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Program MAP_STEEL_ACPROS

  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

The program, which is NOT available from this site, was produced by

Mark Gibbs and David MacKay,
Cavendish Laboratory,
University of Cambridge,
Madingley Road,
Cambridge, CB3 0HE, U.K.

The data files for use with the program were produced by

C.A.L. Bailer-Jones and H.K.D.H. Bhadeshia,
Dept. of Material Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

Application added: April 1999

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Purpose

An application of the Tpros program for predicting the temperature at which Austenite starts to form (Ac1) and that at which Austenite formation is complete (Ac3) during the continuous heating of a steel alloy.

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Specification

The Tpros program is self-contained, but must be downloaded from its own web-site. [Link to Tpros program]

Language:C
Product form:Source code and executable files for UNIX/Linux machines.


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Description

The problem we are interested in is that of predicting the temperature at which Austenite starts to form (Ac1) and that at which Austenite formation is complete (Ac3) during the continuous heating of a steel alloy. This prediction is made as a function of the heating rate and the elemental composition. The modelling procedure is a purely empirical one; the model is trained on a set of experimental data for which these temperatures are known, and creates a kind of non-linear, multi-parameter "regression" of the outputs versus the inputs. This "regression" has already been produced and the model is delivered ready to perform predictions for steels of any desired composition (within certain specified limits). A perusal of the paper by Bailer-Jones et al. [1] is strongly recommended before proceeding further. It provides details about the model and its use.

MAP provides a set of data files which can be used with the Tpros program for calculating the temperatures Ac1 and Ac3. The Tpros program itself is not included with this distribution, as we do not maintain it. (We cannot, therefore, be responsible for any failures due to backward compatibility with later versions of Tpros.) The acpros.tar file, which can be downloaded from here, contains the following files:

acpros.f - A FORTRAN program for un-normalising the output data files.
acpros.man - A manual giving further details about running and using the Tpros program for calculating Ac1 and Ac3.
gpaus.ps - A postscript file of the paper in reference 1.
h.ac1 - Hyperparameters file for Ac1 predictions.
h.ac3 - Hyperparameters file for Ac3 predictions.
inputs.norm - Normalised inputs file (composition of steels and heating rates).
min-max - Minimum and maximum values for the wt% of each element and the heating rate (K/s) used in the original database. (i.e. the minimum and maximum values of each column in the original database before normalisation.
output.ac1.norm - Normalised Ac1 values.
output.ac3.norm - Normalised Ac3 values.
Tspec.pred.ac1 -Tpros specification file for Ac1 predictions.
Tspec.pred.ac3 - Tpros specification file for Ac3 predictions.

These files must be placed in the same directory as the Tpros executable program and should not be changed. The file inputs.norm contains 788 lines of normalised data, specifying a range of different steel compositions and heating rates. The files output.ac1.norm and output.ac3.norm contain the experimentally determined values for the temperatures Ac1 and Ac3 for each entry in the inputs.norm file. These files were fed into the Gaussian Process model, which produced as output the files h.ac1 and h.ac3, containing the parameters of the non-linear, multi-parameter fit to the data. The Tpros program uses these for predicting values of Ac1 and Ac3 for other steel compositions and heating rates. The file acpros.man contains a manual which provides a detailed set of instructions for downloading and running the Tpros program for calculating Ac1 and Ac3. A summary of the information in this manual is given here.

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References

  1. C.A.L. Bailer-Jones, H.K.D.H. Bhadeshia, and D.J.C. MacKay, 1999, Materials Science and Technology, (in press). Gaussian Process Modelling of Austenite Formation in Steel.
  2. Mark Gibbs' Gaussian Processes web page.
  3. David MacKay's Gaussian Processes web page.
  4. A short summary by Coryn Bailer-Jones.
  5. L. Gavard, H.K.D.H. Bhadeshia, D.J.C. MacKay and S. Suzuki, Materials Science and Technology, June 1996, vol. 12, pp. 453-463. A Bayesian Neural Network Model for Austenite Formation in Steels.

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Parameters

Input parameters

The composition and heating rates of the steel for which Ac1 and Ac3 are to be calculated, need to be placed in an input file. Each line of data corresponds to a different steel composition or heating rate. (There is no restriction on the number of lines of data in the input file.)

For each steel, 12 data items must be specified:

Column numberVariable
1 normalised C wt.%
2 normalised Si wt.%
3 normalised Mn wt.%
4 normalised Cu wt.%
5 normalised Ni wt.%
6 normalised Cr wt.%
7 normalised Mo wt.%
8 normalised Nb wt.%
9 normalised V wt.%
10 normalised W wt.%
11 normalised Co wt.%
12 normalised Heating rate (K/s)

The actual composition (in wt%) must be normalised using the equation:

normalised value = (value - Min)/(Max - Min) - 0.5

where the values for Min and Max are defined as follows:

Column numberVariableMinMax
1C (wt.%)00.96
2Si (wt.%)02.13
3Mn (wt.%)03.06
4Cu (wt.%)02.01
5Ni (wt.%)09.12
6Cr (wt.%)017.98
7Mo (wt.%)04.80
8Nb (wt.%)00.17
9V (wt.%)02.45
10W (wt.%)08.59
11Co (wt.%)04.07
12Heating rate (K/s)0.0350

Output parameters

Two output files are produced by the Tpros program:

pred.ac1.norm - contains the predicted values for Ac1
pred.ac3.norm - contains the predicted values for Ac3

Each output file contains 1 line of 5 data items for each line of input data:

column 1-the normalised predicted Ac1 or Ac3 temperature.
column 2-a value for the error (equal to sigma), which includes both the experimental noise of the database and an estimation of the uncertainty in the prediction.
column 3-the predicted output minus sigma.
column 4-the predicted output plus sigma.
column 5-an estimation of the noise level in the database; it is the same for all cases.

The normalised values for the temperatures in columns 1, 3 and 4, must be un-normalised using the equation:

actual value = (normalised value + 0.5)*(Max - Min) + Min

The values in column 2 can be un-normalised using the equation:

actual value = normalised value * (Max - Min)

The values of Min and Max for Ac1 and Ac3 are:

Min Max
Ac1 (C) 530 921
Ac3 (C) 651 1060

The FORTRAN program, acpros.f, can be used to translate the output files to produce the actual values of the temperatures.

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Error Indicators

None.

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Accuracy

See output parameters.

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Further Comments

None.

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Example

1. Program text

Complete program

2. Program data

For a set of steels with the following wt % and heating rates:

   C   Si    Mn  Cu   Ni   Cr   Mo  Nb    V   W  Co Heating rate (K/s)
 0.3  0.25  0.7   0  3.5    0    0   0    0   0   0      5
 0.3  0.25  0.7   0  3.5    0    0   0    0   0   0     25
 0.5  0.28  0.8   0  1.2  0.8    0   0    0   0   0      5
 0.5  0.28  0.8   0  1.2  0.8    0   0    0   0   0     25
 0.6  2.00  0.9   0    0    0    0   0    0   0   0      5
 0.6  2.00  0.9   0    0    0    0   0    0   0   0     25
 0.2  0.25  0.8   0    0  0.7    0   0  0.2   0   0      5
 0.2  0.25  0.8   0    0  0.7    0   0  0.2   0   0     25
 0.2  0.20  0.9   0  0.5  0.5  0.2   0    0   0   0      5
 0.2  0.20  0.9   0  0.5  0.5  0.2   0    0   0   0     25

The input file is:

-0.1875 -0.3826 -0.2712 -0.5 -0.1162 -0.5000 -0.5000 -0.5 -0.5000 -0.5 -0.5 -0.4
-0.1875 -0.3826 -0.2712 -0.5 -0.1162 -0.5000 -0.5000 -0.5 -0.5000 -0.5 -0.5  0.0
 0.0208 -0.3685 -0.2386 -0.5 -0.3684 -0.4555 -0.5000 -0.5 -0.5000 -0.5 -0.5 -0.4
 0.0208 -0.3685 -0.2386 -0.5 -0.3684 -0.4555 -0.5000 -0.5 -0.5000 -0.5 -0.5  0.0
 0.1250  0.4390 -0.2059 -0.5 -0.5000 -0.5000 -0.5000 -0.5 -0.5000 -0.5 -0.5 -0.4
 0.1250  0.4390 -0.2059 -0.5 -0.5000 -0.5000 -0.5000 -0.5 -0.5000 -0.5 -0.5  0.0
-0.2917 -0.3826 -0.2386 -0.5 -0.5000 -0.4611 -0.5000 -0.5 -0.4184 -0.5 -0.5 -0.4
-0.2917 -0.3826 -0.2386 -0.5 -0.5000 -0.4611 -0.5000 -0.5 -0.4184 -0.5 -0.5  0.0
-0.2917 -0.4061 -0.2059 -0.5 -0.4452 -0.4722 -0.4583 -0.5 -0.5000 -0.5 -0.5 -0.4
-0.2917 -0.4061 -0.2059 -0.5 -0.4452 -0.4722 -0.4583 -0.5 -0.5000 -0.5 -0.5  0.0

3. Program results

The output file pred.ac1.norm, which contains the normalised values for Ac1, is:

-0.183674 0.042349 -0.226022 -0.141325 0.037178 
-0.108153 0.089333 -0.197487 -0.018820 0.037178 
-0.019106 0.041362 -0.060468  0.022256 0.037178 
 0.058113 0.078147 -0.020034  0.136260 0.037178 
 0.043198 0.045568 -0.002370  0.088766 0.037178 
 0.047780 0.094182 -0.046402  0.141962 0.037178 
 0.029018 0.042070 -0.013051  0.071088 0.037178 
 0.095363 0.074785  0.020578  0.170148 0.037178 
-0.006991 0.041036 -0.048028  0.034045 0.037178 
 0.063722 0.078547 -0.014825  0.142269 0.037178 

The output file pred.ac3.norm, which contains the normalised values for Ac3, is:

-0.251874 0.047269 -0.299143 -0.204605 0.041144 
-0.143653 0.097767 -0.241419 -0.045886 0.041144 
-0.225746 0.048309 -0.274055 -0.177436 0.041144 
-0.155057 0.108816 -0.263873 -0.046240 0.041144 
-0.112735 0.050867 -0.163603 -0.061868 0.041144 
-0.083389 0.113261 -0.196650  0.029872 0.041144 
 0.000276 0.050614 -0.050339  0.050890 0.041144 
 0.083990 0.082258  0.001732  0.166248 0.041144 
-0.042046 0.045748 -0.087794  0.003702 0.041144 
 0.032149 0.093647 -0.061498  0.125797 0.041144 

The actual values for Ac1 and Ac3 are then:

  Ac1 (deg.C)     error     Range of values for Ac1 (deg. C)
   653.68         16.56           637.13  -   670.24
   683.21         34.93           648.28  -   718.14
   718.03         16.17           701.86  -   734.20
   748.22         30.56           717.67  -   778.78
   742.39         17.82           724.57  -   760.21
   744.18         36.83           707.36  -   781.01
   736.85         16.45           720.40  -   753.30
   762.79         29.24           733.55  -   792.03
   722.77         16.05           706.72  -   738.81
   750.42         30.71           719.70  -   781.13


  Ac3 (deg.C)     error     Range of values for Ac3 (deg. C)
   752.48         19.33           733.15  -   771.82
   796.75         39.99           756.76  -   836.73
   763.17         19.76           743.41  -   782.93
   792.08         44.51           747.58  -   836.59
   809.39         20.80           788.59  -   830.20
   821.39         46.32           775.07  -   867.72
   855.61         20.70           834.91  -   876.31
   889.85         33.64           856.21  -   923.50
   838.30         18.71           819.59  -   857.01
   868.65         38.30           830.35  -   906.95

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Auxiliary Routines

None.

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Keywords

steel, austenite, Ac1, Ac3, Tpros, gaussian process, temperature, heating

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Download

Download data files from MAP
Link to Tpros program

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

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