1. Survey of Analytical Methods for Corrosion Prediction Workshop on Corrosion Management for Sustainable Bridges December 10-12, U of Akron

2. Corrosion Analysis: A Black Art Electro-Chemical (“Physics-based”) Procedural Models Controlled Lab Experiments use Empirical Data Fits for Narrow Statistical Predictions, Uncontrolled Field Data use Data Base Mining for Board Statistical Predictions, Heuristic Data turn to mystics, soothsayers, consultants, and Employ those who practice “AI” (Data Analytics) 2

3. Data Analytics Approach Dimensions (Inputs), X i : Measures (Outputs), Y j : Methods (Techniques), f k : 3 YjYj X1X1 X2X2 X3X3 X4X4 X5X5 X6X6 X7X7 X8X8 X9X9 X 10 fkfk j Y j = f k (x i )

4. Corrosion Modeling Inputs Initial Conditions / State, Time Interval, Detailed 3-D Geometry, Material, Coating System (including Surface Prep), and Micro-environment at Surface (e.g., electrolyte and its properties) Macro Environment / Geographic Location Maintenance and Operating Profile (Dimensions)

5. Measures (Output) Quantitative Deterioration of the Asset Material/Coating System Performance Structural Degradation Assessment Life Cycle Cost Time To and Time Required for Repair

6. Predictive Analytics Methods ANOVA Weibull Analysis Monte Carlo Bayesian Networks Naïve Bayes Markov Model/Chains Neural Nets Genetic Algorithms 6 Procedural (Physics- based: mechanical, electro-chemical, etc.) Decision Trees Rule-based Production Systems Linear/Logarithmic Regression Time Series

7. Physics-based Predictions Volume-Discretisation Techniques: Finite Element Method Finite Difference Method Finite Volume Method

8. Physics-based BEA/BIE Method Assume Bulk Region of the Electrolyte valid at Surface Integral equation is the exact solution: Use Faraday's law for boundary motion to surface flux. Use BCs (Polarization Curves) to fit boundary values into the integral equation, rather than values throughout the space Calculate Green’s Functions Integrate over the Source and Field Patches Galerkin Method (MoM) if Source and Field are the Same Newton-Raphson iterative method for equilibrium at each step. Boundary Element Method/Boundary Integral Equation

9. Advantages of BEM/BIE BEM/BIE used because Potential and Current Density on the surface of corroding materials is of prime concern Sound Mathematical Foundation (e.g. LaPlace Equation in bulk region of the Electrolyte) Can incorporate other physical phenomenon impacting corrosion such as: Stress (in elastic range), and Impressed Current Cathodic Protection Can Relate Metal Loss to Current Density

10. Disadvantages of BEM/BIE Nonlinear relationship exists between the current density and the potential in double layer region close to corroding surface, Need detailed Polarization Curves for every micro- environment to be encountered used as BCs since Laplace equation only applicable to bulk electrolyte Non-linearities (e.g., non-linear Polarization Curves) will reduce the efficiency of the method. Polarization Curves are particular to each specimen, electrolytic environment, stress, time, and other factors, such as temperature and concentration. 3-D geometry require assumptions on extended 2-D/ axisymmetric equations to complex 3-D geometries.

11. Empirical Models via Lab Data Use Standard Form Equation: Polynomial Fit for 3 parameters A, B, C: Where:  0 = Average Response of CR  1..  7 = Coefficients associated with variables A, B and C and their interactions Use ANOVA for Main, Interaction and Variance

12. Uncontrolled Test Data Models Markoff Chains NPMLE (Non-parametric Maximum Likelihood Estimation): Turnbull Analysis If Data is Incomplete (groupings, censoring and/or truncation) Requires an Iterative Algorithm Parametric Failure/Reliability Prediction: Weibull Multi-variant Analysis: Cox Hazard Neural Networks

13. Uncontrolled Data Problems Definition of “Failure” Data is Incomplete Data Not Precise (Scatter and Gaps) Analysis of Secondary Effects Environment, Operational Usage, Location, Command Decisions, Etc.

14. Navy Rating System (D610) 14 It’s Here, per NSTM D610: Level III = 1.0% Loss

15. Markov Chain Approach 15 Time Severity t1t1 t2t2 I II III IV Gap

16. Incomplete Data Five Types of Lifetimes: Exact Failure Time Interval Censored Left Censored: Late Entries Right Censored: Suspension) Unbounded 16

17. Predictions: Two Steps 1. Non-parametric Maximum Likelihood Estimation: Turnbull Analysis If Data is Incomplete (groupings, censoring and/or truncation) Requires an Iterative Algorithm 2. Parametric Failure/Reliability Prediction: Weibull Analysis 17

18. Turnbull-Weibull Prediction 18

19. Multi-State/Mode Behavior 19

20. Multi-phase Model 20 Phase 0 Corrosion Coating Breakdown t t R(R( Weibull 3-State Analysis

21. Predicting Secondary Effects Cox Hazard Method Non-Parametric Technique like NPMLE Fit with Curve like Weibull Technique 21

22. Geographical Location 22

23. Neural Networks (NN) 23 Rating = 2 NNs are superior when there is a large amount of data to process

24. Heuristic Data Models Engineering Lessons Learned, Design Rules, Observations, Subject Matter Expert Opinions, SWAGs Use “AI”/Data Analytics Methods

25. INFERENCE ENGINE AGENDA KNOWLEDGE BASE (RULES) WORKING MEMORY (FACTS) EXPLANATION FACILITY KNOWLEDGE AQUISITION FACILITY USER INTERFACE PRODUCTION SYSTEM Rule-Based Expert System

26. Example rules from CES IF there is water AND there is an electrolyte THEN corrosive environment is present IF there is an electrolyte AND there is water THEN corrosive environment with likelihood=10 IF there is a low resistivity electrolyte THEN there is a corrosive environment IF there is an insulator between metals THEN galvanic corrosion is possible IF there is an insulator between metals AND insulator doesn’t last the life of the vehicle THEN galvanic corrosion is possible 26 Subsumption Redundancy

27. Reasoning under Uncertainty Uncertainty in the Rules Uncertainty in the Evidences 27

28. Bayesian Network + CPT

29. Coating Selection Risk BN

30. BN Result for Ameron + Heavy Statistical Distribution

31. Analysis Framework 31 Initial Condition Damaged State Structural Integrity Assessment Application Utility Inspection Data Statistical-AI Physics, Electro-chemistry Engineering Analysis Finite Element Analysis Influence Diagrams Mission Analysis Utility Theory (Readiness, Cost) Time Analysis Approach

32. Conclusions Hybrid Methods work well for Corrosion/ Deterioration Problems Useful in: Decision Making, Data Analysis/Evaluation Prediction Forecasting Automated Pattern Recognition Classification New Innovative Design Development 32