University of Cambridge Stéphane Forsik 5 th June 2006

1. Neural network: A set of four case studies University of Cambridge Stéphane Forsik 5th June 2006

2. xi xj xk h1 h2 h What does « Neural network analysis » mean for you? Neural network?

3. 4 examples of neural network analysis: • Estimation of the amount of retained austenite in austempered ductile irons • Neural network model of creep strength of austenitic stainless steels • Neural-network analysis of irradiation hardening in low-activation steels • Application of Bayesian Neural Network for modeling and prediction of ferrite number in austenitic stainless steel welds Four practical examples

4. 1 - Identification of a problem which is too complex to be solved. 2 - Compilation of a set of data. 3 - Testing and training of the neural network. 4 - Predictions. How to build a neural network?

5. 4 examples of neural network analysis: • Estimation of the amount of retained austenite in austempered ductile irons • Neural network model of creep strength of austenitic stainless steels • Neural-network analysis of irradiation hardening in low-activation steels • Application of Bayesian Neural Network for modeling and prediction of ferrite number in austenitic stainless steel welds Estimation of the amount of retained austenite in austempered ductile irons

6. Retained austenite helps to optimize the mechanical properties of austempered ductile irons. The maximization of the amount of retained austenite gives the best mechanical properties. Many variables are involved in this calculation and no models can give quantitative accurate predictions. A neural network is the solution. Analysis of the problem

7. Input parameters

8. xi xj xk h1 h2 h • wt% C, wt% Si, wt% Mn, wt% Ni, wt% Cu • Austenising time (min) and temperature (K) • Austempering time (min) and temperature (K) HIDDEN UNITS • Volume fraction of retained austenite (%) Inputs/outputs

9. Training and testing of the model

10. Volume fraction max for ~ 3-3.25 wt% Si. Below ~3.1 wt% Si, more bainitic transformation and more austenite carbon enrichment. Over ~ 3.1 wt% Si, formation of islands of pro-eutectoïd ferrite in the bainite structure. No effect below ~ 3.6 wt% C. Slight stabilization over 3.6 wt% C, possibly longer time to reach equilibrium for high concentrations. Predictions of Si and C

11. Uncertainty over 2 wt% Ni • Uncertainty over 1 wt% Cu • No effect below 2 wt% Ni • Slight stabilization below ~ 1 wt% Cu Predictions of Ni and Cu

12. A neural network can give predictions in agreement with theory and experimental values. • Error bars are an indication of the reliability of the model. • More data should be collected or more experiments should be carried out in the range of concentration where error bars are large. First conclusion

13. 4 examples of neural network analysis: • Estimation of the amount of retained austenite in austempered ductile irons • Neural network model of creep strength of austenitic stainless steels • Neural-network analysis of irradiation hardening in low-activation steels • Application of Bayesian Neural Network for modeling and prediction of ferrite number in austenitic stainless steel welds Neural network model of creep strength of austenitic stainless steels

14. Austenitic stainless steels are used in the power generation industry at 650 °C, 50 MPa or more for more than 100 000 hours. Creep stress rupture is a major problem for those steels. No experiments can be carried out for 100 000 hours and pseudo-linear relations cannot take in account complex interactions between components. A neural network is the solution. Analysis of the problem

15. Input parameters

16. xi xj xk h1 h2 h • wt% Cr, wt% Ni, wt% Mo, wt% Mn, wt% Si, wt% Nb, wt% Ti, wt% V, wt% Cu, wt% N, wt% C, wt% B, wt% B, wt% P, wt% S, wt% Co, wt% Al • Test stress (Mpa), test temp. (°C), log(rupture life, h) • Solution treatment temperature (°C) HIDDEN UNITS • 104 h creep rupture stress Inputs/outputs

17. Training and testing of the model

18. Mechanism is not understood Predictions

19. Neural network Orr-Sherby-Dorn method Experimental values NN predictions are better than the Orr-Sherby-Dorn method For AEG, very good agreement at high temperatures Comparison with other methods

20. Good agreement in trend, limited by error bars. • Good agreement when predictions are compared to experimental values, more precise than other models. Second conclusion

21. 4 examples of neural network analysis: • Estimation of the amount of retained austenite in austempered ductile irons • Neural network model of creep strength of austenitic stainless steels • Neural-network analysis of irradiation hardening in low-activation steels • Application of Bayesian Neural Network for modeling and prediction of ferrite number in austenitic stainless steel welds Neural-network analysis of irradiation hardening in low-activation steels

22. Insterstitials, vacancies • Transmuted helium • Precipitates dpa = displacement-per-atom Hardening, embrittlement Fusion reaction

23. Future fusion power plants will be based on a 100 million degree plasma which will produce 14 MeV neutrons. Energetic neutrons are a major problem for materials composing the magnetic confinement. Today, no fusion sources, no sources of 14 MeV neutrons. Need to extrapolate from fission results. A neural network is the solution. Analysis of the problem

24. Input parameters

25. xi xj xk h1 h2 h • wt% C, wt% Cr, wt% W, wt% Mo, wt% Ta, wt% V, wt% Si, wt% Mn, wt% Mn, wt% N, wt% Al, wt% As, wt% B, wt% Bi, wt% Ce, wt% Co, wt% Cu, wt% Ge, wt% Mg, wt% Nb, wt% Ni, wt% O, wt% P, wt% Pb, wt% S, wt% Sb, wt% Se, wt% Sn, wt% Te, wt% Ti, wt% Zn, wt% Zr • Irradiation and test temperatures (K) • Dose (dpa) and helium concentration (He) • Cold working (%) HIDDEN UNITS • Yield strength (Ys) Inputs/outputs

26. Training and testing of the model

27. Unirradiated steel Good description of the non-linear dependancy of Ys on the temperature. Prediction for an unirradiated steel

28. Trend: hardening until 10 dpa, Ys increases from 450 MPa to 650 MPa. In agreement with theory which predicts a saturation with increasing doses and with experiments. Prediction for an irradiated steel

29. Good prediction, in agreement with experimental data Predictions slightly overestimated but within errors bars Heat treatment missing ! Comparison with experimental data

30. Model gives good predictions. • Good knowledge of the theory and mechanisms is needed. Missing parameters like heat treatment can induce shifts in predictions. Third conclusion

31. 4 examples of neural network analysis: • Estimation of the amount of retained austenite in austempered ductile irons. • Neural network model of creep strength of austenitic stainless steels. • Neural-network analysis of irradiation hardening in low-activation steels. • Application of Bayesian Neural Network for modeling and prediction of ferrite number in austenitic stainless steel welds. Application of Bayesian Neural Network for modeling and prediction of ferrite number in austenitic stainless steel welds

32. Fabrication and service performance of welded structures are determined the amount of ferrite. Hot cracking resistance, embrittlement can be avoided by an appropriate content of ferrite. Constitution diagrams using Creq and Nieq are used to predict the amount of ferrite but no accurate results. A neural network is the solution. Analysis of the problem

33. Input parameters

34. xi xj xk h1 h2 h • wt% C, wt% Mn, wt% Si, wt% Cr, wt% Ni, wt% Mo, wt% N, wt% Nb, wt% Ti, wt% Cu, wt% V, wt% Co, wt% HIDDEN UNITS • Ferrite content (%) Inputs/outputs

35. Training and testing of the model

36. Prediction of the model with data from the training set Prediction of the model with new data (not included in the database) Test of the model

37. Chromium is a strong ferrite stabilizer Significance and influence 1

38. Nickel is a strong austenite stabilizer Significance and influence 2

39. Trend is correctly predicted. Significance is important to determine the influence of an element and can explain some behaviour. Fourth conclusion

40. Trends are generally often correctly predicted. Comparison with experimental value needs to be carefully analysed. Error bars give a limit to the reliability of the predictions. Sum up

41. Significance gives information about the influence of an element. Sum up 2

42. Neural network is a powerful tool when complex relations between parameters cannot be modeled. Building a network is not difficult if care are taken. A neural network can predict trends and be in agreement with experimental data. Reliability of the predictions depends on the precision, size and preparation of the database. Theory and mechanisms of the predicted parameters should be understood before analysis. Conclusions

43. Thank you for you attention