University of Cambridge

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Neural network A set of four case studies
University of Cambridge Stéphane Forsik 5th June
2006
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What does  Neural network analysis  mean for
you?
Neural network?
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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
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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?
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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
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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
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Input parameters
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• 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
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Training and testing of the model
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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
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• No effect below 2 wt Ni

• Slight stabilization below 1 wt Cu

Predictions of Ni and Cu
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• 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
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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
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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
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Input parameters
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• 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
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Training and testing of the model
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Mechanism is not understood
Predictions
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Comparison with other methods
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• Good agreement in trend, limited by error bars.

• Good agreement when predictions are compared to
  experimental values, more precise than other
  models.

Second conclusion
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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
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• Insterstitials, vacancies

• Transmuted helium

• Precipitates

dpa displacement-per-atom
Hardening, embrittlement
Fusion reaction
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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
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Input parameters
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• 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
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Training and testing of the model
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Good description of the non-linear dependancy of
Ys on the temperature.
Prediction for an unirradiated steel
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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
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Heat treatment missing !
Comparison with experimental data
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• 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
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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
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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
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Input parameters
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• 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
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Training and testing of the model
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Test of the model
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Chromium is a strong ferrite stabilizer
Significance and influence 1
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Nickel is a strong austenite stabilizer
Significance and influence 2
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Trend is correctly predicted.
Significance is important to determine the
influence of an element and can explain some
behaviour.
Fourth conclusion
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Sum up
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Sum up 2
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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
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Thank you for you attention