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Subroutine MAP_NEURAL_AC1TEMP

  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.

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Purpose

To predict the Ac1 temperature of steel as a function of the chemical composition and heating rate.

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Specification

Language:FORTRAN
Product form:Source code

SUBROUTINE MAP_NEURAL_AC1TEMP(AW,W1,W2,THETA1,THETA2,AMIN,AMAX,
& IMAX,Y,HT,IERR,IN,IHID,ERROR)

DOUBLE PRECISION AW(22),W1(4,22),W2(4),THETA1(4),THETA2,
& AMIN(22),AMAX(22),Y(20),HT(20),ERROR

INTEGER IERR(20),IMAX,IN,IHID

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Description

MAP_NEURAL_AC1TEMP uses neural network analysis to predict the temperature of the onset of austenite formation.

The neural net was trained using 394 of a database of 788 examples constructed using information from Refs [2 - 7]. The remaining 394 examples were used as `new' experiments to test the trained network. This database is in the file `neural_dataset'.

Two input data files are needed for programs using MAP_NEURAL_AC1TEMP - ACINPUT (which contains the information on the chemical composition of the steel, and is read into the array AW), and AC1 (which contains neural information, and should not be altered). These files are provided with the program MAP_NEURAL_STEEL.

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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, 1996, 12, 453-463.
  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 Transformation 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 22
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 22
AMIN contains the minimum unnormalised values of the input variables (from the input file AC1).

AMAX - real array of dimension 22
AMAX contains the maximum unnormalised values of the input variables (from the input file AC1).

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.

IN - integer
IN is the number of inputs (22 for this model).

IHID - integer
IHID is the number of hidden units (4 for this model).

IMAX - integer
IMAX is the number of heating rates calculated (< 20).

Output parameters

HT - real array of dimension IMAX (< 20)
HT contains the heating rates (in kelvin per second).

Y - real array of dimension IMAX
Y contains the Ac1 temperature for each HT.

IERR - integer array of dimension IMAX
IERR=0 if all inputs are within the range of the training dataset for the neural network (so the 95% confidence error bars are at about ±11%).
IERR=1 if some inputs are outside the range of the training set for the neural network (so the 95% confidence error bars may then be greater than ±11%).
See Ref [1] for further details.

ERROR - real
ERROR is set at ±ERROR/2 for 95% confidence error limits (in joules).

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Error Indicators

IERR is an integer array of dimension IMAX.

IERR=0 if all inputs are within the range of the training dataset for the neural network (so the 95% confidence error bars are at about ±11%).

IERR=1 if some inputs are outside the range of the training set for the neural network (so the 95% confidence error bars may then be greater than ±11%).

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Accuracy

N/A

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Further Comments

Used in the program MAP_NEURAL_STEEL.

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Example

1. Program text

       DOUBLE PRECISION W1(4,22), W2(4),THETA1(4), THETA2
&      AMIN(23),AMAX(23),AW(22),Y(20),HT(20),ERROR
       INTEGER IN,IHID,IDUM,IMAX,IERR(20)
       IN=22
       IHID=4
       IMAX=5
       OPEN(UNIT=1, FILE='ACINPUT')
       DO 10 I=1,22
        READ(1,*) AW(I)
10     CONTINUE
       OPEN(UNIT=2, FILE='AC1')
       DO 20 I=1,IN+1
        READ(2,*) IDUM,AMIN(I),AMAX(I)
20     CONTINUE
       DO 30 I=1,IHID
        READ(2,*) THETA1(I)
        DO 40 J=1,IN
         READ(2,*) W1(I,J)
40      CONTINUE
30     CONTINUE
       READ(2,*) THETA2
       DO 50 I=1,IHID
        READ(2,*) W2(I)
50     CONTINUE
       CALL AC1TEMP(AW,W1,W2,THETA1,THETA2,AMIN,AMAX,IMAX,Y,HT,
&      IERR,IN,IHID,ERROR)
       DO 100 I=1,IMAX
        WRITE(6,200) HT(I),Y(I),IERR(I)
200    FORMAT(5X,2F11.4,2X,I2)
100    CONTINUE
       STOP
       END

2. Program data

An example ACINPUT file:-

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

3. Program results

  0.0100  855.7674    1
  0.1000  855.9666    0
  1.0000  857.9337    0
 10.000   874.2388    0
100.00    636.1600    1

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Auxiliary Routines

None.

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Keywords

neural network, austenite formation

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Download

Download source code

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

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