Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2017 Principal component analysis (PCA) as a statistical tool for identifying key indicators of nuclear power plant cable insulation degradation Chamila Chandima De Silva Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Materials Science and Engineering Commons, Mechanics of Materials Commons, and the Statistics and Probability Commons Recommended Citation De Silva, Chamila Chandima, "Principal component analysis (PCA) as a statistical tool for identifying key indicators of nuclear power plant cable insulation degradation" (2017). Graduate Theses and Dissertations. 16120. https://lib.dr.iastate.edu/etd/16120 This Thesis 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 Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Principal component analysis (PCA) as a statistical tool for identifying key indicators of nuclear power plant cable insulation degradation by Chamila C. De Silva A thesis submitted to the graduate faculty in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Major: Materials Science and Engineering Program of Study Committee: Nicola Bowler, Major Professor Richard LeSar Steve Martin The student author and the program of study committee are solely responsible for the content of this thesis. The Graduate College will ensure this thesis is globally accessible and will not permit alterations after a degree is conferred. Iowa State University Ames, Iowa 2017 Copyright © Chamila C. De Silva 2017. All rights reserved. ii DEDICATION This thesis is dedicated to Jaden and Amelia for being so joyful all the time. iii iii TABLE OF CONTENTS Page LIST OF FIGURES ................................................................................................... v LIST OF TABLES ..................................................................................................... vi NOMENCLATURE .................................................................................................. vii ACKNOWLEDGMENTS ......................................................................................... viii ABSTRACT………………………………. .............................................................. vi CHAPTER 1 INTRODUCTION .......................................................................... 1 1.1 Background of Nuclear power plant cable insulator degradation .................. 1 1.2 Research Question ......................................................................................... 2 1.3 Characterization methods used in assessing cable insulation materials…… 2 1.4 Principal Component Analysis (PCA) ........................................................... 3 1.5 Regression Analysis ....................................................................................... 5 1.6 Organization of this Thesis ............................................................................ 6 CHAPTER 2 CHARACTERIZATION METHODS ............................................ 7 2.1 Sample preparation ........................................................................................ 7 2.2 Characterization Methods .............................................................................. 8 2.2.1 Mass Loss.............................................................................................. 8 2.2.2 Elongation at Break (EAB) ................................................................... 8 2.2.3 Indenter Modulus (IM) ......................................................................... 9 2.2.4 Density .................................................................................................. 10 2.2.5 Oxidation Induction Time (OIT) .......................................................... 11 CHAPTER 3 PRINCIPAL COMPONENT ANALYSIS 13 3.1 Definition of PCA .......................................................................................... 13 3.1.1 Practical Interpretation of eigenvalues and eigenvectors PCA ............. 15 3.1.2 Projection of original data into eigenvectors ....................................... 16 3.1.3 Choosing the number of Eigenvalues .................................................. 17 3.2 Multiple Linear Regression Model ............................................................... 19 3.2.1 Basic steps of Multiple Linear Regression ........................................... 20 CHAPTER 4 RESULTS AND DISCUSSION ..................................................... 22 4.1 General PCA Classification Scheme ............................................................. 22 4.2 Classification of samples aged at 90 °C ......................................................... 22 4.2.1 Classification using Eigenvalues .......................................................... 24 4.2.2 Classification using Eigenvectors ......................................................... 25 iv 4.2.3 Special features of the PCA plots ......................................................... 26 4.2.4 Discussion ............................................................................................. 29 4.3 Classification of samples aged at 60 °C ......................................................... 30 4.3.1 Classification using Eigenvalues .......................................................... 30 4.3.2 Classification using Eigenvectors ......................................................... 33 4.3.3 Special features of PCA plot ................................................................. 33 4.3.4 Discussion ............................................................................................ 35 4.4 Classification of combined samples aged at both 60 °C and at 90 °C ........... 35 4.4.1 Classification using Eigenvalues .......................................................... 35 4.4.2 Classification using Eigenvectors ......................................................... 37 4.4.3 Special features of the PCA plots ......................................................... 38 4.4.4 Discussion ............................................................................................. 39 4.5 Classification of combined samples aged at both 60 °C and at 90 °C with only thermally aged samples. ........................................................................ 41 4.5.1 Classification using Eigenvalues .......................................................... 41 4.5.2 Classification using Eigenvectors ......................................................... 43 4.5.3 Special features of the PCA plots ......................................................... 43 4.5.4 Discussion ............................................................................................. 47 4.6 Regression – Construction of universal equation for measuring damage in samples aged at both 60 °C and at 90 °C ....................................................... 50 4.6.1 General Regression Classification Scheme .......................................... 50 4.6.2 Fitting equations for the training set ..................................................... 51 4.6.3 MLR model for 60-OIT ........................................................................ 51 Predicting 60-OIT from radiation aging conditions.............................. 51 Predicting 60-OIT from radiation aging conditions and other attributes 52 4.6.4 MLR model for 90-OIT ........................................................................ 54 Predicting 90-OIT from radiation aging conditions.............................. 54 Predicting 60-OIT from radiation aging conditions and other attributes 54 Predicting 90-OIT from radiation aging conditions and with respect to 60-OIT................................................................................................... 55 4.6.5 Discussion ............................................................................................. 56 CHAPTER 5 SUMMARY AND CONCLUSIONS ............................................. 58 5.1 Summary of Research .................................................................................... 58 5.2 Conclusions / Future work ............................................................................. 61 REFERENCES .......................................................................................................... 63 APPENDIX A CHARACTERIZATION DATA MEASURED ON XLPE SAMPLES AGED AT 90 °C AND AT 60 °C WITH RADIATION AND WITHOUT RADIATION AGING ............................................................................ 65 APPENDIX B SUPERPOSITION PLOTS FOR ADDITIONAL PCS, ANALYZED ON CHARACTERIZATION DATA MEASURED ON XLPE SAMPLES AGED AT 90 °C AND AT 60 °C WITH RADIATION AND WITHOUT RADIATION AGING. ........................................................................... 67 v LIST OF FIGURES Page Figure 1.1 Flow chart of the basic steps of PCA ....................................................... 3 Figure 1.2 Samples thermally aged at 90 °C and radiation aged 230 Gy/h for 5 days. Samples labeled A-C are straw samples and sample D contains the intact central conductor (WC) ........................................................................................................ 8 Figure 2.1 Conceptual diagrams for