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H.K.D.H. Bhadeshia,

Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

To predict the Ac_{3} temperature of steel as a function of the chemical composition and the heating rate.

Language: | FORTRAN |

Product form: | Source code |

SUBROUTINE MAP_NEURAL_AC3TEMP(AW,W1B,W2B,THETB1,THETB2,AMIN,AMAX,

& IMAX,Y,HT,IERR,IN,IHID,ERROR)

DOUBLE PRECISION AW(22),W1B(2,22),W2B(2),THETB1(2),THETB2,

& AMIN(22),AMAX(22),Y(20),HT(20),ERROR

INTEGER IERR(20),IMAX,IN,IHID

MAP_NEURAL_AC3TEMP uses neural network analysis to predict the temperature at the completion 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_AC3TEMP - ACINPUT (which contains the information on the chemical composition of the steel, and is read into the array AW), and AC3 (which contains neural information, and should not be altered). These files are provided with the program MAP_NEURAL_STEEL.

- 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. - G.F. Vander Vroot, ed., Atlas of Time-Temperature- Transformation Diagrams for Irons and Steels, ASM International, Ohio, USA, (1991).
- Special Report 56, Atlas of Isothermal Transformation Diagrams of B.S. En Steels, 2nd edition, Iron and Steel Institute, London, (1956).
- T. Cool, Systematic Design of Welding Alloys for Power Plant Steels, CPGS Thesis, University of Cambridge, (1994).
- K. Akibo, Scientific American (Japanese Edition), (January 1993), 20-29.
- R. Reed, Ph.D. Thesis, University of Cambridge, (1987).
- Phase Transformation Kinetics and Hardenability of Medium Alloy Steels, Climax Molybdenum Company, Connecticut, USA, (1972).

**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).
**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 Ac
_{3}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 Ac
_{3}temperature. **IN**- integer- IN is the number of inputs (22 for this model).
**IHID**- integer- IHID is the number of hidden units (2 for this model).
**IMAX**- integer- IMAX is the number of heating rates calculated (< 20).

**HT**- real array of dimension IMAX (< 20)- HT contains the heating rates (in kelvin per second).
**Y**- real array of dimension IMAX- Y conains the Ac
_{3}temperature associated with each heating rate in 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% cofidence error limits (in joules).

The elements of the array `IERR` take values:

`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 [1] for further details.

N/A

Used in the program MAP_NEURAL_STEEL.

DOUBLE PRECISION W1B(2,22),W2B(2),THETB1(2),THETB2, & AMIN(23),AMAX(23),AW(22),Y(20),HT(20),ERROR INTEGER IN,IHID,IDUM,IMAX,IERR(20) IN=22 IHID=2 IMAX=5 OPEN(UNIT=1, FILE='ACINPUT') DO 10 I=1,22 READ(1,*) AW(I) 10 CONTINUE OPEN(UNIT=3, FILE='AC3') DO 20 I=1,IN+1 READ(3,*) IDUM,AMIN(I),AMAX(I) 20 CONTINUE DO 30 I=1,IHID READ(3,*) THETB1(I) DO 40 J=1,IN READ(3,*) W1B(I,J) 40 CONTINUE 30 CONTINUE READ(3,*) THETB2 DO 50 I=1,IHID READ(3,*) W2B(I) 50 CONTINUE CALL AC3TEMP(AW,W1B,W2B,THETB1,THETB2,AMIN,AMAX,IMAX, & Y,HT,IERR,IN,IHID,ERROR) DO 200 I=1,IMAX WRITE(6,300) HT(I),Y(I),IERR(I) 300 FORMAT(5X,2F11.4,2X,I2) 200 CONTINUE STOP END

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

0.0100 823.6380 1 0.1000 823.8549 0 1.0000 826.0161 0 10.000 846.5887 0 100.00 903.1055 1

None.

neural network, austenite formation

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