University of Cambridge

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19 Οκτ 2013 (πριν από 3 χρόνια και 11 μήνες)

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University of Cambridge

Stéphane Forsik

5
th

June 2006

Neural network:

A set of four case studies

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What does «

Neural network analysis

» mean for you?

Neural network?

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

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.

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

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.

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)


Volume fraction of retained austenite (%)

HIDDEN UNITS

Inputs/outputs

Training and testing of the model

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.


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

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.

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

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.

Input parameters

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i

x
j

x
k

h
2

h
1

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

Training and testing of the model

Predictions

Mechanism is not understood

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

Second conclusion


Good agreement in trend, limited by error bars.


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

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

Fusion reaction


Insterstitials, vacancies


Transmuted helium


Precipitates

Hardening, embrittlement

dpa = displacement
-
per
-
atom

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.

Input parameters

x
i

x
j

x
k

h
2

h
1

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

Training and testing of the model

Unirradiated steel

Good description of the non
-
linear dependancy of Y
s

on the temperature.

Prediction for an unirradiated steel

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

Comparison with experimental data

Good prediction, in agreement with experimental data

Predictions slightly overestimated but within errors bars

Heat treatment missing !

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.

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

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.

Input parameters

x
i

x
j

x
k

h
2

h
1

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

Training and testing of the model

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)

Significance and influence 1

Chromium is a strong ferrite stabilizer

Significance and influence 2

Nickel is a strong austenite stabilizer

Fourth conclusion

Significance is important to determine the influence of an
element and can explain some behaviour.

Trend is correctly predicted.

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.

Sum up 2

Significance gives information about
the influence of an element.

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.

Thank you for you attention