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Program MAP_NEURAL_STEEL

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of subroutine's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary subroutines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

Program modified: March 1999.

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Purpose

To predict the Ac1 and Ac3 temperatures of steel as functions of the chemical compositions and the heating rate.

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Specification

Language:FORTRAN
Product form:Source code;
Compiled program for a PC with MSDOS. It will run on any IBM PC clone.

DOUBLE PRECISION THETA2, THETB2, ERROR
DOUBLE PRECISION AMIN(23),AMAX(23),AW(23),HT(20),THETA1(4)
DOUBLE PRECISION THETB1(2),W1(4,22),W1B(2,22),W2(4),W2B(2),Y(20) 
INTEGER IERR(20),I,IHID,IMAX,IN

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Description

MAP_NEURAL_STEEL uses neural network analysis to predict the Ac1 and Ac3 temperatures of steel. The Ac1 temperature is the temperature at the onset of austenite formation. The Ac3 temperature is the temperature at the completion of austenite formation.

The neural net was trained using 394 of a database of 788 examples, that was constructed using information from published literature (Refs [2-7]). The remaining 394 examples were used as `new' experiments to test the trained network.

Optimum values for the number of hidden units (4 for Ac1 and 2 for Ac3) were obtained from this. The whole dataset was then used to retrain the net to give more accurate values for the weights.

The data that were used originally to train the neural network are are also available for downloading. These data are not necessary to use the software for the estimation of Ac1 and Ac3 temperature. They are nevertheless available should you wish to conduct your own analysis. The file data.notes contains information about the data in the database.

To run the program MAP_NEURAL_STEEL the following input files are required :-

ACINPUT
contains information on the chemical composition of the steel. An example ACINPUT is provided along with the source code.
NB: It is necessary to properly specify the trace elements, which are in practice always there even though you may not have the analysis data. If the latter is true, then it is better to set the trace elements to average values rather than zero, since zero has a very significant meaning.

AC1, AC3
contain neural information, and should not be altered. These files are also provided.

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References

  1. L. Gavard, H.K.D.H. Bhadeshia, D.J.C. MacKay, and S. Suzuki, Bayesian Neural Network Model for Austenite Formation in Steels, Materials Science and Technology, 12, (1996), 453-463.
    [Link to paper]

  2. G.F. Vander Vroot, ed., Atlas of Time-Temperature-Transformation Diagrams for Irons and Steels, ASM International, Ohio, USA, (1991).

  3. Special Report 56, Atlas of Isothermal Transformation Diagrams of B.S. En Steels}, 2nd edition, Iron and Steel Institute, London, (1956).

  4. T. Cool, Systematic Design of Welding Alloys for Power Plant Steels, CPGS Thesis, University of Cambridge, (1994).

  5. K. Akibo, Scientific American (Japanese Edition), (January 1993), 20-29.

  6. R. Reed, Ph.D. Thesis, University of Cambridge, (1987).

  7. Phase Transormation Kinetics and Hardenability of Medium Alloy Steels, Climax Molybdenum Company, Connecticut, USA, (1972).

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Parameters

Input parameters

AW - real array of dimension 23
AW contains the input data from the file ACINPUT, which includes the chemical composition of the steel. See below for details of an example file.

AMIN - real array of dimension 23
AMIN contains the minimum unnormalised values of the input variables (from the input files AC1 and AC3).

AMAX - real array of dimension 23
AMAX contains the maximum unnormalised values of the input variables (from the input files AC1 and AC3).

THETA1 - real array of dimension 4
THETA1 contains the biases associated with W1, and is read in from the file AC1.

THETA2 - real
THETA2 is the bias associated with W2, and is read in from the file AC1.

W1 - real array of dimension (4,22)
W1 contains weights read in from the file AC1, which are coefficients used in the prediction of the Ac1 temperature.

W2 - real array of dimension 4
W2 contains weights read in from the file AC1, which are coefficients used in the prediction of the Ac1 temperature.

THETB1 - real array of dimension 2
THETB1 contains the biases associated with W1B, and is read in from the file AC3.

THETB2 - real
THETB2 is the bias associated with W2B, and is read in from the file AC3.

W1B - real array of dimension (2,22)
W1B contains weights read in from the file AC3, which are coefficients used in the prediction of the Ac3 temperature.

W2B - real array of dimension 2
W2B contains weights read in from the file AC3, which are coefficients used in the prediction of the Ac3 temperature.

Output parameters

The program gives the Ac1 and Ac3 temperatures for a range of heating rates. See below for an example showing the format of the output.

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Error Indicators

None.

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Accuracy

The neural net was trained using 394 examples from the available database.

The error is set at ±20% for 95% error limits.

If the temperature should become negative during the course of the calculation of the Ac1 or Ac3 temperatures it is set to zero.

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Further Comments

None.

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Example

1. Program text

Complete program.

2. Program data

0.2      C
0.0      Si
0.0      Mn
0.0      S
0.0      P
0.0      Cu
0.0      Ni
5.0      Cr
0.0      Mo
0.0      Nb
0.0      V
0.0      Ti
0.0      Al
0.0      B
0.0      W
0.0      As
0.0      Sn
0.0      Zr
0.0      Co
0.0      N
0.0      O
1.0      Heating rate

3. Program results

      **      Austenite Formation Temperatures    **           

Carbon       0.200  wt.% Silicon            0.000  wt.%
Manganese    0.000  wt.% Sulphur            0.000  wt.%
Phosphorus   0.000  wt.% Copper             0.000  wt.%
Nickel       0.000  wt.% Chromium           5.000  wt.%
Molybdenum   0.000  wt.% Niobium            0.0000 wt.%   
Vanadium     0.000  wt.%
Titanium     0.000  wt.% Aluminium          0.000  wt.%
Boron        0.0000 wt.% Tungsten           0.000  wt.%
Arsenic      0.000  wt.% Tin                0.000  wt.%
Zirconium    0.000  wt.% Cobalt             0.000  wt.%
Nitrogen     0.0000 wt.% Oxygen             0.0000 wt.%   


Ac1  C       +- Error  C      Heating Rate  C/s
     856.       > 40.                0.0100
     856.         40.                0.1000
     858.         40.                1.0000
     874.         40.               10.0000
     636.       > 40.              100.0000

Ac3  C       +- Error  C      Heating Rate  C/s
     824.       > 40.                0.0100
     824.         40.                0.1000
     826.         40.                1.0000
     847.         40.               10.0000
     903.       > 40.              100.0000

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Auxiliary Routines

MAP_NEURAL_AC1TEMP
MAP_NEURAL_AC3TEMP

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Keywords

neural network, austenite formation

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Download

Download source code, data files and sample input data file
Download compiled program
Download previous network data

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MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

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