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

2. xixi xjxj xkxk h2h2 h1h1 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. How to build a neural network? 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.

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. Analysis of the problem 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.

7. Input parameters

8. xixi xjxj xkxk h2h2 h1h1 h wt% C, wt% Si, wt% Mn, wt% Ni, wt% Cu Austenising time (min) and temperature (K) Austempering time (min) and temperature (K) Volume fraction of retained austenite (%) HIDDEN UNITS Inputs/outputs

9. Training and testing of the model

10. Predictions of Si and C Volume fraction max for ~ 3-3.25 wt% Si. No effect below ~ 3.6 wt% C. 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. Slight stabilization over 3.6 wt% C, possibly longer time to reach equilibrium for high concentrations.

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

12. First conclusion 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.

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. Analysis of the problem 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.

15. Input parameters

16. xixi xjxj xkxk h2h2 h1h1 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) 10 4 h creep rupture stress HIDDEN UNITS Inputs/outputs

17. Training and testing of the model

18. Predictions Mechanism is not understood

19. Comparison with other methods 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

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

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

23. Analysis of the problem 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.

24. Input parameters

25. xixi xjxj xkxk h2h2 h1h1 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) Yield strength (Y s ) HIDDEN UNITS Cold working (%) Inputs/outputs

26. Training and testing of the model

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

28. Trend: hardening until 10 dpa, Y s 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. Comparison with experimental data Good prediction, in agreement with experimental data Predictions slightly overestimated but within errors bars Heat treatment missing !

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

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. Analysis of the problem 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 Cr eq and Ni eq are used to predict the amount of ferrite but no accurate results. A neural network is the solution.

33. Input parameters

34. xixi xjxj xkxk h2h2 h1h1 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% Ferrite content (%) HIDDEN UNITS Inputs/outputs

35. Training and testing of the model

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

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

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

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

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

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

42. Conclusions Neural network is a powerful tool when complex relations between parameters cannot be modeled. Building a network is not difficult if care are taken. 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. A neural network can predict trends and be in agreement with experimental data.

43. Thank you for you attention