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  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

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

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To estimate the bainite plate thickness of low-alloy steels as a function of transformation temperature, the chemical free energy available for nucleation and the strength of austenite at the transformation temperature over a limited range of inputs as stated in [1].

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Product form:Source code

DOUBLE PRECISION X(15), W1(4,14), W2(4),THETA1(14), H(4)
& AMIN(15), AMAX(15)

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MAP_NEURAL_BAINITEPLATE_THICKNESS is an interactive program which uses the results of a neural network training process to permit the estimation of the bainite plate thickness. This is as a function of the following variables, within the stated ranges [1]:-

Parameter Minimum Maximum
Temperature/C 0.2600D+03 0.4600D+03
Free energy/J/mole -0.2174D+04 -0.8500D+03
Austenite strength/MPa 0.6924D+02 0.1672D+03
Bainite plate thickness/micron 0.4600D-01 0.3300D+00

The program uses the file "WEIGHTS" to obtain the neural network training information.

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  1. S.B. Singh and H.K.D.H. Bhadeshia, 1998, Materials Science and Engineering A, 245, 72-79.

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Input parameters

X - real array of dimension 15
X contains the normalized values of the input variables.

W1 - real array of dimension (4,14)
W1 contains weights read in from file "WEIGHTS".

W2 - real array of dimension 4
W2 contains weights read in from file "WEIGHTS".

THETA1 - real array of dimension 14
THETA1 contains biases read in from file "WEIGHTS".

H - real array of dimension 4
H contains a part of the transfer function.

AMIN - real array of dimension 15
AMIN contains the minimum value of the variables in the experimental dataset used to develop the model.

AMAX - real array of dimension 15
AMAX contains the maximum value of the variables in the experimental dataset used to develop the model.

Output parameters

The program gives the bainite plate thickness in microns.

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Error Indicators


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The full calculation of the error bars as presented in [1] is not reproduced in this program. An average error of 0.03 micron may be assumed reasonable but will not be reliable in all cases.

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Further Comments


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1. Program text

       Complete Program.

2. Program data

                     Transformation Temperature (centigrade)?
                     Free energy for nucleation (J/mole)?
                     Austenite strength at temperature (MPa)?

3. Program results

                               ** BAINITE SUBUNIT THICKNESS **           

                                  University of Cambridge  

                         S. B. Singh and H. K. D. H. Bhadeshia  

           Temperature         400.  C 
           Gmax              -1400.  J/mole 
           Yield Strength      110.  MPa 

           Thickness /microns           0.12
           Error     /microns           0.03

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Auxiliary Routines


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neural network, bainite plate thickness

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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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