . . . . . . . . . . . . . . . . . . . . . . . 6.5 Stage 4 (G4): PCA implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Stage 5 (G5): Damage indices and thresholds . . . . . . . . . . . . . . . . . . . . 6.7 Stage 6 (G6): Decision: normality or abnormality . . . . . . . . . . . . . . . . . . iv experimental validation 7 experimental validation 7.1 Unmanned Air Vehicle (UAV) wing section made in composite materials . . 7.2 Lattice spacecraft structural element made of composite materials . . . . . 7.3 Wind turbine blade made of composite materials . . . . . . . . . . . . . . . . 7.3.1 Prototype manufacturing and sensors integration . . . . . . . . . . . 7.3.2 Preliminary prototype testing . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Final prototype testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Aluminum beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Static tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.2 Dynamic tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 results 8.1 Unmanned Air Vehicle (UAV) wing section made of composite materials . . 8.1.1 PCA results for wing section . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 h-NLPCA results for wing section . . . . . . . . . . . . . . . . . . . . . 8.2 Lattice spacecraft structural element made of composite materials (isogrid) 8.2.1 PCA results for isogrid . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 h-NLPCA for isogrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Wind turbine blade made of composite materials . . . . . . . . . . . . . . . . 8.3.1 Preliminary blade prototype testing, PCA results . . . . . . . . . . . . 8.3.2 Preliminary blade prototype testing, h-NLPCA results . . . . . . . . . 8.3.3 Final blade prototype testing with FBGs, PCA results . . . . . . . . . 8.3.4 Final blade prototype testing with FBGs, h-NLPCA results . . . . . . 8.3.5 Final blade prototype testing with OBR, PCA results . . . . . . . . . .. . . . .. . . . . . . . . . . . . . . . . . .. . . . .. . . . . . . . . . . . . . . . . . .. . . . .. . . . . . . . . . . . . . . . . . .. . . . .. 65 65 68 72. . . . . . . . . . . . . . . . . . .. 77 79 79 79 79 81 82 82 84 84 84 87 90 90 91 93 94 95 96 96. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. . . . . . . . . . . . .. 99 101 101 104 107 108 112 115 119 123 123 127 127 127 130 132 133 135 137 137 139 140 143 144.

(15) contents. 8.3.6 Final blade prototype testing with OBR, h-NLPCA results 8.4 Aluminum beam: manual pre-classification . . . . . . . . . . . . 8.4.1 Static tests with FBGs . . . . . . . . . . . . . . . . . . . . . 8.4.2 Static tests with OBR . . . . . . . . . . . . . . . . . . . . . 8.4.3 Dynamic tests with FBGs . . . . . . . . . . . . . . . . . . . 8.5 Aluminum beam: automatic clustering and classification . . . . 8.5.1 Static tests with FBGs . . . . . . . . . . . . . . . . . . . . . 8.5.2 Dynamic tests with FBGs . . . . . . . . . . . . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. 149 150 152 154 157 161 161 166. v conclusions 9 conclusions, recommendations and future work. 173 175. vi appendix a extended experimental results a.1 Aluminum beam experiment. Static tests with FBGs, PCA . . . a.1.1 Load case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.1.2 Load case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.1.3 Load case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.1.4 Load case 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.1.5 Load case 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.1.6 Load case 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.1.7 Load case 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.1.8 Load case 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.2 Aluminum beam experiment. Static tests with FBGs, h-NLPCA a.2.1 Load case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.2.2 Load case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.2.3 Load case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.2.4 Load case 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.2.5 Load case 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.2.6 Load case 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.2.7 Load case 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.2.8 Load case 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.3 Aluminum beam experiment. Static test with OBR, PCA . . . . a.3.1 Load case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.3.2 Load case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.3.3 Load case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.3.4 Load case 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.3.5 Load case 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.3.6 Load case 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.3.7 Load case 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.3.8 Load case 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.4 Aluminum beam experiment. Static test with OBR, h-NLPCA . a.4.1 Load case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.4.2 Load case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.4.3 Load case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.4.4 Load case 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.4.5 Load case 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.4.6 Load case 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.4.7 Load case 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . a.4.8 Load case 9 . . . . . . . . . . . . . . . . . . . . . . . . . . .. 181 183 183 183 184 185 186 187 188 189 190 191 191 192 192 193 194 194 195 196 196 196 197 198 199 200 201 202 203 204 204 205 206 206 207 208 208 209. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xv.

(16) xvi. contents. a.5 Aluminum beam experiment. Dynamic tests, PCA . . . . . . . . . . . . . . . a.5.1 Load case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.5.2 Load case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.5.3 Load case 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.5.4 Load case 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.5.5 Load case 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.6 Aluminum beam experiment. Dynamic tests, h-NLPCA . . . . . . . . . . . a.6.1 Load case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.6.2 Load case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.6.3 Load case 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.6.4 Load case 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.6.5 Load case 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.7 Automatic clustering and classification. Static tests, PCA and h-NLPCA . . a.7.1 Cluster 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.7.2 Cluster 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.7.3 Cluster 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.7.4 Cluster 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.7.5 Cluster 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.8 Automatic clustering and classification. Dynamic tests, PCA and h-NLPCA a.8.1 Cluster 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.8.2 Cluster 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a.8.3 Cluster 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . bibliography. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. 210 210 211 212 213 214 215 215 215 216 217 217 218 218 219 221 222 223 225 225 226 227 229.

(17) LIST OF FIGURES. Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9. Figure 10. Figure 11. Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19. Figure 20. Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27. Taxonomy of principal dimensional reduction techniques. . . . . . . . . . . . . 15 Taxonomy of principal classification techniques. . . . . . . . . . . . . . . . . . 16 Schematic representation of an optical fiber. . . . . . . . . . . . . . . . . . . . . 17 General scheme of FOS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Fiber Bragg Gratings operating principle scheme. . . . . . . . . . . . . . . . . . 20 Temperature sensor based on FBG. . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Wavelengths of the backscattered radiation. . . . . . . . . . . . . . . . . . . . . 25 Basic OFDR network layout. [Soller et al., 2005a] . . . . . . . . . . . . . . . . . 26 a) Wavelength spectra along a 5 mm fiber optic piece for a heated (solid line) and unheated (dashed line) measurements. b) Cross-correlation of the heated with baseline spectra. [Kreger et al., 2006] . . . . . . . . . . . . . . . . . . . . . 27 Photoelastic imaging of a hole in a polycarbonate plate under axial tension. Example of strain/stress field. [Photograph: University of Pennsylvania. Sophomore Design Lab. http://medesign.seas.upenn.edu/index.php/Main/HomeHistory. 10 Oct. 2013.] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Example of Saint-Venant‘s principle. Stress distribution in different cross sections of a bar, caused by three different force systems with the same resultant. [da Silva, 2005] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Example of differential strains for two neighboring sensors for a healthy condition (square and round markers) and six different damages. . . . . . . . . . 37 Feature extraction and data condensation for raw data. [Sohn and Oh, 2009] . 41 Scheme of supervised learning for an ANN. . . . . . . . . . . . . . . . . . . . . 42 Scheme of a simplified MLP ANN. [Reed, 2009] . . . . . . . . . . . . . . . . . . 43 Scheme of a RBF ANN. [Reed, 2009] . . . . . . . . . . . . . . . . . . . . . . . . . 44 AANN with one hidden neuron and a linear activation function. . . . . . . . . 45 Different way of unfolding tridimensional data arrays. . . . . . . . . . . . . . . 51 Network layout for NLPCA. σ represents the sigmoid transfer functions and l represents linear transfer functions (or nonlinear functions if desired). Each layer has a hidden bias node. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Linear PCA model vs. NLPCA model. Real example of the strain vs. strain response for two different couples of sensors during the PTS test described in Section 7.3.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Updating process. The BMU and its neighbors are moved towards the input sample x̄n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Example of sequence of the different stages of clustering DS2L-SOM algorithm. [Cabanes et al., 2012] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Scheme of the proposed system for monitoring and detection of defects. Stages 1 to 6 (G1 to G6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Distance between neighbor sensors under tension and compression. . . . . . . 81 Main structural failure modes in wind turbine blades. Adapted from Sørensen et al. [2004] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Location of maximums and minimums in a damped harmonic oscillator affected by artificial noise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Example of algorithm for maximum and minimum detection in real strain responses for two experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87. xvii.

(18) xviii. List of Figures. Figure 28. Figure 29. Figure 30. Figure 31 Figure 32. Figure 33 Figure 34 Figure 35 Figure 36 Figure 37 Figure 38 Figure 39 Figure 40 Figure 41 Figure 42 Figure 43 Figure 44 Figure 45 Figure 46 Figure 47 Figure 48 Figure 49 Figure 50 Figure 51 Figure 52 Figure 53 Figure 54 Figure 55 Figure 56 Figure 57 Figure 58 Figure 59 Figure 60 Figure 61 Figure 62 Figure 63 Figure 64. Experimental results for strains measurements in a 53 m long blade of a 4.5 MW wind turbine (E112 type). At the left, response of two opposite sensors located at upwind and downwind sides for different positions showed at the right. Adapted from Schroeder et al. 2006. . . . . . . . . . . . . . . . . . . . . . Example of strains measurements at 8.4 rpm for a E112 wind turbine. In the upper, response of a sensor located close to the root of blade in the downwind side. In the lower, response of two opposite sensors located at upwind and downwind sides and near to the tip pf the blade. Adapted from Schroeder et al. 2006 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Portion of the strain vs. strain response for the same couple of sensors for a 13.5 m long wind turbine blade in four different test with different pitch angles. (see Figure 56 for details about LTT, PTS, STP and TTL meaning). . . . Example of results without clustering load conditions. . . . . . . . . . . . . . . Example of parametrization effect for the strain gathered during the STP test (see Section 7.3.3) for a 13.5 m long wind turbine blade. OBR measurements for 7 load magnitudes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Proposed multi-load unfolding methodology. . . . . . . . . . . . . . . . . . . . Scheme of PCA as model for damage identification. . . . . . . . . . . . . . . . Decision tree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tested wing section (dashed line). . . . . . . . . . . . . . . . . . . . . . . . . . . Scheme of wing structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detail of the wing attachment to the testing bench. . . . . . . . . . . . . . . . . Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensors and damage locations. All units in mm. . . . . . . . . . . . . . . . . . . Detailed view of induced damages. . . . . . . . . . . . . . . . . . . . . . . . . . Scheme of cylindrical isogrid structure. All units in mm. . . . . . . . . . . . . Example of strain vs. time response for all the 36 FBGs. . . . . . . . . . . . . . Details of experimental setup and failure after test. . . . . . . . . . . . . . . . . Sensors network developed. Installation in the PVC foam core. . . . . . . . . . General idea of monitoring system. Wind turbine image adapted from Amirat et al. [2009] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fixation and protection of sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . Positioning of the fabrics and the core pieces in the bottom of the mold. . . . Positioning of the root’s core in the bottom of the mold and details of routing Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensors and damage locations in first prototype. All units in mm. . . . . . . . Examples of damages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensors and damage locations in second prototype. All units in mm. . . . . . Installation of plain fiber optics for distributed sensing. . . . . . . . . . . . . . . Experimental setup. TTL position. . . . . . . . . . . . . . . . . . . . . . . . . . . Position of the blade in the different tests. . . . . . . . . . . . . . . . . . . . . . Load spectrum for tests performed. . . . . . . . . . . . . . . . . . . . . . . . . . Detailed view of damage 1 (D1). Debonding plus transversal cutting. . . . . . Details of second and third damages (D2 and D3). . . . . . . . . . . . . . . . . . Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scheme of used beam and layup of sensors at cross section. . . . . . . . . . . . Detailed view of sensors distribution across the beam. Red arrows represents the points of load application. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Induced damages locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Strain vs. length response for distributed sensing measurements. Load case 1.. 88. 88. 89 90. 93 94 95 97 101 101 102 102 103 104 105 105 106 107 108 110 111 111 113 114 114 115 115 116 117 118 118 119 120 120 121 122 123.

(19) List of Figures. Figure 65 Figure 66 Figure 67 Figure 68. Figure 69. Figure 70. Figure 71 Figure 72. Figure 73. Figure 74 Figure 75 Figure 76. Figure 77. Figure 78. Figure 79. Figure 80. Figure 81. Figure 82. Figure 83. Example of strain versus time response for FBGs measurements for dynamic experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load cases for dynamic experiments (only using FBGs). . . . . . . . . . . . . . Load cases for static experiments (using FBGs and OBR). . . . . . . . . . . . . . PCA model for UAV wing section experiment: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCA model for UAV wing section experiment: Q index vs. T 2 index and φ index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCA model for UAV wing section experiment: projection into the two first principal components with damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Buckling under highest load magnitude and most severe damage. . . . . . . . h-NLPCA model for UAV wing section experiment: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . h-NLPCA model for UAV wing section experiment: Q index vs. T 2 index and projection into the two first principal components with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). UAV wing section experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCA model for isogrid experiment: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). Example of nonlinearities observed in the isogrid experiments. . . . . . . . . . PCA model for isogrid experiment: Q index vs. T 2 index and φ index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCA model for isogrid experiment: projection into the two first principal components with damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). . . . . . . . h-NLPCA model for isogrid experiment: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . h-NLPCA model for isogrid experiment: Q index vs. T 2 index and projection into the two first principal components with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . PCA model for preliminary prototype of wind turbine blade experiment: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . PCA model for preliminary prototype of wind turbine blade experiment: Q index vs. T 2 index and φ index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . PCA model for preliminary prototype of wind turbine blade experiment: projection into the two first principal components with damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . h-NLPCA model for preliminary prototype of wind turbine blade experiment: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . .. 124 125 126. 128. 128. 129 130. 131. 132 133 134. 134. 135. 136. 136. 137. 138. 139. 139. xix.

(20) xx. List of Figures. Figure 84. Figure 85. Figure 86. Figure 87. Figure 88. Figure 89. Figure 90. Figure 91. Figure 92. Figure 93 Figure 94 Figure 95. Figure 96. Figure 97. Figure 98. h-NLPCA model for preliminary prototype of wind turbine blade experiment: Q index vs. T 2 index and projection into the two first principal components with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCA model for final prototype of wind turbine blade experiment using the FBGs: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . PCA model for final prototype of wind turbine blade experiment using the FBGs: Q index vs. T 2 index and φ index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . PCA model for final prototype of wind turbine blade experiment using the FBGs: projection into the two first principal components with damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . h-NLPCA model for final prototype of wind turbine blade experiment using the FBGs: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . h-NLPCA model for final prototype of wind turbine blade experiment using the FBGs: Q index vs. T 2 index and projection into the two first principal components with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . PCA model for final prototype of wind turbine blade experiment using the OBR: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . PCA model for final prototype of wind turbine blade experiment using the OBR: Q index vs. T 2 index and φ index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . PCA model for final prototype of wind turbine blade experiment using the OBR: projection into the two first principal components with damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . ROC curve for Q index for different number of sensors. . . . . . . . . . . . . . Parametrized strain profile for two different amount of sensors. . . . . . . . . h-NLPCA model for final prototype of wind turbine blade experiment using the FBGs: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . h-NLPCA model for final prototype of wind turbine blade experiment using the FBGs: Q index vs. T 2 index and projection into the two first principal components with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). Final prototype of wind turbine blade experiment using the FBGs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCA model for static tests with FBGs for the aluminum beam experiment: Q index and T 2 index and damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . PCA model for static tests with FBGs for the aluminum beam experiment: Q index vs. T 2 index and φ index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . .. 140. 141. 142. 142. 143. 144. 145. 145. 146 148 149. 150. 150. 152. 153.

(21) List of Figures. Figure 99. Figure 100. Figure 101. Figure 102. Figure 103. Figure 104. Figure 105. Figure 106. Figure 107. Figure 108. Figure 109. Figure 110 Figure 111 Figure 112. Figure 113. Figure 114. PCA model for static tests with FBGs for the aluminum beam experiment: projection into the two first principal components of the PCA model and damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . h-NLPCA model for static tests with FBGs for the aluminum beam experiment: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . h-NLPCA model for static tests with FBGs for the aluminum beam experiment: Q index vs. T 2 index and projection into the two first principal components with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment: Q index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment: T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment: projection into the two first principal components with damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . PCA model for dynamic tests with FBGs for the aluminum beam experiment for the Load case 1: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . PCA model for dynamic tests with FBGs for the aluminum beam experiment for the Load case 1: Q index vs. T 2 index and φ index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . . . . . . . . . . . . h-NLPCA model for dynamic tests with FBGs for the aluminum beam experiment for the Load case 1: Q index and T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . h-NLPCA model for dynamic tests with FBGs for the aluminum beam experiment for the Load case 1: Q index vs. T 2 index and projection into the two first principal components with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . U-matrix and cluster groups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Combination of similar load cases into clusters. . . . . . . . . . . . . . . . . . . PCA and h-NLPCA models for static tests with FBGs for the aluminum beam experiment for the Cluster 4: Q index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . PCA and h-NLPCA models for static tests with FBGs for the aluminum beam experiment for the Cluster 4: T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . PCA and h-NLPCA models for static tests with FBGs for the aluminum beam experiment for the Cluster 4: Q index vs. T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . .. 153. 154. 155. 156. 156. 157. 158. 159. 159. 160. 161 162 163. 164. 165. 166. xxi.

(22) xxii. List of Figures. Figure 115. Figure 116 Figure 117. Figure 118 Figure 119. Figure 120. Figure 121. Figure 122. Figure 123. Figure 124. Figure 125. Figure 126. Figure 127. Figure 128. Figure 129. Figure 130. PCA and h-NLPCA models for static tests with FBGs for the aluminum beam experiment for the Cluster 4: projection into the two first principal components with Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . U-matrix and cluster groups. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PCA and h-NLPCA models for dynamic tests with FBGs for the aluminum beam experiment for the Cluster 4: Q index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . ROC curve for Q index for PCA and h-NLPCA models. . . . . . . . . . . . . . PCA and h-NLPCA models for dynamic tests with FBGs for the aluminum beam experiment for the Cluster 4: T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . PCA and h-NLPCA models for dynamic tests with FBGs for the aluminum beam experiment for the Cluster 4: Q index vs. T 2 index with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for dynamic tests with FBGs for the aluminum beam experiment for the Cluster 4: projection into the two first principal components with damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 2. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . Load case 2. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . Load case 2. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . Load case 3. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . Load case 3. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . Load case 3. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . Load case 4. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . Load case 4. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . Load case 4. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . .. 166 167. 169 169. 170. 170. 171. 183. 183. 184. 184. 184. 185. 185. 185. 186.

(23) List of Figures. Figure 131. Figure 132. Figure 133. Figure 134. Figure 135. Figure 136. Figure 137. Figure 138. Figure 139. Figure 140. Figure 141. Figure 142. Figure 143. Figure 144. Figure 145. Load case 5. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . Load case 5. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . Load case 5. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . Load case 6. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . Load case 6. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . Load case 6. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . Load case 7. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . Load case 7. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . Load case 7. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . Load case 8. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . Load case 8. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . Load case 8. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . Load case 9. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . Load case 9. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . Load case 9. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . .. 186. 186. 187. 187. 187. 188. 188. 188. 189. 189. 189. 190. 190. 190. 191. xxiii.

(24) xxiv. List of Figures. Figure 146. Figure 147. Figure 148. Figure 149. Figure 150. Figure 151. Figure 152. Figure 153. Figure 154. Figure 155. Figure 156. Figure 157. Figure 158. Figure 159. Load case 2. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). h-NLPCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . Load case 2. Q index vs. T 2 index and projection into the two first principal components of the h-NLPCA model. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). Final prototype of wind turbine blade experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 3. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). h-NLPCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . Load case 3. Q index vs. T 2 index and projection into the two first principal components of the h-NLPCA model. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). Final prototype of wind turbine blade experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 4. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). h-NLPCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . Load case 4. Q index vs. T 2 index and projection into the two first principal components of the h-NLPCA model. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). Final prototype of wind turbine blade experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 5. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). h-NLPCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . Load case 5. Q index vs. T 2 index and projection into the two first principal components of the h-NLPCA model. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). Final prototype of wind turbine blade experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 6. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). h-NLPCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . Load case 6. Q index vs. T 2 index and projection into the two first principal components of the h-NLPCA model. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). Final prototype of wind turbine blade experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 7. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). h-NLPCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . Load case 7. Q index vs. T 2 index and projection into the two first principal components of the h-NLPCA model. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). Final prototype of wind turbine blade experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 8. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). h-NLPCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . Load case 8. Q index vs. T 2 index and projection into the two first principal components of the h-NLPCA model. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). Final prototype of wind turbine blade experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 191. 191. 192. 192. 192. 193. 193. 193. 194. 194. 194. 195. 195. 195.

(25) List of Figures. Figure 160. Figure 161. Figure 162. Figure 163. Figure 164. Figure 165. Figure 166. Figure 167. Figure 168. Figure 169. Figure 170. Figure 171. Figure 172. Load case 9. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). h-NLPCA model for static tests with FBGs for the aluminum beam experiment. . . . . . . . . . . . . Load case 9. Q index vs. T 2 index and projection into the two first principal components of the h-NLPCA model. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). Final prototype of wind turbine blade experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 2. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 2. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 2. Projection into the two first principal components of the PCA and h-NLPCA models. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution for PCA and h-NLPCA respectively (dashed line and solid line respectively). Static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 3. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 3. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 3. Projection into the two first principal components of the PCA and h-NLPCA models. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution for PCA and h-NLPCA respectively (dashed line and solid line respectively). Static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 4. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 4. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 4. Projection into the two first principal components of the PCA and h-NLPCA models. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution for PCA and h-NLPCA respectively (dashed line and solid line respectively). Static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 5. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 5. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . .. 196. 196. 196. 197. 197. 197. 198. 198. 198. 199. 199. 199. 200. xxv.

(26) xxvi. List of Figures. Figure 173. Figure 174. Figure 175. Figure 176. Figure 177. Figure 178. Figure 179. Figure 180. Figure 181. Figure 182. Figure 183. Figure 184. Figure 185. Load case 5. Projection into the two first principal components of the PCA and h-NLPCA models. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution for PCA and h-NLPCA respectively (dashed line and solid line respectively). Static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 6. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 6. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 6. Projection into the two first principal components of the PCA and h-NLPCA models. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution for PCA and h-NLPCA respectively (dashed line and solid line respectively). Static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 7. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 7. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 7. Projection into the two first principal components of the PCA and h-NLPCA models. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution for PCA and h-NLPCA respectively (dashed line and solid line respectively). Static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 8. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 8. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 8. Projection into the two first principal components of the PCA and h-NLPCA models. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution for PCA and h-NLPCA respectively (dashed line and solid line respectively). Static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load case 9. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 9. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 9. Projection into the two first principal components of the PCA and h-NLPCA models. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution for PCA and h-NLPCA respectively (dashed line and solid line respectively). Static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 200. 200. 201. 201. 201. 202. 202. 202. 203. 203. 203. 204. 204.

(27) List of Figures. Figure 186. Figure 187. Figure 188. Figure 189. Figure 190. Figure 191. Figure 192. Figure 193. Figure 194. Figure 195. Figure 196. Figure 197. Figure 198. Figure 199. Figure 200. Figure 201. Load case 2. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 2. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 3. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 3. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 4. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 4. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 5. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 5. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 6. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 6. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 7. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 7. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 8. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 8. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 9. Q index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . . Load case 9. T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA and h-NLPCA models for static tests with OBR for the aluminum beam experiment. . . . . . . . . . . . . . . .. 204. 205. 205. 205. 206. 206. 206. 207. 207. 207. 208. 208. 208. 209. 209. 209. xxvii.

(28) xxviii. List of Figures. Figure 202. Figure 203. Figure 204. Figure 205. Figure 206. Figure 207. Figure 208. Figure 209. Figure 210. Figure 211. Figure 212. Figure 213. Figure 214. Figure 215. Figure 216. Load case 3. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . Load case 3. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for dynamic tests with FBGs for the aluminum beam experiment. Load case 1. Load case 3. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . . . Load case 4. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . Load case 4. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for dynamic tests with FBGs for the aluminum beam experiment. Load case 1. Load case 4. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . . . Load case 5. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . Load case 5. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for dynamic tests with FBGs for the aluminum beam experiment. Load case 1. Load case 5. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . . . Load case 6. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . Load case 6. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for dynamic tests with FBGs for the aluminum beam experiment. Load case 1. Load case 6. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . . . Load case 8. Q index and T 2 index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . Load case 8. Q index vs. T 2 index and φ index. Damage thresholds for 95% and 99% of confidence (dashed line and solid line respectively). PCA model for dynamic tests with FBGs for the aluminum beam experiment. Load case 1. Load case 8. Projection into the two first principal components of the PCA model. Damage thresholds for 95% and 99% of confidence for a normal and a Kernel distribution (dashed line and solid line respectively). Dynamic tests with FBGs for the aluminum beam experiment. Load case 1. . . . . . . . . . .. 210. 210. 210. 211. 211. 211. 212. 212. 212. 213. 213. 213. 214. 214. 214.